diff options
Diffstat (limited to 'libs/windfield/mlib')
| -rw-r--r-- | libs/windfield/mlib/Changes.txt | 568 | ||||
| -rw-r--r-- | libs/windfield/mlib/LICENSE.md | 17 | ||||
| -rw-r--r-- | libs/windfield/mlib/README.md | 890 | ||||
| -rw-r--r-- | libs/windfield/mlib/mlib.lua | 1152 |
4 files changed, 2627 insertions, 0 deletions
diff --git a/libs/windfield/mlib/Changes.txt b/libs/windfield/mlib/Changes.txt new file mode 100644 index 0000000..4e7fc52 --- /dev/null +++ b/libs/windfield/mlib/Changes.txt @@ -0,0 +1,568 @@ +0.11.0 +==== +Added: +---- +- mlib.vec2 component + +To-Do: +---- +- Update README.md +- Update spec.lua +- Fix tabbing + +0.10.1 +==== +Added: +---- +- Point category + - point.rotate + - point.scale + - point.polarToCartesian + - point.cartesianToPolar + +Changed: +---- +- math.getPercent now returns decimals (instead of percentages) since those are more common to use. + +To-Do: +---- +- Determine if isCompletelyInsideFunctions should return true with tangents. +- Check argument order for logicality and consistency. +- Add error checking. +- Make sure to see if any aliases were missed. (e.g. isSegmentInside) +- Clean up and correct README (add "Home" link, etc.) + +0.10.0 +==== +Added: +---- + +Changed: +---- +- mlib.line.segment is now mlib.segment. +- mlib.line.getIntercept has been renamed to mlib.line.getYIntercept +- mlib.line.getYIntercept now returns the x-coordinate for vertical lines instead of false. +- mlib.line.getYIntercept now returns the value `isVertical` as the second return value. +- mlib.line.getPerpendicularBisector is now mlib.segment.getPerpendicularBisector. + +Fixed: +---- +- mlib.line.getIntersection now should handle vertical slopes better. +- mlib.line.getClosestPoint now uses local function checkFuzzy for checking horizontal lines. +- Fixed possible bug in mlib.line.getSegmentIntersection and vertical lines. +- mlib.segment.getIntersection now uses fuzzy checking for parallel lines. +- mlib.math.round is now much more efficient. +- Removed some useless code from mlib.polygon.isSegmentInside. + +To-Do: +---- +- Determine if isCompletelyInsideFunctions should return true with tangents. +- Check argument order for logicality and consistency. +- Improve speed. +- Add error checking. +- Make sure to see if any aliases were missed. (e.g. isSegmentInside) +- Implement mlib.shapes again(?) +- Clean up and correct README (add "Home" link, etc.) + +0.9.4 +==== +Added: +---- + +Changed: +---- +- mlib.line.getDistance is now slightly faster. +- Made code much easier to debug by using new utility `cycle`. +- Added new utility. +- Various other minor changes. + +Removed: +---- +- Unused local utility function copy + +To-Do +---- +- Determine if isCompletelyInsideFunctions should return true with tangents. +- Make argument order more logical. +- Improve speed and error checking. +- Make sure to see if any aliases were missed. (e.g. isSegmentInside) +- Implement mlib.shapes again(?) +- Clean up README (add "Home" link, etc.) + +0.9.3 +==== +Added: +---- +- milb.circle.isCircleCompletelyInside +- mlib.circle.isPolygonCompletelyInside +- milb.circle.isSegmentCompletelyInside +- mlib.polygon.isCircleCompletelyInside +- mlib.polygon.isPolygonCompletelyInside +- mlib.polygon.isSegmentCompletelyInside + + - ALIASES - +- mlib.circle.getPolygonIntersection +- mlib.circle.isCircleInsidePolygon +- mlib.circle.isCircleCompletelyInsidePolygon +- milb.line.getCircleIntersection +- milb.line.getPolygonIntersection +- milb.line.getLineIntersection +- mlib.line.segment.getCircleIntersection +- mlib.line.segment.getPolygonIntersection +- mlib.line.segment.getLineIntersection +- mlib.line.segment.getSegmentIntersection +- mlib.line.segment.isSegmentCompletelyInsideCircle +- mlib.line.segment.isSegmentCompletelyInsidePolygon +- mlib.polygon.isCircleCompletelyOver + +Changed: +---- +- mlib.circle.getCircleIntersection now returns 'inside' instead of 'intersection' if the point has not intersections but is within the circle. +- Fixed problem involving mlib.circle.getSegmentIntersection + +- README.md now has more information on how to run specs and other minor improvements. +- Fixed some commenting on explanation of derivation of mlib.line.getIntersection. +- Updated the example to use the current version of mlib. +- Made/Changed some comments in the example main.lua. + +Removed: +---- + +To-Do +---- +- Make examples file on github (examples/shapes/main.lua, etc.) not just one line. +- Determine if isCompletelyInsideFunctions should return true with tangents. +- Make argument order more logical. +- Make sure to see if any aliases were missed. (e.g. isSegmentInside) +- Update spec links in README + +0.9.2 +==== +Added: +---- + +Changed: +---- +- mlib.polygon.getPolygonIntersection now does not create duplicate local table. +- mlib.line.getPerpendicularSlope now does not create a global variable. +- mlib.math.getSummation now allows the error to go through instead of returning false if the stop value is not a number. + +- Changed any instance of the term "userdata" with "input" + +Removed: +---- + +0.9.1 +==== +Added: +---- +- Added mlib.statistics.getCentralTendency +- Added mlib.statistics.getDispersion +- Added mlib.statistics.getStandardDeviation +- Added mlib.statistics.getVariation +- Added mlib.statistics.getVariationRatio + +Removed: +---- + +Changed: +---- +- FIX: mlib.polygon.checkPoint now handles vertices better. + + +To-Do +---- +- Add more functions. + +0.9.0 +==== +Added: +---- +- mlib.line.getDistance as an alias for mlib.line.getLength. +- mlib.line.checkPoint +- Internal documentation. + +Removed: +---- +- mlib.circle.isPointInCircle is replaced with mlib.circle.checkPoint +- mlib.circle.checkPoint is replaced with mlib.circle.isPointOnCircle +- Variation of mlib.circle.getLineIntersection( cx, cy, radius, slope, intercept ) is no longer supported, as it can cause errors with vertical lines. + +Changed: +---- +- CHANGE: mlib.line.getIntersection now returns true for colinear lines. +- CHANGE: mlib.line.getIntersection now returns true if the line are collinear. +- CHANGE: mlib.line.getIntersection now returns true if vertical lines are collinear. +- CHANGE: mlib.line.getSegmentIntersection now returns true if the line and segment are collinear. +- CHANGE: Changed the order of mlib.line.segment.checkPoint arguments. +- NAME: mlib.polygon.lineIntersects is now mlib.polygon.getLineIntersection +- NAME: mlib.polygon.lineSegmentIntersects is now mlib.polygon.getSegmentIntersection +- NAME: mlib.polygon.isLineSegmentInside is now mlib.polygon.isSegmentInside +- NAME: mlib.polygon.polygonIntersects is now mlib.polygon.getPolygonIntersection +- CHANGED: mlib.circle.checkPoint now takes arguments ( px, py, cx, cy, radius ). +- CHANGED: mlib.circle.isPointOnCircle now takes arguments ( px, py, cx, cy, radius ). +- NAME: mlib.polygon.circleIntersects is now mlib.polygon.getCircleIntersection +- NAME: mlib.circle.isLineSecant is now mlib.circle.getLineIntersection +- NAME: mlib.circle.isSegmentSecant is now mlib.circle.getSegmentIntersection +- NAME: mlib.circle.circlesIntersects is now mlib.circle.getCircleIntersection +- CHANGE: Added types 'tangent' and 'intersection' to mlib.circle.getCircleIntersection. +- NAME: mlib.math.getRootsOfQuadratic is now mlib.math.getQuadraticRoots +- CHANGE: mlib.math.getRoot now only returns the positive, since it there is not always negatives. +- NAME: mlib.math.getPercent is now mlib.math.getPercentage + +- Cleaned up code (added comments, spaced lines, etc.) +- Made syntax that uses camelCase instead of CamelCase. + - Match style of more programmers. + - Easier to type. +- Moved to semantic numbering. +- Made any returns strings lower-case. +- Updated specs for missing functions. + +To-Do +---- +- Update readme. +- Add mlib.statistics.getStandardDeviation +- Add mlib.statistics.getMeasuresOfCentralTendency +- Add mlib.statistics.getMeasuresOfDispersion + +1.1.0.2 +==== +Added: +---- +- MLib.Polygon.IsPolygonInside + +Removed: +---- +- Removed all MLib.Shape: + - Was very slow. + - Could not define custom callbacks. + - Allow for flexibility. + +Changed: +---- +- Switched MLib.Line.GetIntersection back to the old way +- MLib.Line.GetSegmentIntersection now returns 4 values if the lines are parallel. + +TODO: +- Make it so that MLib.Shape objects can use ':' syntax for other functions (i.e. MLib.Line.GetLength for Line objects, etc.) +- Intuitive error messages. + + +1.1.0.1 +==== +Added: +---- + +Removed: +---- + +Changed: +- MLib.Line.GetIntersection now returns true, instead of two points. + +---- + +Fixed: +---- +- MLib.Line.GetIntersection now handles vertical lines: returns true if they collide, false otherwise. +- MLib.Polygon.LineIntersects now also handles verticals. + +TODO: +- Fix + - MLib.Shape Table can't have metatables. + +1.1.0.0 +==== +Added: +---- +- MLib.Polygon.IsCircleInside +- MLib.Polygon.LineSegmentIntersects +- MLib.Polygon.IsLineSegmentInside +- MLib.Statistics.GetFrequency +- MLib.Math.Factorial +- MLib.Math.SystemOfEquations + +Removed: +---- + +Changed: +---- +- MLib.Polygon.LineIntersects is now MLib.Polygon.LineSegmentIntersects. +- Put Word-wrap on Changes.txt + +Fixed: +---- +- Problems with numberous MLib.Polygon and MLib.Circle problems. + +TODO: +- Fix + - MLib.Shape Table can't have metatables. + +1.0.0.3 +==== +Added: +---- + +Removed: +---- + +Changed: +---- + +Fixed: +---- +- README.md + +TODO: +- Add: + - Frequency + - Binomial Probability + - Standard Deviation + - Conditional Probability + +1.0.0.2 +==== +Added: +---- + +Removed: +---- +- Ability to use a direction for Math.GetAngle's 5th argument instead of having a third point. See Fixed for more. + +Changed: +---- +- Changed README.md for clarity and consistency. +- Updated spec.lua +- See Fixed for more. + +Fixed: +---- +- Circle.IsSegmentSecant now properly accounts for chords actually being chords, and not secants. +- Circle.CircleIntersects now can return 'Colinear' or 'Equal' if the circles have same x and y but different radii (Colinear) or are exactly the same (Equal). +- Statistics.GetMode now returns a table with the modes, and the second argument as the number of times they appear. +- Math.GetRoot now returns the negative number as a second argument. +- Math.GetPercentOfChange now works for 0 to 0 (previously false). +- Math.GetAngle now takes only three points and no direction option. +- Typos in Shape.CheckCollisions and Shape.Remove. +- Fixed nil problems in Shape.CheckCollisions. +- Improved readablility and DRYness of Shape.CheckCollisions. +- Bugs in Shape.Remove and Shape.CheckCollisions regarding passing tables as arguments. + +TODO: +- Add: + - Frequency + - Binomial Probability + - Standard Deviation + - Conditional Probability + +1.0.0.1 +==== +Added: +---- + +Removed: +---- + +Changed: +---- +- Changes.txt now expanded to include short excertps from all previous commits. +- Changed release number from 3.0.0 to 1.0.0.1 +- Math.Round now can round to decimal places as the second argument. +- Commented unnecessary call of Segment.CheckPoint in Polygon.LineIntersects. +- Polygon.LineIntersects now returns where the lines intersect. + - false if not intersection. + - A table with all of the intersections { { px, py } } +- Same with Polygon.PolygonIntersects, Polygon.CircleIntersects, + +Fixed: +---- +- Error with GetSlope being called incorrectly. +- README.md Line.GetPerpendicularSlope misdirection. +- Same with Line.GetPerpendicularBisector, Line.Segment.GetIntersection, Circle.IsLineSecant, Circle.IsSegmentSecant, Statistics.GetMean, Median, Mode, and Range, and Shape:Remove, and fixed the naming for Shape:CheckCollisions and Shape:Remove. +- Clarified README.md +- Made util SortWithReferences local. +- Errors caused by local functions. + +TODO: +- Add: + - Frequency + - Binomial Probability + - Standard Deviation + - Conditional Probability + +3.0.0 +----- +ADDED: +- Added function GetSignedArea. +REMOVED: +- Removed drawing functions. +- Removed MLib.Line.Functions entirely. +CHANGED: +- Changed all the names to CamelCase. +- Changed module name to MLib. +- Changed return order of GetPerpendicualrBisector from Slope, Midpoint to Midpoint, Slope. +- Changed returned string of MLib.circle.isLineSecant to be upper-case. +- Changed IsPrime to accept only one number at a time. +- Changed NewShape's type to Capitals. + +Related to code: +- Added more accuarate comments. +- Made code more DRY. +- Made code monkey-patchable and saved space (by declaring all functions as local values then inserted them into a large table. + +TODO: +- Make LineIntersectsPolygon return where intersection occurs. +- Ditto with PolygonIntersectsPolygon. +- Add: + - Frequency + - Binomial Probability + - Standard Deviation + - Conditional Probability + + +Not as accurately maintained before 2.0.2 +----------------------------------------- + +2.0.2 +----- +- Cleaned up code, mostly. + +2.0.1 +----- +- Bug fixes, mlib.shape:remove & demos added. + +2.0.0 +----- +- Added mlib.shape and various bug fixes. + +2.0.0 +----- +- Made mlib.shape and made numberous bug fixes. + +1.9.4 +----- +- Made mlib.math.prime faster and removed ability to test multiple numbers at once. Thanks Robin! + +1.9.3 +----- +- Fixed polygon.area and polygon.centroid + +1.9.2 +----- +- Updated to LOVE 0.9.0. + +1.9.1 +----- +- Made mlib.line.closestPoint able to take either two points on the slope or the slope and intercept. + +1.9.0 +----- +- Added mlib.lineSegmentIntersects (no affiliation with previous one (changed to mlib.line.segment.intersect)) and mlib.line.closestPoint + +1.8.3 +----- +- Changed naming mechanism to be more organized. + +1.8.2 +----- +- "Fixed" mlib.lineSegmentsIntersect AGAIN!!!! :x + +1.8.1 +----- +- Removed a print statement. + +1.8.0 +----- +- mlib.pointInPolygon added + +1.7.5 +----- +- mlib.lineSegmentsIntersect vertical lines fixed again. This time for real. I promise... or hope, at least... :P + +1.7.4 +----- +- mlib.lineSegmentsIntersect vertical parallels fixed + +1.7.3 +----- +- mlib.lineSegmentsIntersect parallels fixed + +1.7.2 +----- +- mlib.lineSegmentsIntersect now handles vertical lines + +1.7.1 +----- +- mlib.lineSegmentsIntersect now returns the two places in between where the line segments begin to intersect. + +1.7.0 +----- +- Added mlib.circlesIntersect, mlib.pointOnLineSegment, mlib.linesIntersect, and mlib.lineSegmentsIntersect + +1.6.1 +----- +- Employed usage of summations for mlib.getPolygonArea and mlib.getPolygonCentroid and removed area as an argument for mlib.getPolygonCentroid. + +1.6.0 +----- +- Added several functions. + +1.5.0 +----- +- Made lots of changes to syntax to make it easier to use (hopefully). I also put out specs. + +1.4.1 +----- +- Localized mlib. Thanks, Yonaba! + +1.4.0 +----- +- Added mlib.getPolygonCentroid (gets the midpoint of a non-self-intersecting polygons) + +1.3.2 +----- +- Made mlib.getPrime take tables as arguments, so you can check all the values of a table. + +1.3.1 +----- +- Changed name method to mlib.getPolygonArea + +1.3.0 +----- +- Added mlib.get_polygon_area and removed mlib.get_convex_area and mlib.get_triangle_area since they are repetitive. + +1.2.2 +----- +- Made functions return faster, functions that previously returned tables now return multiple arguments. + +1.2.1 +----- +- Localized functions, made tables acceptable as arguments, refined function speed, mlib.get_mode now returns number most repeated as well as how many times. + +1.2.0 +----- +- Added mlib.get_angle + +1.1.0 +----- +- Added mlib.get_convex_area + +1.0.4 +----- +- Fixed get_mode to handle bimodials. + +1.0.3 +----- +- Prime Checker optimized (hopefully final update on this.) + +1.0.2 +----- +- Prime checker now works! (At least to 1000. I haven't tested any +further) + +1.0.1 +----- +- 'Fixed' the prime checker + +1.0.0 +----- +- Initial release diff --git a/libs/windfield/mlib/LICENSE.md b/libs/windfield/mlib/LICENSE.md new file mode 100644 index 0000000..38331e3 --- /dev/null +++ b/libs/windfield/mlib/LICENSE.md @@ -0,0 +1,17 @@ +Copyright (c) 2015 Davis Claiborne + +This software is provided 'as-is', without any express or implied +warranty. In no event will the authors be held liable for any damages +arising from the use of this software. + +Permission is granted to anyone to use this software for any purpose, +including commercial applications, and to alter it and redistribute it +freely, subject to the following restrictions: + +1. The origin of this software must not be misrepresented; you must not + claim that you wrote the original software. If you use this software + in a product, an acknowledgement in the product documentation would be + appreciated but is not required. +2. Altered source versions must be plainly marked as such, and must not be + misrepresented as being the original software. +3. This notice may not be removed or altered from any source distribution. diff --git a/libs/windfield/mlib/README.md b/libs/windfield/mlib/README.md new file mode 100644 index 0000000..6bbfdb2 --- /dev/null +++ b/libs/windfield/mlib/README.md @@ -0,0 +1,890 @@ +MLib +==== + +__MLib__ is a math and shape-intersection detection library written in Lua. It's aim is to be __robust__ and __easy to use__. + +__NOTE:__ +- I am (slowly) working on completely rewriting this in order to be easier to use and less bug-prone. You can check out the progress [here](../../tree/dev). +- I am currently slowing development of MLib while moving over to helping with [CPML](https://github.com/excessive/cpml). To discuss this, please comment [here](../../issues/12). + +If you are looking for a library that handles updating/collision responses for you, take a look at [hxdx](https://github.com/adonaac/hxdx). It uses MLib functions as well as Box2d to handle physics calculations. + +## Downloading +You can download the latest __stable__ version of MLib by downloading the latest [release](../../releases/). +You can download the latest __working__ version of MLib by downloading the latest [commit](../../commits/master/). Documentation will __only__ be updated upon releases, not upon commits. + +## Implementing +To use MLib, simply place [mlib.lua](mlib.lua) inside the desired folder in your project. Then use the `require 'path.to.mlib'` to use any of the functions. + +## Examples +If you don't have [LÖVE](https://love2d.org/) installed, you can download the .zip of the demo from the [Executables](Examples/Executables) folder and extract and run the .exe that way. +You can see some examples of the code in action [here](Examples). +All examples are done using the *awesome* engine of [LÖVE](https://love2d.org/). +To run them properly, download the [.love file](Examples/LOVE) and install LÖVE to your computer. +After that, make sure you set .love files to open with "love.exe". +For more, see [here](https://love2d.org/). + +## When should I use MLib? +- If you need to know exactly where two objects intersect. +- If you need general mathematical equations to be done. +- If you need very precise details about point intersections. + +## When should I __not__ use MLib? +- All of the objects in a platformer, or other game, for instance, should not be registered with MLib. Only ones that need very specific information. +- When you don't need precise information/odd shapes. + +## Specs +#### For Windows +If you run Windows and have Telescope in `%USERPROFILE%\Documents\GitHub` (you can also manually change the path in [test.bat](test.bat)) you can simply run [test.bat](test.bat) and it will display the results, and then clean up after it's finished. + +#### Default +Alternatively, you can find the tests [here](spec.lua). Keep in mind that you may need to change certain semantics to suit your OS. +You can run them via [Telescope](https://github.com/norman/telescope/) and type the following command in the command-line of the root folder: +``` +tsc -f specs.lua +``` +If that does not work, you made need to put a link to Lua inside of the folder for `telescope` and run the following command: +``` +lua tsc -f specs.lua +``` +If you encounter further errors, try to run the command line as an administrator (usually located in `C:\Windows\System32\`), then right-click on `cmd.exe` and select `Run as administrator`, then do +``` +cd C:\Path\to\telescope\ +``` +And __then__ run one of the above commands. If none of those work, just take my word for it that all the tests pass and look at this picture. + + +## Functions +- [mlib.line](#mlibline) + - [mlib.line.checkPoint](#mliblinecheckpoint) + - [mlib.line.getClosestPoint](#mliblinegetclosestpoint) + - [mlib.line.getYIntercept](#mliblinegetintercept) + - [mlib.line.getIntersection](#mliblinegetintersection) + - [mlib.line.getLength](#mliblinegetlength) + - [mlib.line.getMidpoint](#mliblinegetmidpoint) + - [mlib.line.getPerpendicularSlope](#mliblinegetperpendicularslope) + - [mlib.line.getSegmentIntersection](#mliblinegetsegmentintersection) + - [mlib.line.getSlope](#mliblinegetslope) +- [mlib.segment](#mlibsegment) + - [mlib.segment.checkPoint](#mlibsegmentcheckpoint) + - [mlib.segment.getPerpendicularBisector](#mlibsegmentgetperpendicularbisector) + - [mlib.segment.getIntersection](#mlibsegmentgetintersection) +- [mlib.polygon](#mlibpolygon) + - [mlib.polygon.checkPoint](#mlibpolygoncheckpoint) + - [mlib.polygon.getCentroid](#mlibpolygongetcentroid) + - [mlib.polygon.getCircleIntersection](#mlibpolygongetcircleintersection) + - [mlib.polygon.getLineIntersection](#mlibpolygongetlineintersection) + - [mlib.polygon.getPolygonArea](#mlibpolygongetpolygonarea) + - [mlib.polygon.getPolygonIntersection](#mlibpolygongetpolygonintersection) + - [mlib.polygon.getSegmentIntersection](#mlibpolygongetsegmentintersection) + - [mlib.polygon.getSignedPolygonArea](#mlibpolygongetsignedpolygonarea) + - [mlib.polygon.getTriangleHeight](#mlibpolygongettriangleheight) + - [mlib.polygon.isCircleInside](#mlibpolygoniscircleinside) + - [mlib.polygon.isCircleCompletelyInside](#mlibpolygoniscirclecompletelyinside) + - [mlib.polygon.isPolygonInside](#mlibpolygonispolygoninside) + - [mlib.polygon.isPolygonCompletelyInside](#mlibpolygonispolygoncompletelyinside) + - [mlib.polygon.isSegmentInside](#mlibpolygonissegmentinside) + - [mlib.polygon.isSegmentCompletelyInside](#mlibpolygonissegmentcompletelyinside) +- [mlib.circle](#mlibcircle) + - [mlib.circle.checkPoint](#mlibcirclecheckpoint) + - [mlib.circle.getArea](#mlibcirclegetarea) + - [mlib.circle.getCircleIntersection](#mlibcirclegetcircleintersection) + - [mlib.circle.getCircumference](#mlibcirclegetcircumference) + - [mlib.circle.getLineIntersection](#mlibcirclegetlineintersection) + - [mlib.circle.getSegmentIntersection](#mlibcirclegetsegmentintersection) + - [mlib.circle.isCircleCompletelyInside](#mlibcircleiscirclecompletelyinside) + - [mlib.circle.isCircleCompletelyInsidePolygon](#mlibcircleiscirclecompletelyinsidepolygon) + - [mlib.circle.isPointOnCircle](#mlibcircleispointoncircle) + - [mlib.circle.isPolygonCompletelyInside](#mlibcircleispolygoncompletelyinside) +- [mlib.statistics](#mlibstatistics) + - [mlib.statistics.getCentralTendency](#mlibstatisticsgetcentraltendency) + - [mlib.statistics.getDispersion](#mlibstatisticsgetdispersion) + - [mlib.statistics.getMean](#mlibstatisticsgetmean) + - [mlib.statistics.getMedian](#mlibstatisticsgetmedian) + - [mlib.statistics.getMode](#mlibstatisticsgetmode) + - [mlib.statistics.getRange](#mlibstatisticsgetrange) + - [mlib.statistics.getStandardDeviation](#mlibstatisticsgetstandarddeviation) + - [mlib.statistics.getVariance](#mlibstatisticsgetvariance) + - [mlib.statistics.getVariationRatio](#mlibstatisticsgetvariationratio) +- [mlib.math](#mlibmath) + - [mlib.math.getAngle](#mlibmathgetangle) + - [mlib.math.getPercentage](#mlibmathgetpercentage) + - [mlib.math.getPercentOfChange](#mlibmathgetpercentofchange) + - [mlib.math.getQuadraticRoots](#mlibmathgetquadraticroots) + - [mlib.math.getRoot](#mlibmathgetroot) + - [mlib.math.getSummation](#mlibmathgetsummation) + - [mlib.math.isPrime](#mlibmathisprime) + - [mlib.math.round](#mlibmathround) +- [Aliases](#aliases) + +#### mlib.line +- Deals with linear aspects, such as slope and length. + +##### mlib.line.checkPoint +- Checks if a point lies on a line. +- Synopsis: + - `onPoint = mlib.line.checkPoint( px, px, x1, y1, x2, y2 )` +- Arguments: + - `px`, `py`: Numbers. The x and y coordinates of the point being tested. + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates of the line being tested. +- Returns: + - `onPoint`: Boolean. + - `true` if the point is on the line. + - `false` if it does not. +- Notes: + - You cannot use the format `mlib.line.checkPoint( px, px, slope, intercept )` because this would lead to errors on vertical lines. + +##### mlib.line.getClosestPoint +- Gives the closest point to a line. +- Synopses: + - `cx, cy = mlib.line.getClosestPoint( px, py, x1, y1, x2, y2 )` + - `cx, cy = mlib.line.getClosestPoint( px, py, slope, intercept )` +- Arguments: + - `x`, `y`: Numbers. The x and y coordinates of the point. + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates on the line. + - `slope`, `intercept`: + - Numbers. The slope and y-intercept of the line. + - Booleans (`false`). The slope and y-intercept of a vertical line. +- Returns: + - `cx`, `cy`: Numbers. The closest points that lie on the line to the point. + +##### mlib.line.getYIntercept +- Gives y-intercept of the line. +- Synopses: + - `intercept, isVertical = mlib.line.getYIntercept( x1, y1, x2, y2 )` + - `intercept, isVertical = mlib.line.getYIntercept( x1, y1, slope )` +- Arguments: + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates that lie on the line. + - `slope`: + - Number. The slope of the line. +- Returns: + - `intercept`: + - Number. The y-intercept of the line. + - Number. The `x1` coordinate of the line if the line is vertical. + - `isVertical`: + - Boolean. `true` if the line is vertical, `false` if the line is not vertical. + +##### mlib.line.getIntersection +- Gives the intersection of two lines. +- Synopses: + - `x, y = mlib.line.getIntersection( x1, y1, x2, y2, x3, y3, x4, y4 )` + - `x, y = mlib.line.getIntersection( slope1, intercept1, x3, y3, x4, y4 )` + - `x, y = mlib.line.getIntersection( slope1, intercept1, slope2, intercept2 )` +- Arguments: + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates that lie on the first line. + - `x3`, `y3`, `x4`, `y4`: Numbers. Two x and y coordinates that lie on the second line. + - `slope1`, `intercept1`: + - Numbers. The slope and y-intercept of the first line. + - Booleans (`false`). The slope and y-intercept of the first line (if the first line is vertical). + - `slope2`, `intercept2`: + - Numbers. The slope and y-intercept of the second line. + - Booleans (`false`). The slope and y-intercept of the second line (if the second line is vertical). +- Returns: + - `x`, `y`: + - Numbers. The x and y coordinate where the lines intersect. + - Boolean: + - `true`, `nil`: The lines are collinear. + - `false`, `nil`: The lines are parallel and __not__ collinear. + +##### mlib.line.getLength +- Gives the distance between two points. +- Synopsis: + - `length = mlib.line.getLength( x1, y1, x2, y2 ) +- Arguments: + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates. +- Returns: + - `length`: Number. The distance between the two points. + +##### mlib.line.getMidpoint +- Gives the midpoint of two points. +- Synopsis: + - `x, y = mlib.line.getMidpoint( x1, y1, x2, y2 )` +- Arguments: + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates. +- Returns: + - `x`, `y`: Numbers. The midpoint x and y coordinates. + +##### mlib.line.getPerpendicularSlope +- Gives the perpendicular slope of a line. +- Synopses: + - `perpSlope = mlib.line.getPerpendicularSlope( x1, y1, x2, y2 )` + - `perpSlope = mlib.line.getPerpendicularSlope( slope )` +- Arguments: + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates. + - `slope`: Number. The slope of the line. +- Returns: + - `perpSlope`: + - Number. The perpendicular slope of the line. + - Boolean (`false`). The perpendicular slope of the line (if the original line was horizontal). + +##### mlib.line.getSegmentIntersection +- Gives the intersection of a line segment and a line. +- Synopses: + - `x1, y1, x2, y2 = mlib.line.getSegmentIntersection( x1, y1, x2, y2, x3, y3, x4, y4 )` + - `x1, y1, x2, y2 = mlib.line.getSegmentIntersection( x1, y1, x2, y2, slope, intercept )` +- Arguments: + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates that lie on the line segment. + - `x3`, `y3`, `x4`, `y4`: Numbers. Two x and y coordinates that lie on the line. + - `slope`, `intercept`: + - Numbers. The slope and y-intercept of the the line. + - Booleans (`false`). The slope and y-intercept of the line (if the line is vertical). +- Returns: + - `x1`, `y1`, `x2`, `y2`: + - Number, Number, Number, Number. + - The points of the line segment if the line and segment are collinear. + - Number, Number, Boolean (`nil`), Boolean (`nil`). + - The coordinate of intersection if the line and segment intersect and are not collinear. + - Boolean (`false`), Boolean (`nil`), Boolean (`nil`), + - Boolean (`nil`). If the line and segment don't intersect. + +##### mlib.line.getSlope +- Gives the slope of a line. +- Synopsis: + - `slope = mlib.line.getSlope( x1, y1, x2, y2 ) +- Arguments: + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates. +- Returns: + - `slope`: + - Number. The slope of the line. + - Boolean (`false`). The slope of the line (if the line is vertical). + +#### mlib.segment +- Deals with line segments. + +##### mlib.segment.checkPoint +- Checks if a point lies on a line segment. +- Synopsis: + - `onSegment = mlib.segment.checkPoint( px, py, x1 y1, x2, y2 )` +- Arguments: + - `px`, `py`: Numbers. The x and y coordinates of the point being checked. + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates. +- Returns: + - `onSegment`: Boolean. + - `true` if the point lies on the line segment. + - `false` if the point does not lie on the line segment. + +##### mlib.segment.getPerpendicularBisector +- Gives the perpendicular bisector of a line. +- Synopsis: + - `x, y, slope = mlib.segment.getPerpendicularBisector( x1, y1, x2, y2 )` +- Arguments: + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates. +- Returns: + - `x`, `y`: Numbers. The midpoint of the line. + - `slope`: + - Number. The perpendicular slope of the line. + - Boolean (`false`). The perpendicular slope of the line (if the original line was horizontal). + +##### mlib.segment.getIntersection +- Checks if two line segments intersect. +- Synopsis: + - `cx1, cy1, cx2, cy2 = mlib.segment.getIntersection( x1, y1, x2, y2, x3, y3 x4, y4 )` +- Arguments: + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates of the first line segment. + - `x3`, `y3`, `x4`, `y4`: Numbers. Two x and y coordinates of the second line segment. +- Returns: + - `cx1`, `cy1`, `cx2`, `cy2`: + - Number, Number, Number, Number. + - The points of the resulting intersection if the line segments are collinear. + - Number, Number, Boolean (`nil`), Boolean (`nil`). + - The point of the resulting intersection if the line segments are not collinear. + - Boolean (`false`), Boolean (`nil`), Boolean (`nil`) , Boolean (`nil`). + - If the line segments don't intersect. + +#### mlib.polygon +- Handles aspects involving polygons. + +##### mlib.polygon.checkPoint +- Checks if a point is inside of a polygon. +- Synopses: + - `inPolygon = mlib.polygon.checkPoint( px, py, vertices )` + - `inPolygon = mlib.polygon.checkPoint( px, py, ... )` +- Arguments: + - `px`, `py`: Numbers. The x and y coordinate of the point being checked. + - `vertices`: Table. The vertices of the polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `...`: Numbers. The x and y coordinates of the polygon. (Same as using `unpack( vertices )`) +- Returns: + - `inPolygon`: Boolean. + - `true` if the point is inside the polygon. + - `false` if the point is not inside the polygon. + +##### mlib.polygon.getCentroid +- Returns the centroid of the polygon. +- Synopses: + - `cx, cy = mlib.polygon.getCentroid( vertices )` + - `cx, cy = mlib.polygon.getCentroid( ... )` +- Arguments: + - `vertices`: Table. The vertices of the polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `...`: Numbers. The x and y coordinates of the polygon. (Same as using `unpack( vertices )`) +- Returns: + - `cx`, `cy`: Numbers. The x and y coordinates of the centroid. + +##### mlib.polygon.getCircleIntersection +- Returns the coordinates of where a circle intersects a polygon. +- Synopses: + - `intersections = mlib.polygon.getCircleIntersection( cx, cy, radius, vertices )` + - `intersections = mlib.polygon.getCircleIntersection( cx, cy, radius, ... ) +- Arguments: + - `cx`, `cy`: Number. The coordinates of the center of the circle. + - `radius`: Number. The radius of the circle. + - `vertices`: Table. The vertices of the polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `...`: Numbers. The x and y coordinates of the polygon. (Same as using `unpack( vertices )`) +- Returns: + - `intersections`: Table. Contains the intersections and type. +- Example: +```lua +local tab = _.polygon.getCircleIntersection( 5, 5, 1, 4, 4, 6, 4, 6, 6, 4, 6 ) +for i = 1, # tab do + print( i .. ':', unpack( tab[i] ) ) +end +-- 1: tangent 5 4 +-- 2: tangent 6 5 +-- 3: tangent 5 6 +-- 4: tagnent 4 5 +``` +- For more see [mlib.circle.getSegmentIntersection](#mlibcirclegetsegmentintersection) or the [specs](spec.lua# L676) + +##### mlib.polygon.getLineIntersection +- Returns the coordinates of where a line intersects a polygon. +- Synopses: + - `intersections = mlib.polygon.getLineIntersection( x1, y1, x2, y2, vertices )` + - `intersections = mlib.polygon.getLineIntersection( x1, y1, x2, y2, ... ) +- Arguments: + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates. + - `vertices`: Table. The vertices of the polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `...`: Numbers. The x and y coordinates of the polygon. (Same as using `unpack( vertices )`) +- Returns: + - `intersections`: Table. Contains the intersections. +- Notes: + - With collinear lines, they are actually broken up. i.e. `{ 0, 4, 0, 0 }` would become `{ 0, 4 }, { 0, 0 }`. + +##### mlib.polygon.getPolygonArea +- Gives the area of a polygon. +- Synopses: + - `area = mlib.polygon.getArea( vertices )` + - `area = mlib.polygon.getArea( ... ) +- Arguments: + - `vertices`: Table. The vertices of the polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `...`: Numbers. The x and y coordinates of the polygon. (Same as using `unpack( vertices )`) +- Returns: + - `area`: Number. The area of the polygon. + +##### mlib.polygon.getPolygonIntersection +- Gives the intersection of two polygons. +- Synopsis: + - `intersections = mlib.polygon.getPolygonIntersections( polygon1, polygon2 )` +- Arguments: + - `polygon1`: Table. The vertices of the first polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `polygon2`: Table. The vertices of the second polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` +- Returns: + - `intersections`: Table. A table of the points of intersection. + +##### mlib.polygon.getSegmentIntersection +- Returns the coordinates of where a line segmeing intersects a polygon. +- Synopses: + - `intersections = mlib.polygon.getSegmentIntersection( x1, y1, x2, y2, vertices )` + - `intersections = mlib.polygon.getSegmentIntersection( x1, y1, x2, y2, ... ) +- Arguments: + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates. + - `vertices`: Table. The vertices of the polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `...`: Numbers. The x and y coordinates of the polygon. (Same as using `unpack( vertices )`) +- Returns: + - `intersections`: Table. Contains the intersections. +- Notes: + - With collinear line segments, they are __not__ broken up. See the [specs](spec.lua# L508) for more. + +##### mlib.polygon.getSignedPolygonArea +- Gets the signed area of the polygon. If the points are ordered counter-clockwise the area is positive. If the points are ordered clockwise the number is negative. +- Synopses: + - `area = mlib.polygon.getLineIntersection( vertices )` + - `area = mlib.polygon.getLineIntersection( ... ) +- Arguments: + - `vertices`: Table. The vertices of the polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `...`: Numbers. The x and y coordinates of the polygon. (Same as using `unpack( vertices )`) +- Returns: + - `area`: Number. The __signed__ area of the polygon. If the points are ordered counter-clockwise the area is positive. If the points are ordered clockwise the number is negative. + +##### mlib.polygon.getTriangleHeight +- Gives the height of a triangle. +- Synopses: + - `height = mlib.polygon.getTriangleHeigh( base, x1, y1, x2, y2, x3, y3 )` + - `height = mlib.polygon.getTriangleHeight( base, area )` +- Arguments: + - `base`: Number. The length of the base of the triangle. + - `x1`, `y1`, `x2`, `y2`, `x3`, `y3`: Numbers. The x and y coordinates of the triangle. + - `area`: Number. The regular area of the triangle. __Not__ the signed area. +- Returns: + - `height`: Number. The height of the triangle. + +##### mlib.polygon.isCircleInside +- Checks if a circle is inside the polygon. +- Synopses: + - `inPolygon = mlib.polygon.isCircleInside( cx, cy, radius, vertices )` + - `inPolygon = mlib.polygon.isCircleInside( cx, cy, radius, ... )` +- Arguments: + - `cx`, `cy`: Numbers. The x and y coordinates for the center of the circle. + - `radius`: Number. The radius of the circle. + - `vertices`: Table. The vertices of the polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `...`: Numbers. The x and y coordinates of the polygon. (Same as using `unpack( vertices )`) +- Returns: + - `inPolygon`: Boolean. + - `true` if the circle is inside the polygon. + - `false` if the circle is not inside the polygon. +- Notes: + - Only returns true if the center of the circle is inside the circle. + +##### mlib.polygon.isCircleCompletelyInside +- Checks if a circle is completely inside the polygon. +- Synopses: + - `inPolygon = mlib.polygon.isCircleCompletelyInside( cx, cy, radius, vertices )` + - `inPolygon = mlib.polygon.isCircleCompletelyInside( cx, cy, radius, ... )` +- Arguments: + - `cx`, `cy`: Numbers. The x and y coordinates for the center of the circle. + - `radius`: Number. The radius of the circle. + - `vertices`: Table. The vertices of the polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `...`: Numbers. The x and y coordinates of the polygon. (Same as using `unpack( vertices )`) +- Returns: + - `inPolygon`: Boolean. + - `true` if the circle is __completely__ inside the polygon. + - `false` if the circle is not inside the polygon. + +##### mlib.polygon.isPolygonInside +- Checks if a polygon is inside a polygon. +- Synopsis: + - `inPolygon = mlib.polygon.isPolygonInside( polygon1, polygon2 )` +- Arguments: + - `polygon1`: Table. The vertices of the first polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `polygon2`: Table. The vertices of the second polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` +- Returns: + - `inPolygon`: Boolean. + - `true` if the `polygon2` is inside of `polygon1`. + - `false` if `polygon2` is not inside of `polygon2`. +- Notes: + - Returns true as long as any of the line segments of `polygon2` are inside of the `polygon1`. + +##### mlib.polygon.isPolygonCompletelyInside +- Checks if a polygon is completely inside a polygon. +- Synopsis: + - `inPolygon = mlib.polygon.isPolygonCompletelyInside( polygon1, polygon2 )` +- Arguments: + - `polygon1`: Table. The vertices of the first polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `polygon2`: Table. The vertices of the second polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` +- Returns: + - `inPolygon`: Boolean. + - `true` if the `polygon2` is __completely__ inside of `polygon1`. + - `false` if `polygon2` is not inside of `polygon2`. + +##### mlib.polygon.isSegmentInside +- Checks if a line segment is inside a polygon. +- Synopses: + - `inPolygon = mlib.polygon.isSegmentInside( x1, y1, x2, y2, vertices )` + - `inPolygon = mlib.polygon.isSegmentInside( x1, y1, x2, y2, ... )` +- Arguments: + - `x1`, `y1`, `x2`, `y2`: Numbers. The x and y coordinates of the line segment. + - `vertices`: Table. The vertices of the polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `...`: Numbers. The x and y coordinates of the polygon. (Same as using `unpack( vertices )`) +- Returns: + - `inPolygon`: Boolean. + - `true` if the line segment is inside the polygon. + - `false` if the line segment is not inside the polygon. +- Note: + - Only one of the points has to be in the polygon to be considered 'inside' of the polygon. + - This is really just a faster version of [mlib.polygon.getPolygonIntersection](#mlibpolygongetpolygonintersection) that does not give the points of intersection. + +##### mlib.polygon.isSegmentCompletelyInside +- Checks if a line segment is completely inside a polygon. +- Synopses: + - `inPolygon = mlib.polygon.isSegmentCompletelyInside( x1, y1, x2, y2, vertices )` + - `inPolygon = mlib.polygon.isSegmentCompletelyInside( x1, y1, x2, y2, ... )` +- Arguments: + - `x1`, `y1`, `x2`, `y2`: Numbers. The x and y coordinates of the line segment. + - `vertices`: Table. The vertices of the polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `...`: Numbers. The x and y coordinates of the polygon. (Same as using `unpack( vertices )`) +- Returns: + - `inPolygon`: Boolean. + - `true` if the line segment is __completely__ inside the polygon. + - `false` if the line segment is not inside the polygon. + +#### mlib.circle +- Handles aspects involving circles. + +##### mlib.circle.checkPoint +- Checks if a point is on the inside or on the edge the circle. +- Synopsis: + - `inCircle = mlib.circle.checkPoint( px, px, cx, cy, radius )` +- Arguments: + - `px`, `py`: Numbers. The x and y coordinates of the point being tested. + - `cx`, `cy`: Numbers. The x and y coordinates of the center of the circle. + - `radius`: Number. The radius of the circle. +- Returns: + - `inCircle`: Boolean. + - `true` if the point is inside or on the circle. + - `false` if the point is outside of the circle. + +##### mlib.circle.getArea +- Gives the area of a circle. +- Synopsis: + - `area = mlib.circle.getArea( radius )` +- Arguments: + - `radius`: Number. The radius of the circle. +- Returns: + - `area`: Number. The area of the circle. + +##### mlib.circle.getCircleIntersection +- Gives the intersections of two circles. +- Synopsis: + - `intersections = mlib.circle.getCircleIntersection( c1x, c1y, radius1, c2x, c2y, radius2 ) +- Arguments: + - `c1x`, `c1y`: Numbers. The x and y coordinate of the first circle. + - `radius1`: Number. The radius of the first circle. + - `c2x`, `c2y`: Numbers. The x and y coordinate of the second circle. + - `radius2`: Number. The radius of the second circle. +- Returns: + - `intersections`: Table. A table that contains the type and where the circle collides. See the [specs](spec.lua# L698) for more. + +##### mlib.circle.getCircumference +- Returns the circumference of a circle. +- Synopsis: + - `circumference = mlib.circle.getCircumference( radius )` +- Arguments: + - `radius`: Number. The radius of the circle. +- Returns: + - `circumference`: Number. The circumference of a circle. + +##### mlib.circle.getLineIntersection +- Returns the intersections of a circle and a line. +- Synopsis: + - `intersections = mlib.circle.getLineIntersections( cx, cy, radius, x1, y1, x2, y2 )` +- Arguments: + - `cx`, `cy`: Numbers. The x and y coordinates for the center of the circle. + - `radius`: Number. The radius of the circle. + - `x1`, `y1`, `x2`, `y2`: Numbers. Two x and y coordinates the lie on the line. +- Returns: + - `intersections`: Table. A table with the type and where the intersections happened. Table is formatted: + - `type`, `x1`, `y1`, `x2`, `y2` + - String (`'secant'`), Number, Number, Number, Number + - The numbers are the x and y coordinates where the line intersects the circle. + - String (`'tangent'`), Number, Number, Boolean (`nil`), Boolean (`nil`) + - `x1` and `x2` represent where the line intersects the circle. + - Boolean (`false`), Boolean (`nil`), Boolean (`nil`), Boolean (`nil`), Boolean (`nil`) + - No intersection. + - For more see the [specs](spec.lua# L660). + +##### mlib.circle.getSegmentIntersection +- Returns the intersections of a circle and a line segment. +- Synopsis: + - `intersections = mlib.circle.getSegmentIntersections( cx, cy, radius, x1, y1, x2, y2 )` +- Arguments: + - `cx`, `cy`: Numbers. The x and y coordinates for the center of the circle. + - `radius`: Number. The radius of the circle. + - `x1`, `y1`, `x2`, `y2`: Numbers. The two x and y coordinates of the line segment. +- Returns: + - `intersections`: Table. A table with the type and where the intersections happened. Table is formatted: + - `type`, `x1`, `y1`, `x2`, `y2` + - String (`'chord'`), Number, Number, Number, Number + - The numbers are the x and y coordinates where the line segment is on both edges of the circle. + - String (`'enclosed'`), Number, Number, Number, Number + - The numbers are the x and y coordinates of the line segment if it is fully inside of the circle. + - String (`'secant'`), Number, Number, Number, Number + - The numbers are the x and y coordinates where the line segment intersects the circle. + - String (`'tangent'`), Number, Number, Boolean (`nil`), Boolean (`nil`) + - `x1` and `x2` represent where the line segment intersects the circle. + - Boolean (`false`), Boolean (`nil`), Boolean (`nil`), Boolean (`nil`), Boolean (`nil`) + - No intersection. + - For more see the [specs](spec.lua# L676). + +##### mlib.circle.isCircleCompletelyInside +- Checks if one circle is completely inside of another circle. +- Synopsis: + - `completelyInside = mlib.circle.isCircleCompletelyInside( c1x, c1y, c1radius, c2x, c2y, c2radius )` +- Arguments: + - `c1x`, `c1y`: Numbers. The x and y coordinates of the first circle. + - `c1radius`: Number. The radius of the first circle. + - `c2x`, `c2y`: Numbers. The x and y coordinates of the second circle. + - `c2radius`: Number. The radius of the second circle. +- Returns: + - `completelyInside`: Boolean. + - `true` if circle1 is inside of circle2. + - `false` if circle1 is not __completely__ inside of circle2. + +##### mlib.circle.isCircleCompletelyInsidePolygon +- Checks if a circle is completely inside the polygon. +- Synopses: + - `inPolygon = mlib.polygon.isCircleCompletelyInside( cx, cy, radius, vertices )` + - `inPolygon = mlib.polygon.isCircleCompletelyInside( cx, cy, radius, ... )` +- Arguments: + - `cx`, `cy`: Numbers. The x and y coordinates for the center of the circle. + - `radius`: Number. The radius of the circle. + - `vertices`: Table. The vertices of the polygon in the format `{ x1, y1, x2, y2, x3, y3, ... }` + - `...`: Numbers. The x and y coordinates of the polygon. (Same as using `unpack( vertices )`) +- Returns: + - `inPolygon`: Boolean. + - `true` if the circle is __completely__ inside the polygon. + - `false` if the circle is not inside the polygon. + +##### mlib.circle.isPointOnCircle +- Checks if a point is __exactly__ on the edge of the circle. +- Synopsis: + - `onCircle = mlib.circle.checkPoint( px, px, cx, cy, radius )` +- Arguments: + - `px`, `py`: Numbers. The x and y coordinates of the point being tested. + - `cx`, `cy`: Numbers. The x and y coordinates of the center of the circle. + - `radius`: Number. The radius of the circle. +- Returns: + - `onCircle`: Boolean. + - `true` if the point is on the circle. + - `false` if the point is on the inside or outside of the circle. +- Notes: + - Will return false if the point is inside __or__ outside of the circle. + +##### mlib.circle.isPolygonCompletelyInside +- Checks if a polygon is completely inside of a circle. +- Synopsis: + - `completelyInside = mlib.circle.isPolygonCompletelyInside( circleX, circleY, circleRadius, vertices )` + - `completelyInside = mlib.circle.isPolygonCompletelyInside( circleX, circleY, circleRadius, ... )` +- Arguments: + - `circleX`, `circleY`: Numbers. The x and y coordinates of the circle. + - `circleRadius`: Number. The radius of the circle. + - `vertices`: Table. A table containing all of the vertices of the polygon. + - `...`: Numbers. All of the points of the polygon. +- Returns: + - `completelyInside`: Boolean. + - `true` if the polygon is inside of the circle. + - `false` if the polygon is not __completely__ inside of the circle. + +#### mlib.statistics +- Handles statistical aspects of math. + +##### mlib.statistics.getCentralTendency +- Gets the central tendency of the data. +- Synopses: + - `modes, occurrences, median, mean = mlib.statistics.getCentralTendency( data )` + - `modes, occurrences, median, mean = mlib.statistics.getCentralTendency( ... )` +- Arguments: + - `data`: Table. A table containing the values of data. + - `...`: Numbers. All of the numbers in the data set. +- Returns: + - `modes, occurrences`: Table, Number. The modes of the data and the number of times it occurs. See [mlib.statistics.getMode](#mlibstatisticsgetmode). + - `median`: Number. The median of the data set. + - `mean`: Number. The mean of the data set. + +##### mlib.statistics.getDispersion +- Gets the dispersion of the data. +- Synopses: + - `variationRatio, range, standardDeviation = mlib.statistics.getDispersion( data )` + - `variationRatio, range, standardDeviation = mlib.statistics.getDispersion( ... )` +- Arguments: + - `data`: Table. A table containing the values of data. + - `...`: Numbers. All of the numbers in the data set. +- Returns: + - `variationRatio`: Number. The variation ratio of the data set. + - `range`: Number. The range of the data set. + - `standardDeviation`: Number. The standard deviation of the data set. + +##### mlib.statistics.getMean +- Gets the arithmetic mean of the data. +- Synopses: + - `mean = mlib.statistics.getMean( data )` + - `mean = mlib.statistics.getMean( ... )` +- Arguments: + - `data`: Table. A table containing the values of data. + - `...`: Numbers. All of the numbers in the data set. +- Returns: + - `mean`: Number. The arithmetic mean of the data set. + +##### mlib.statistics.getMedian +- Gets the median of the data set. +- Synopses: + - `median = mlib.statistics.getMedian( data )` + - `median = mlib.statistics.getMedian( ... )` +- Arguments: + - `data`: Table. A table containing the values of data. + - `...`: Numbers. All of the numbers in the data set. +- Returns: + - `median`: Number. The median of the data. + +##### mlib.statistics.getMode +- Gets the mode of the data set. +- Synopses: + - `mode, occurrences = mlib.statistics.getMode( data )` + - `mode, occurrences = mlib.statistics.getMode( ... )` +- Arguments: + - `data`: Table. A table containing the values of data. + - `...`: Numbers. All of the numbers in the data set. +- Returns: + - `mode`: Table. The mode(s) of the data. + - `occurrences`: Number. The number of time the mode(s) occur. + +##### mlib.statistics.getRange +- Gets the range of the data set. +- Synopses: + - `range = mlib.statistics.getRange( data )` + - `range = mlib.statistics.getRange( ... )` +- Arguments: + - `data`: Table. A table containing the values of data. + - `...`: Numbers. All of the numbers in the data set. +- Returns: + - `range`: Number. The range of the data. + +##### mlib.statistics.getStandardDeviation +- Gets the standard deviation of the data. +- Synopses: + - `standardDeviation = mlib.statistics.getStandardDeviation( data )` + - `standardDeviation = mlib.statistics.getStandardDeviation( ... )` +- Arguments: + - `data`: Table. A table containing the values of data. + - `...`: Numbers. All of the numbers in the data set. +- Returns: + - `standardDeviation`: Number. The standard deviation of the data set. + +##### mlib.statistics.getVariance +- Gets the variation of the data. +- Synopses: + - `variance = mlib.statistics.getVariance( data )` + - `variance = mlib.statistics.getVariance( ... )` +- Arguments: + - `data`: Table. A table containing the values of data. + - `...`: Numbers. All of the numbers in the data set. +- Returns: + - `variance`: Number. The variation of the data set. + +##### mlib.statistics.getVariationRatio +- Gets the variation ratio of the data. +- Synopses: + - `variationRatio = mlib.statistics.getVariationRatio( data )` + - `variationRatio = mlib.statistics.getVariationRatio( ... )` +- Arguments: + - `data`: Table. A table containing the values of data. + - `...`: Numbers. All of the numbers in the data set. +- Returns: + - `variationRatio`: Number. The variation ratio of the data set. + +#### mlib.math +- Miscellaneous functions that have no home. + +##### mlib.math.getAngle +- Gets the angle between three points. +- Synopsis: + - `angle = mlib.math.getAngle( x1, y1, x2, y2, x3, y3 )` +- Arguments: + - `x1`, `y1`: Numbers. The x and y coordinates of the first point. + - `x2`, `y2`: Numbers. The x and y coordinates of the vertex of the two points. + - `x3`, `y3`: Numbers. The x and y coordinates of the second point. + +##### mlib.math.getPercentage +- Gets the percentage of a number. +- Synopsis: + - `percentage = mlib.math.getPercentage( percent, number )` +- Arguments: + - `percent`: Number. The decimal value of the percent (i.e. 100% is 1, 50% is .5). + - `number`: Number. The number to get the percentage of. +- Returns: + - `percentage`: Number. The `percent`age or `number`. + +##### mlib.math.getPercentOfChange +- Gets the percent of change from one to another. +- Synopsis: + - `change = mlib.math.getPercentOfChange( old, new )` +- Arguments: + - `old`: Number. The original number. + - `new`: Number. The new number. +- Returns: + - `change`: Number. The percent of change from `old` to `new`. + +##### mlib.math.getQuadraticRoots +- Gets the quadratic roots of the the equation. +- Synopsis: + - `root1, root2 = mlib.math.getQuadraticRoots( a, b, c )` +- Arguments: + - `a`, `b`, `c`: Numbers. The a, b, and c values of the equation `a * x ^ 2 + b * x ^ 2 + c`. +- Returns: + - `root1`, `root2`: Numbers. The roots of the equation (where `a * x ^ 2 + b * x ^ 2 + c = 0`). + +##### mlib.math.getRoot +- Gets the `n`th root of a number. +- Synopsis: + - `x = mlib.math.getRoot( number, root )` +- Arguments: + - `number`: Number. The number to get the root of. + - `root`: Number. The root. +- Returns: + - `x`: The `root`th root of `number`. +- Example: +```lua +local a = mlib.math.getRoot( 4, 2 ) -- Same as saying 'math.pow( 4, .5 )' or 'math.sqrt( 4 )' in this case. +local b = mlib.math.getRoot( 27, 3 ) + +print( a, b ) --> 2, 3 +``` + - For more, see the [specs](spec.lua# L860). + +##### mlib.math.getSummation +- Gets the summation of numbers. +- Synopsis: + - `summation = mlib.math.getSummation( start, stop, func )` +- Arguments: + - `start`: Number. The number at which to start the summation. + - `stop`: Number. The number at which to stop the summation. + - `func`: Function. The method to add the numbers. + - Arguments: + - `i`: Number. Index. + - `previous`: Table. The previous values used. +- Returns: + - `Summation`: Number. The summation of the numbers. + - For more, see the [specs](spec.lua# L897). + +##### mlib.math.isPrime +- Checks if a number is prime. +- Synopsis: + - `isPrime = mlib.math.isPrime( x )` +- Arguments: + - `x`: Number. The number to check if it's prime. +- Returns: + - `isPrime`: Boolean. + - `true` if the number is prime. + - `false` if the number is not prime. + +##### mlib.math.round +- Rounds a number to the given decimal place. +- Synopsis: + - `rounded = mlib.math.round( number, [place] ) +- Arguments: + - `number`: Number. The number to round. + - `place (1)`: Number. The decimal place to round to. Defaults to 1. +- Returns: + - The rounded number. + - For more, see the [specs](spec.lua# L881). + +#### Aliases +| Alias | Corresponding Function | +| ----------------------------------------------|:---------------------------------------------------------------------------------:| +| milb.line.getDistance | [mlib.line.getLength](#mliblinegetlength) | +| mlib.line.getCircleIntersection | [mlib.circle.getLineIntersection](#mlibcirclegetlineintersection) | +| milb.line.getPolygonIntersection | [mlib.polygon.getLineIntersection](#mlibpolygongetlineintersection) | +| mlib.line.getLineIntersection | [mlib.line.getIntersection](#mliblinegetintersection) | +| mlib.segment.getCircleIntersection | [mlib.circle.getSegmentIntersection](#mlibcirclegetsegmentintersection) | +| milb.segment.getPolygonIntersection | [mlib.pollygon.getSegmentIntersection](#mlibpollygongetsegmentintersection) | +| mlib.segment.getLineIntersection | [mlib.line.getSegmentIntersection](#mliblinegetsegmentintersection) | +| mlib.segment.getSegmentIntersection | [mlib.segment.getIntersection](#mlibsegmentgetintersection) | +| milb.segment.isSegmentCompletelyInsideCircle | [mlib.circle.isSegmentCompletelyInside](#mlibcircleissegmentcompletelyinside) | +| mlib.segment.isSegmentCompletelyInsidePolygon | [mlib.polygon.isSegmentCompletelyInside](#mlibpolygonissegmentcompletelyinside) | +| mlib.circle.getPolygonIntersection | [mlib.polygon.getCircleIntersection](#mlibpolygongetcircleintersection) | +| mlib.circle.isCircleInsidePolygon | [mlib.polygon.isCircleInside](#mlibpolygoniscircleinside) | +| mlib.circle.isCircleCompletelyInsidePolygon | [mlib.polygon.isCircleCompletelyInside](#mlibpolygoniscirclecompletelyinside) | +| mlib.polygon.isCircleCompletelyOver | [mlib.circleisPolygonCompletelyInside](#mlibcircleispolygoncompletelyinside) | + +## License +A math library made in Lua +copyright (C) 2014 Davis Claiborne +This program is free software; you can redistribute it and/or modify +it under the terms of the GNU General Public License as published by +the Free Software Foundation; either version 2 of the License, or +(at your option) any later version. +This program is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU General Public License for more details. +You should have received a copy of the GNU General Public License along +with this program; if not, write to the Free Software Foundation, Inc., +51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. +Contact me at davisclaib at gmail.com diff --git a/libs/windfield/mlib/mlib.lua b/libs/windfield/mlib/mlib.lua new file mode 100644 index 0000000..488fdb7 --- /dev/null +++ b/libs/windfield/mlib/mlib.lua @@ -0,0 +1,1152 @@ +--[[ License + A math library made in Lua + copyright (C) 2014 Davis Claiborne + This program is free software; you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation; either version 2 of the License, or + (at your option) any later version. + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + You should have received a copy of the GNU General Public License along + with this program; if not, write to the Free Software Foundation, Inc., + 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. + Contact me at davisclaib@gmail.com +]] + +-- Local Utility Functions ---------------------- {{{ +local unpack = table.unpack or unpack + +-- Used to handle variable-argument functions and whether they are passed as func{ table } or func( unpack( table ) ) +local function checkInput( ... ) + local input = {} + if type( ... ) ~= 'table' then input = { ... } else input = ... end + return input +end + +-- Deals with floats / verify false false values. This can happen because of significant figures. +local function checkFuzzy( number1, number2 ) + return ( number1 - .00001 <= number2 and number2 <= number1 + .00001 ) +end + +-- Remove multiple occurrences from a table. +local function removeDuplicatePairs( tab ) + for index1 = #tab, 1, -1 do + local first = tab[index1] + for index2 = #tab, 1, -1 do + local second = tab[index2] + if index1 ~= index2 then + if type( first[1] ) == 'number' and type( second[1] ) == 'number' and type( first[2] ) == 'number' and type( second[2] ) == 'number' then + if checkFuzzy( first[1], second[1] ) and checkFuzzy( first[2], second[2] ) then + table.remove( tab, index1 ) + end + elseif first[1] == second[1] and first[2] == second[2] then + table.remove( tab, index1 ) + end + end + end + end + return tab +end + + +local function removeDuplicates4Points( tab ) + for index1 = #tab, 1, -1 do + local first = tab[index1] + for index2 = #tab, 1, -1 do + local second = tab[index2] + if index1 ~= index2 then + if type( first[1] ) ~= type( second[1] ) then return false end + if type( first[2] ) == 'number' and type( second[2] ) == 'number' and type( first[3] ) == 'number' and type( second[3] ) == 'number' then + if checkFuzzy( first[2], second[2] ) and checkFuzzy( first[3], second[3] ) then + table.remove( tab, index1 ) + end + elseif checkFuzzy( first[1], second[1] ) and checkFuzzy( first[2], second[2] ) and checkFuzzy( first[3], second[3] ) then + table.remove( tab, index1 ) + end + end + end + end + return tab +end + + +-- Add points to the table. +local function addPoints( tab, x, y ) + tab[#tab + 1] = x + tab[#tab + 1] = y +end + +-- Like removeDuplicatePairs but specifically for numbers in a flat table +local function removeDuplicatePointsFlat( tab ) + for i = #tab, 1 -2 do + for ii = #tab - 2, 3, -2 do + if i ~= ii then + local x1, y1 = tab[i], tab[i + 1] + local x2, y2 = tab[ii], tab[ii + 1] + if checkFuzzy( x1, x2 ) and checkFuzzy( y1, y2 ) then + table.remove( tab, ii ); table.remove( tab, ii + 1 ) + end + end + end + end + return tab +end + + +-- Check if input is actually a number +local function validateNumber( n ) + if type( n ) ~= 'number' then return false + elseif n ~= n then return false -- nan + elseif math.abs( n ) == math.huge then return false + else return true end +end + +local function cycle( tab, index ) return tab[( index - 1 ) % #tab + 1] end + +local function getGreatestPoint( points, offset ) + offset = offset or 1 + local start = 2 - offset + local greatest = points[start] + local least = points[start] + for i = 2, #points / 2 do + i = i * 2 - offset + if points[i] > greatest then + greatest = points[i] + end + if points[i] < least then + least = points[i] + end + end + return greatest, least +end + +local function isWithinBounds( min, num, max ) + return num >= min and num <= max +end + +local function distance2( x1, y1, x2, y2 ) -- Faster since it does not use math.sqrt + local dx, dy = x1 - x2, y1 - y2 + return dx * dx + dy * dy +end -- }}} + +-- Points -------------------------------------- {{{ +local function rotatePoint( x, y, rotation, ox, oy ) + ox, oy = ox or 0, oy or 0 + return ( x - ox ) * math.cos( rotation ) + ox - ( y - oy ) * math.sin( rotation ), ( x - ox ) * math.sin( rotation ) + ( y - oy ) * math.cos( rotation ) + oy +end + +local function scalePoint( x, y, scale, ox, oy ) + ox, oy = ox or 0, oy or 0 + return ( x - ox ) * scale + ox, ( y - oy ) * scale + oy +end +-- }}} + +-- Lines --------------------------------------- {{{ +-- Returns the length of a line. +local function getLength( x1, y1, x2, y2 ) + local dx, dy = x1 - x2, y1 - y2 + return math.sqrt( dx * dx + dy * dy ) +end + +-- Gives the midpoint of a line. +local function getMidpoint( x1, y1, x2, y2 ) + return ( x1 + x2 ) / 2, ( y1 + y2 ) / 2 +end + +-- Gives the slope of a line. +local function getSlope( x1, y1, x2, y2 ) + if checkFuzzy( x1, x2 ) then return false end -- Technically it's undefined, but this is easier to program. + return ( y1 - y2 ) / ( x1 - x2 ) +end + +-- Gives the perpendicular slope of a line. +-- x1, y1, x2, y2 +-- slope +local function getPerpendicularSlope( ... ) + local input = checkInput( ... ) + local slope + + if #input ~= 1 then + slope = getSlope( unpack( input ) ) + else + slope = unpack( input ) + end + + if not slope then return 0 -- Vertical lines become horizontal. + elseif checkFuzzy( slope, 0 ) then return false -- Horizontal lines become vertical. + else return -1 / slope end +end + +-- Gives the y-intercept of a line. +-- x1, y1, x2, y2 +-- x1, y1, slope +local function getYIntercept( x, y, ... ) + local input = checkInput( ... ) + local slope + + if #input == 1 then + slope = input[1] + else + slope = getSlope( x, y, unpack( input ) ) + end + + if not slope then return x, true end -- This way we have some information on the line. + return y - slope * x, false +end + +-- Gives the intersection of two lines. +-- slope1, slope2, x1, y1, x2, y2 +-- slope1, intercept1, slope2, intercept2 +-- x1, y1, x2, y2, x3, y3, x4, y4 +local function getLineLineIntersection( ... ) + local input = checkInput( ... ) + local x1, y1, x2, y2, x3, y3, x4, y4 + local slope1, intercept1 + local slope2, intercept2 + local x, y + + if #input == 4 then -- Given slope1, intercept1, slope2, intercept2. + slope1, intercept1, slope2, intercept2 = unpack( input ) + + -- Since these are lines, not segments, we can use arbitrary points, such as ( 1, y ), ( 2, y ) + y1 = slope1 and slope1 * 1 + intercept1 or 1 + y2 = slope1 and slope1 * 2 + intercept1 or 2 + y3 = slope2 and slope2 * 1 + intercept2 or 1 + y4 = slope2 and slope2 * 2 + intercept2 or 2 + x1 = slope1 and ( y1 - intercept1 ) / slope1 or intercept1 + x2 = slope1 and ( y2 - intercept1 ) / slope1 or intercept1 + x3 = slope2 and ( y3 - intercept2 ) / slope2 or intercept2 + x4 = slope2 and ( y4 - intercept2 ) / slope2 or intercept2 + elseif #input == 6 then -- Given slope1, intercept1, and 2 points on the other line. + slope1, intercept1 = input[1], input[2] + slope2 = getSlope( input[3], input[4], input[5], input[6] ) + intercept2 = getYIntercept( input[3], input[4], input[5], input[6] ) + + y1 = slope1 and slope1 * 1 + intercept1 or 1 + y2 = slope1 and slope1 * 2 + intercept1 or 2 + y3 = input[4] + y4 = input[6] + x1 = slope1 and ( y1 - intercept1 ) / slope1 or intercept1 + x2 = slope1 and ( y2 - intercept1 ) / slope1 or intercept1 + x3 = input[3] + x4 = input[5] + elseif #input == 8 then -- Given 2 points on line 1 and 2 points on line 2. + slope1 = getSlope( input[1], input[2], input[3], input[4] ) + intercept1 = getYIntercept( input[1], input[2], input[3], input[4] ) + slope2 = getSlope( input[5], input[6], input[7], input[8] ) + intercept2 = getYIntercept( input[5], input[6], input[7], input[8] ) + + x1, y1, x2, y2, x3, y3, x4, y4 = unpack( input ) + end + + if not slope1 and not slope2 then -- Both are vertical lines + if x1 == x3 then -- Have to have the same x positions to intersect + return true + else + return false + end + elseif not slope1 then -- First is vertical + x = x1 -- They have to meet at this x, since it is this line's only x + y = slope2 and slope2 * x + intercept2 or 1 + elseif not slope2 then -- Second is vertical + x = x3 -- Vice-Versa + y = slope1 * x + intercept1 + elseif checkFuzzy( slope1, slope2 ) then -- Parallel (not vertical) + if checkFuzzy( intercept1, intercept2 ) then -- Same intercept + return true + else + return false + end + else -- Regular lines + x = ( -intercept1 + intercept2 ) / ( slope1 - slope2 ) + y = slope1 * x + intercept1 + end + + return x, y +end + +-- Gives the closest point on a line to a point. +-- perpendicularX, perpendicularY, x1, y1, x2, y2 +-- perpendicularX, perpendicularY, slope, intercept +local function getClosestPoint( perpendicularX, perpendicularY, ... ) + local input = checkInput( ... ) + local x, y, x1, y1, x2, y2, slope, intercept + + if #input == 4 then -- Given perpendicularX, perpendicularY, x1, y1, x2, y2 + x1, y1, x2, y2 = unpack( input ) + slope = getSlope( x1, y1, x2, y2 ) + intercept = getYIntercept( x1, y1, x2, y2 ) + elseif #input == 2 then -- Given perpendicularX, perpendicularY, slope, intercept + slope, intercept = unpack( input ) + x1, y1 = 1, slope and slope * 1 + intercept or 1 -- Need x1 and y1 in case of vertical/horizontal lines. + end + + if not slope then -- Vertical line + x, y = x1, perpendicularY -- Closest point is always perpendicular. + elseif checkFuzzy( slope, 0 ) then -- Horizontal line + x, y = perpendicularX, y1 + else + local perpendicularSlope = getPerpendicularSlope( slope ) + local perpendicularIntercept = getYIntercept( perpendicularX, perpendicularY, perpendicularSlope ) + x, y = getLineLineIntersection( slope, intercept, perpendicularSlope, perpendicularIntercept ) + end + + return x, y +end + +-- Gives the intersection of a line and a line segment. +-- x1, y1, x2, y2, x3, y3, x4, y4 +-- x1, y1, x2, y2, slope, intercept +local function getLineSegmentIntersection( x1, y1, x2, y2, ... ) + local input = checkInput( ... ) + + local slope1, intercept1, x, y, lineX1, lineY1, lineX2, lineY2 + local slope2, intercept2 = getSlope( x1, y1, x2, y2 ), getYIntercept( x1, y1, x2, y2 ) + + if #input == 2 then -- Given slope, intercept + slope1, intercept1 = input[1], input[2] + lineX1, lineY1 = 1, slope1 and slope1 + intercept1 + lineX2, lineY2 = 2, slope1 and slope1 * 2 + intercept1 + else -- Given x3, y3, x4, y4 + lineX1, lineY1, lineX2, lineY2 = unpack( input ) + slope1 = getSlope( unpack( input ) ) + intercept1 = getYIntercept( unpack( input ) ) + end + + if not slope1 and not slope2 then -- Vertical lines + if checkFuzzy( x1, lineX1 ) then + return x1, y1, x2, y2 + else + return false + end + elseif not slope1 then -- slope1 is vertical + x, y = input[1], slope2 * input[1] + intercept2 + elseif not slope2 then -- slope2 is vertical + x, y = x1, slope1 * x1 + intercept1 + else + x, y = getLineLineIntersection( slope1, intercept1, slope2, intercept2 ) + end + + local length1, length2, distance + if x == true then -- Lines are collinear. + return x1, y1, x2, y2 + elseif x then -- There is an intersection + length1, length2 = getLength( x1, y1, x, y ), getLength( x2, y2, x, y ) + distance = getLength( x1, y1, x2, y2 ) + else -- Lines are parallel but not collinear. + if checkFuzzy( intercept1, intercept2 ) then + return x1, y1, x2, y2 + else + return false + end + end + + if length1 <= distance and length2 <= distance then return x, y else return false end +end + +-- Checks if a point is on a line. +-- Does not support the format using slope because vertical lines would be impossible to check. +local function checkLinePoint( x, y, x1, y1, x2, y2 ) + local m = getSlope( x1, y1, x2, y2 ) + local b = getYIntercept( x1, y1, m ) + + if not m then -- Vertical + return checkFuzzy( x, x1 ) + end + return checkFuzzy( y, m * x + b ) +end -- }}} + +-- Segment -------------------------------------- {{{ +-- Gives the perpendicular bisector of a line. +local function getPerpendicularBisector( x1, y1, x2, y2 ) + local slope = getSlope( x1, y1, x2, y2 ) + local midpointX, midpointY = getMidpoint( x1, y1, x2, y2 ) + return midpointX, midpointY, getPerpendicularSlope( slope ) +end + +-- Gives whether or not a point lies on a line segment. +local function checkSegmentPoint( px, py, x1, y1, x2, y2 ) + -- Explanation around 5:20: https://www.youtube.com/watch?v=A86COO8KC58 + local x = checkLinePoint( px, py, x1, y1, x2, y2 ) + if not x then return false end + + local lengthX = x2 - x1 + local lengthY = y2 - y1 + + if checkFuzzy( lengthX, 0 ) then -- Vertical line + if checkFuzzy( px, x1 ) then + local low, high + if y1 > y2 then low = y2; high = y1 + else low = y1; high = y2 end + + if py >= low and py <= high then return true + else return false end + else + return false + end + elseif checkFuzzy( lengthY, 0 ) then -- Horizontal line + if checkFuzzy( py, y1 ) then + local low, high + if x1 > x2 then low = x2; high = x1 + else low = x1; high = x2 end + + if px >= low and px <= high then return true + else return false end + else + return false + end + end + + local distanceToPointX = ( px - x1 ) + local distanceToPointY = ( py - y1 ) + local scaleX = distanceToPointX / lengthX + local scaleY = distanceToPointY / lengthY + + if ( scaleX >= 0 and scaleX <= 1 ) and ( scaleY >= 0 and scaleY <= 1 ) then -- Intersection + return true + end + return false +end + +-- Gives the point of intersection between two line segments. +local function getSegmentSegmentIntersection( x1, y1, x2, y2, x3, y3, x4, y4 ) + local slope1, intercept1 = getSlope( x1, y1, x2, y2 ), getYIntercept( x1, y1, x2, y2 ) + local slope2, intercept2 = getSlope( x3, y3, x4, y4 ), getYIntercept( x3, y3, x4, y4 ) + + if ( ( slope1 and slope2 ) and checkFuzzy( slope1, slope2 ) ) or ( not slope1 and not slope2 ) then -- Parallel lines + if checkFuzzy( intercept1, intercept2 ) then -- The same lines, possibly in different points. + local points = {} + if checkSegmentPoint( x1, y1, x3, y3, x4, y4 ) then addPoints( points, x1, y1 ) end + if checkSegmentPoint( x2, y2, x3, y3, x4, y4 ) then addPoints( points, x2, y2 ) end + if checkSegmentPoint( x3, y3, x1, y1, x2, y2 ) then addPoints( points, x3, y3 ) end + if checkSegmentPoint( x4, y4, x1, y1, x2, y2 ) then addPoints( points, x4, y4 ) end + + points = removeDuplicatePointsFlat( points ) + if #points == 0 then return false end + return unpack( points ) + else + return false + end + end + + local x, y = getLineLineIntersection( x1, y1, x2, y2, x3, y3, x4, y4 ) + if x and checkSegmentPoint( x, y, x1, y1, x2, y2 ) and checkSegmentPoint( x, y, x3, y3, x4, y4 ) then + return x, y + end + return false +end -- }}} + +-- Math ----------------------------------------- {{{ +-- Get the root of a number (i.e. the 2nd (square) root of 4 is 2) +local function getRoot( number, root ) + return number ^ ( 1 / root ) +end + +-- Checks if a number is prime. +local function isPrime( number ) + if number < 2 then return false end + + for i = 2, math.sqrt( number ) do + if number % i == 0 then + return false + end + end + return true +end + +-- Rounds a number to the xth decimal place (round( 3.14159265359, 4 ) --> 3.1416) +local function round( number, place ) + local pow = 10 ^ ( place or 0 ) + return math.floor( number * pow + .5 ) / pow +end + +-- Gives the summation given a local function +local function getSummation( start, stop, func ) + local returnValues = {} + local sum = 0 + for i = start, stop do + local value = func( i, returnValues ) + returnValues[i] = value + sum = sum + value + end + return sum +end + +-- Gives the percent of change. +local function getPercentOfChange( old, new ) + if old == 0 and new == 0 then + return 0 + else + return ( new - old ) / math.abs( old ) + end +end + +-- Gives the percentage of a number. +local function getPercentage( percent, number ) + return percent * number +end + +-- Returns the quadratic roots of an equation. +local function getQuadraticRoots( a, b, c ) + local discriminant = b ^ 2 - ( 4 * a * c ) + if discriminant < 0 then return false end + discriminant = math.sqrt( discriminant ) + local denominator = ( 2 * a ) + return ( -b - discriminant ) / denominator, ( -b + discriminant ) / denominator +end + +-- Gives the angle between three points. +local function getAngle( x1, y1, x2, y2, x3, y3 ) + local a = getLength( x3, y3, x2, y2 ) + local b = getLength( x1, y1, x2, y2 ) + local c = getLength( x1, y1, x3, y3 ) + + return math.acos( ( a * a + b * b - c * c ) / ( 2 * a * b ) ) +end -- }}} + +-- Circle --------------------------------------- {{{ +-- Gives the area of the circle. +local function getCircleArea( radius ) + return math.pi * ( radius * radius ) +end + +-- Checks if a point is within the radius of a circle. +local function checkCirclePoint( x, y, circleX, circleY, radius ) + return getLength( circleX, circleY, x, y ) <= radius +end + +-- Checks if a point is on a circle. +local function isPointOnCircle( x, y, circleX, circleY, radius ) + return checkFuzzy( getLength( circleX, circleY, x, y ), radius ) +end + +-- Gives the circumference of a circle. +local function getCircumference( radius ) + return 2 * math.pi * radius +end + +-- Gives the intersection of a line and a circle. +local function getCircleLineIntersection( circleX, circleY, radius, x1, y1, x2, y2 ) + slope = getSlope( x1, y1, x2, y2 ) + intercept = getYIntercept( x1, y1, slope ) + + if slope then + local a = ( 1 + slope ^ 2 ) + local b = ( -2 * ( circleX ) + ( 2 * slope * intercept ) - ( 2 * circleY * slope ) ) + local c = ( circleX ^ 2 + intercept ^ 2 - 2 * ( circleY ) * ( intercept ) + circleY ^ 2 - radius ^ 2 ) + + x1, x2 = getQuadraticRoots( a, b, c ) + + if not x1 then return false end + + y1 = slope * x1 + intercept + y2 = slope * x2 + intercept + + if checkFuzzy( x1, x2 ) and checkFuzzy( y1, y2 ) then + return 'tangent', x1, y1 + else + return 'secant', x1, y1, x2, y2 + end + else -- Vertical Lines + local lengthToPoint1 = circleX - x1 + local remainingDistance = lengthToPoint1 - radius + local intercept = math.sqrt( -( lengthToPoint1 ^ 2 - radius ^ 2 ) ) + + if -( lengthToPoint1 ^ 2 - radius ^ 2 ) < 0 then return false end + + local bottomX, bottomY = x1, circleY - intercept + local topX, topY = x1, circleY + intercept + + if topY ~= bottomY then + return 'secant', topX, topY, bottomX, bottomY + else + return 'tangent', topX, topY + end + end +end + +-- Gives the type of intersection of a line segment. +local function getCircleSegmentIntersection( circleX, circleY, radius, x1, y1, x2, y2 ) + local Type, x3, y3, x4, y4 = getCircleLineIntersection( circleX, circleY, radius, x1, y1, x2, y2 ) + if not Type then return false end + + local slope, intercept = getSlope( x1, y1, x2, y2 ), getYIntercept( x1, y1, x2, y2 ) + + if isPointOnCircle( x1, y1, circleX, circleY, radius ) and isPointOnCircle( x2, y2, circleX, circleY, radius ) then -- Both points are on line-segment. + return 'chord', x1, y1, x2, y2 + end + + if slope then + if checkCirclePoint( x1, y1, circleX, circleY, radius ) and checkCirclePoint( x2, y2, circleX, circleY, radius ) then -- Line-segment is fully in circle. + return 'enclosed', x1, y1, x2, y2 + elseif x3 and x4 then + if checkSegmentPoint( x3, y3, x1, y1, x2, y2 ) and not checkSegmentPoint( x4, y4, x1, y1, x2, y2 ) then -- Only the first of the points is on the line-segment. + return 'tangent', x3, y3 + elseif checkSegmentPoint( x4, y4, x1, y1, x2, y2 ) and not checkSegmentPoint( x3, y3, x1, y1, x2, y2 ) then -- Only the second of the points is on the line-segment. + return 'tangent', x4, y4 + else -- Neither of the points are on the circle (means that the segment is not on the circle, but "encasing" the circle) + if checkSegmentPoint( x3, y3, x1, y1, x2, y2 ) and checkSegmentPoint( x4, y4, x1, y1, x2, y2 ) then + return 'secant', x3, y3, x4, y4 + else + return false + end + end + elseif not x4 then -- Is a tangent. + if checkSegmentPoint( x3, y3, x1, y1, x2, y2 ) then + return 'tangent', x3, y3 + else -- Neither of the points are on the line-segment (means that the segment is not on the circle or "encasing" the circle). + local length = getLength( x1, y1, x2, y2 ) + local distance1 = getLength( x1, y1, x3, y3 ) + local distance2 = getLength( x2, y2, x3, y3 ) + + if length > distance1 or length > distance2 then + return false + elseif length < distance1 and length < distance2 then + return false + else + return 'tangent', x3, y3 + end + end + end + else + local lengthToPoint1 = circleX - x1 + local remainingDistance = lengthToPoint1 - radius + local intercept = math.sqrt( -( lengthToPoint1 ^ 2 - radius ^ 2 ) ) + + if -( lengthToPoint1 ^ 2 - radius ^ 2 ) < 0 then return false end + + local topX, topY = x1, circleY - intercept + local bottomX, bottomY = x1, circleY + intercept + + local length = getLength( x1, y1, x2, y2 ) + local distance1 = getLength( x1, y1, topX, topY ) + local distance2 = getLength( x2, y2, topX, topY ) + + if bottomY ~= topY then -- Not a tangent + if checkSegmentPoint( topX, topY, x1, y1, x2, y2 ) and checkSegmentPoint( bottomX, bottomY, x1, y1, x2, y2 ) then + return 'chord', topX, topY, bottomX, bottomY + elseif checkSegmentPoint( topX, topY, x1, y1, x2, y2 ) then + return 'tangent', topX, topY + elseif checkSegmentPoint( bottomX, bottomY, x1, y1, x2, y2 ) then + return 'tangent', bottomX, bottomY + else + return false + end + else -- Tangent + if checkSegmentPoint( topX, topY, x1, y1, x2, y2 ) then + return 'tangent', topX, topY + else + return false + end + end + end +end + +-- Checks if one circle intersects another circle. +local function getCircleCircleIntersection( circle1x, circle1y, radius1, circle2x, circle2y, radius2 ) + local length = getLength( circle1x, circle1y, circle2x, circle2y ) + if length > radius1 + radius2 then return false end -- If the distance is greater than the two radii, they can't intersect. + if checkFuzzy( length, 0 ) and checkFuzzy( radius1, radius2 ) then return 'equal' end + if checkFuzzy( circle1x, circle2x ) and checkFuzzy( circle1y, circle2y ) then return 'collinear' end + + local a = ( radius1 * radius1 - radius2 * radius2 + length * length ) / ( 2 * length ) + local h = math.sqrt( radius1 * radius1 - a * a ) + + local p2x = circle1x + a * ( circle2x - circle1x ) / length + local p2y = circle1y + a * ( circle2y - circle1y ) / length + local p3x = p2x + h * ( circle2y - circle1y ) / length + local p3y = p2y - h * ( circle2x - circle1x ) / length + local p4x = p2x - h * ( circle2y - circle1y ) / length + local p4y = p2y + h * ( circle2x - circle1x ) / length + + if not validateNumber( p3x ) or not validateNumber( p3y ) or not validateNumber( p4x ) or not validateNumber( p4y ) then + return 'inside' + end + + if checkFuzzy( length, radius1 + radius2 ) or checkFuzzy( length, math.abs( radius1 - radius2 ) ) then return 'tangent', p3x, p3y end + return 'intersection', p3x, p3y, p4x, p4y +end + +-- Checks if circle1 is entirely inside of circle2. +local function isCircleCompletelyInsideCircle( circle1x, circle1y, circle1radius, circle2x, circle2y, circle2radius ) + if not checkCirclePoint( circle1x, circle1y, circle2x, circle2y, circle2radius ) then return false end + local Type = getCircleCircleIntersection( circle2x, circle2y, circle2radius, circle1x, circle1y, circle1radius ) + if ( Type ~= 'tangent' and Type ~= 'collinear' and Type ~= 'inside' ) then return false end + return true +end + +-- Checks if a line-segment is entirely within a circle. +local function isSegmentCompletelyInsideCircle( circleX, circleY, circleRadius, x1, y1, x2, y2 ) + local Type = getCircleSegmentIntersection( circleX, circleY, circleRadius, x1, y1, x2, y2 ) + return Type == 'enclosed' +end -- }}} + +-- Polygon -------------------------------------- {{{ +-- Gives the signed area. +-- If the points are clockwise the number is negative, otherwise, it's positive. +local function getSignedPolygonArea( ... ) + local points = checkInput( ... ) + + -- Shoelace formula (https://en.wikipedia.org/wiki/Shoelace_formula). + points[#points + 1] = points[1] + points[#points + 1] = points[2] + + return ( .5 * getSummation( 1, #points / 2, + function( index ) + index = index * 2 - 1 -- Convert it to work properly. + return ( ( points[index] * cycle( points, index + 3 ) ) - ( cycle( points, index + 2 ) * points[index + 1] ) ) + end + ) ) +end + +-- Simply returns the area of the polygon. +local function getPolygonArea( ... ) + return math.abs( getSignedPolygonArea( ... ) ) +end + +-- Gives the height of a triangle, given the base. +-- base, x1, y1, x2, y2, x3, y3, x4, y4 +-- base, area +local function getTriangleHeight( base, ... ) + local input = checkInput( ... ) + local area + + if #input == 1 then area = input[1] -- Given area. + else area = getPolygonArea( input ) end -- Given coordinates. + + return ( 2 * area ) / base, area +end + +-- Gives the centroid of the polygon. +local function getCentroid( ... ) + local points = checkInput( ... ) + + points[#points + 1] = points[1] + points[#points + 1] = points[2] + + local area = getSignedPolygonArea( points ) -- Needs to be signed here in case points are counter-clockwise. + + -- This formula: https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon + local centroidX = ( 1 / ( 6 * area ) ) * ( getSummation( 1, #points / 2, + function( index ) + index = index * 2 - 1 -- Convert it to work properly. + return ( ( points[index] + cycle( points, index + 2 ) ) * ( ( points[index] * cycle( points, index + 3 ) ) - ( cycle( points, index + 2 ) * points[index + 1] ) ) ) + end + ) ) + + local centroidY = ( 1 / ( 6 * area ) ) * ( getSummation( 1, #points / 2, + function( index ) + index = index * 2 - 1 -- Convert it to work properly. + return ( ( points[index + 1] + cycle( points, index + 3 ) ) * ( ( points[index] * cycle( points, index + 3 ) ) - ( cycle( points, index + 2 ) * points[index + 1] ) ) ) + end + ) ) + + return centroidX, centroidY +end + +-- Returns whether or not a line intersects a polygon. +-- x1, y1, x2, y2, polygonPoints +local function getPolygonLineIntersection( x1, y1, x2, y2, ... ) + local input = checkInput( ... ) + local choices = {} + + local slope = getSlope( x1, y1, x2, y2 ) + local intercept = getYIntercept( x1, y1, slope ) + + local x3, y3, x4, y4 + if slope then + x3, x4 = 1, 2 + y3, y4 = slope * x3 + intercept, slope * x4 + intercept + else + x3, x4 = x1, x1 + y3, y4 = y1, y2 + end + + for i = 1, #input, 2 do + local x1, y1, x2, y2 = getLineSegmentIntersection( input[i], input[i + 1], cycle( input, i + 2 ), cycle( input, i + 3 ), x3, y3, x4, y4 ) + if x1 and not x2 then choices[#choices + 1] = { x1, y1 } + elseif x1 and x2 then choices[#choices + 1] = { x1, y1, x2, y2 } end + -- No need to check 2-point sets since they only intersect each poly line once. + end + + local final = removeDuplicatePairs( choices ) + return #final > 0 and final or false +end + +-- Returns if the line segment intersects the polygon. +-- x1, y1, x2, y2, polygonPoints +local function getPolygonSegmentIntersection( x1, y1, x2, y2, ... ) + local input = checkInput( ... ) + local choices = {} + + for i = 1, #input, 2 do + local x1, y1, x2, y2 = getSegmentSegmentIntersection( input[i], input[i + 1], cycle( input, i + 2 ), cycle( input, i + 3 ), x1, y1, x2, y2 ) + if x1 and not x2 then choices[#choices + 1] = { x1, y1 } + elseif x2 then choices[#choices + 1] = { x1, y1, x2, y2 } end + end + + local final = removeDuplicatePairs( choices ) + return #final > 0 and final or false +end + +-- Checks if the point lies INSIDE the polygon not on the polygon. +local function checkPolygonPoint( px, py, ... ) + local points = { unpack( checkInput( ... ) ) } -- Make a new table, as to not edit values of previous. + + local greatest, least = getGreatestPoint( points, 0 ) + if not isWithinBounds( least, py, greatest ) then return false end + greatest, least = getGreatestPoint( points ) + if not isWithinBounds( least, px, greatest ) then return false end + + local count = 0 + for i = 1, #points, 2 do + if checkFuzzy( points[i + 1], py ) then + points[i + 1] = py + .001 -- Handles vertices that lie on the point. + -- Not exactly mathematically correct, but a lot easier. + end + if points[i + 3] and checkFuzzy( points[i + 3], py ) then + points[i + 3] = py + .001 -- Do not need to worry about alternate case, since points[2] has already been done. + end + local x1, y1 = points[i], points[i + 1] + local x2, y2 = points[i + 2] or points[1], points[i + 3] or points[2] + + if getSegmentSegmentIntersection( px, py, greatest, py, x1, y1, x2, y2 ) then + count = count + 1 + end + end + + return count and count % 2 ~= 0 +end + +-- Returns if the line segment is fully or partially inside. +-- x1, y1, x2, y2, polygonPoints +local function isSegmentInsidePolygon( x1, y1, x2, y2, ... ) + local input = checkInput( ... ) + + local choices = getPolygonSegmentIntersection( x1, y1, x2, y2, input ) -- If it's partially enclosed that's all we need. + if choices then return true end + + if checkPolygonPoint( x1, y1, input ) or checkPolygonPoint( x2, y2, input ) then return true end + return false +end + +-- Returns whether two polygons intersect. +local function getPolygonPolygonIntersection( polygon1, polygon2 ) + local choices = {} + + for index1 = 1, #polygon1, 2 do + local intersections = getPolygonSegmentIntersection( polygon1[index1], polygon1[index1 + 1], cycle( polygon1, index1 + 2 ), cycle( polygon1, index1 + 3 ), polygon2 ) + if intersections then + for index2 = 1, #intersections do + choices[#choices + 1] = intersections[index2] + end + end + end + + for index1 = 1, #polygon2, 2 do + local intersections = getPolygonSegmentIntersection( polygon2[index1], polygon2[index1 + 1], cycle( polygon2, index1 + 2 ), cycle( polygon2, index1 + 3 ), polygon1 ) + if intersections then + for index2 = 1, #intersections do + choices[#choices + 1] = intersections[index2] + end + end + end + + choices = removeDuplicatePairs( choices ) + for i = #choices, 1, -1 do + if type( choices[i][1] ) == 'table' then -- Remove co-linear pairs. + table.remove( choices, i ) + end + end + + return #choices > 0 and choices +end + +-- Returns whether the circle intersects the polygon. +-- x, y, radius, polygonPoints +local function getPolygonCircleIntersection( x, y, radius, ... ) + local input = checkInput( ... ) + local choices = {} + + for i = 1, #input, 2 do + local Type, x1, y1, x2, y2 = getCircleSegmentIntersection( x, y, radius, input[i], input[i + 1], cycle( input, i + 2 ), cycle( input, i + 3 ) ) + if x2 then + choices[#choices + 1] = { Type, x1, y1, x2, y2 } + elseif x1 then choices[#choices + 1] = { Type, x1, y1 } end + end + + local final = removeDuplicates4Points( choices ) + + return #final > 0 and final +end + +-- Returns whether the circle is inside the polygon. +-- x, y, radius, polygonPoints +local function isCircleInsidePolygon( x, y, radius, ... ) + local input = checkInput( ... ) + return checkPolygonPoint( x, y, input ) +end + +-- Returns whether the polygon is inside the polygon. +local function isPolygonInsidePolygon( polygon1, polygon2 ) + local bool = false + for i = 1, #polygon2, 2 do + local result = false + result = isSegmentInsidePolygon( polygon2[i], polygon2[i + 1], cycle( polygon2, i + 2 ), cycle( polygon2, i + 3 ), polygon1 ) + if result then bool = true; break end + end + return bool +end + +-- Checks if a segment is completely inside a polygon +local function isSegmentCompletelyInsidePolygon( x1, y1, x2, y2, ... ) + local polygon = checkInput( ... ) + if not checkPolygonPoint( x1, y1, polygon ) + or not checkPolygonPoint( x2, y2, polygon ) + or getPolygonSegmentIntersection( x1, y1, x2, y2, polygon ) then + return false + end + return true +end + +-- Checks if a polygon is completely inside another polygon +local function isPolygonCompletelyInsidePolygon( polygon1, polygon2 ) + for i = 1, #polygon1, 2 do + local x1, y1 = polygon1[i], polygon1[i + 1] + local x2, y2 = polygon1[i + 2] or polygon1[1], polygon1[i + 3] or polygon1[2] + if not isSegmentCompletelyInsidePolygon( x1, y1, x2, y2, polygon2 ) then + return false + end + end + return true +end + +-------------- Circle w/ Polygons -------------- +-- Gets if a polygon is completely within a circle +-- circleX, circleY, circleRadius, polygonPoints +local function isPolygonCompletelyInsideCircle( circleX, circleY, circleRadius, ... ) + local input = checkInput( ... ) + local function isDistanceLess( px, py, x, y, circleRadius ) -- Faster, does not use math.sqrt + local distanceX, distanceY = px - x, py - y + return distanceX * distanceX + distanceY * distanceY < circleRadius * circleRadius -- Faster. For comparing distances only. + end + + for i = 1, #input, 2 do + if not checkCirclePoint( input[i], input[i + 1], circleX, circleY, circleRadius ) then return false end + end + return true +end + +-- Checks if a circle is completely within a polygon +-- circleX, circleY, circleRadius, polygonPoints +local function isCircleCompletelyInsidePolygon( circleX, circleY, circleRadius, ... ) + local input = checkInput( ... ) + if not checkPolygonPoint( circleX, circleY, ... ) then return false end + + local rad2 = circleRadius * circleRadius + + for i = 1, #input, 2 do + local x1, y1 = input[i], input[i + 1] + local x2, y2 = input[i + 2] or input[1], input[i + 3] or input[2] + if distance2( x1, y1, circleX, circleY ) <= rad2 then return false end + if getCircleSegmentIntersection( circleX, circleY, circleRadius, x1, y1, x2, y2 ) then return false end + end + return true +end -- }}} + +-- Statistics ----------------------------------- {{{ +-- Gets the average of a list of points +-- points +local function getMean( ... ) + local input = checkInput( ... ) + + mean = getSummation( 1, #input, + function( i, t ) + return input[i] + end + ) / #input + + return mean +end + +local function getMedian( ... ) + local input = checkInput( ... ) + + table.sort( input ) + + local median + if #input % 2 == 0 then -- If you have an even number of terms, you need to get the average of the middle 2. + median = getMean( input[#input / 2], input[#input / 2 + 1] ) + else + median = input[#input / 2 + .5] + end + + return median +end + +-- Gets the mode of a number. +local function getMode( ... ) + local input = checkInput( ... ) + + table.sort( input ) + local sorted = {} + for i = 1, #input do + local value = input[i] + sorted[value] = sorted[value] and sorted[value] + 1 or 1 + end + + local occurrences, least = 0, {} + for i, value in pairs( sorted ) do + if value > occurrences then + least = { i } + occurrences = value + elseif value == occurrences then + least[#least + 1] = i + end + end + + if #least >= 1 then return least, occurrences + else return false end +end + +-- Gets the range of the numbers. +local function getRange( ... ) + local input = checkInput( ... ) + local high, low = math.max( unpack( input ) ), math.min( unpack( input ) ) + return high - low +end + +-- Gets the variance of a set of numbers. +local function getVariance( ... ) + local input = checkInput( ... ) + local mean = getMean( ... ) + local sum = 0 + for i = 1, #input do + sum = sum + ( mean - input[i] ) * ( mean - input[i] ) + end + return sum / #input +end + +-- Gets the standard deviation of a set of numbers. +local function getStandardDeviation( ... ) + return math.sqrt( getVariance( ... ) ) +end + +-- Gets the central tendency of a set of numbers. +local function getCentralTendency( ... ) + local mode, occurrences = getMode( ... ) + return mode, occurrences, getMedian( ... ), getMean( ... ) +end + +-- Gets the variation ratio of a data set. +local function getVariationRatio( ... ) + local input = checkInput( ... ) + local numbers, times = getMode( ... ) + times = times * #numbers -- Account for bimodal data + return 1 - ( times / #input ) +end + +-- Gets the measures of dispersion of a data set. +local function getDispersion( ... ) + return getVariationRatio( ... ), getRange( ... ), getStandardDeviation( ... ) +end -- }}} + +return { + _VERSION = 'MLib 0.10.0', + _DESCRIPTION = 'A math and shape-intersection detection library for Lua', + _URL = 'https://github.com/davisdude/mlib', + point = { + rotate = rotatePoint, + scale = scalePoint, + }, + line = { + getLength = getLength, + getMidpoint = getMidpoint, + getSlope = getSlope, + getPerpendicularSlope = getPerpendicularSlope, + getYIntercept = getYIntercept, + getIntersection = getLineLineIntersection, + getClosestPoint = getClosestPoint, + getSegmentIntersection = getLineSegmentIntersection, + checkPoint = checkLinePoint, + + -- Aliases + getDistance = getLength, + getCircleIntersection = getCircleLineIntersection, + getPolygonIntersection = getPolygonLineIntersection, + getLineIntersection = getLineLineIntersection, + }, + segment = { + checkPoint = checkSegmentPoint, + getPerpendicularBisector = getPerpendicularBisector, + getIntersection = getSegmentSegmentIntersection, + + -- Aliases + getCircleIntersection = getCircleSegmentIntersection, + getPolygonIntersection = getPolygonSegmentIntersection, + getLineIntersection = getLineSegmentIntersection, + getSegmentIntersection = getSegmentSegmentIntersection, + isSegmentCompletelyInsideCircle = isSegmentCompletelyInsideCircle, + isSegmentCompletelyInsidePolygon = isSegmentCompletelyInsidePolygon, + }, + math = { + getRoot = getRoot, + isPrime = isPrime, + round = round, + getSummation = getSummation, + getPercentOfChange = getPercentOfChange, + getPercentage = getPercentage, + getQuadraticRoots = getQuadraticRoots, + getAngle = getAngle, + }, + circle = { + getArea = getCircleArea, + checkPoint = checkCirclePoint, + isPointOnCircle = isPointOnCircle, + getCircumference = getCircumference, + getLineIntersection = getCircleLineIntersection, + getSegmentIntersection = getCircleSegmentIntersection, + getCircleIntersection = getCircleCircleIntersection, + isCircleCompletelyInside = isCircleCompletelyInsideCircle, + isPolygonCompletelyInside = isPolygonCompletelyInsideCircle, + isSegmentCompletelyInside = isSegmentCompletelyInsideCircle, + + -- Aliases + getPolygonIntersection = getPolygonCircleIntersection, + isCircleInsidePolygon = isCircleInsidePolygon, + isCircleCompletelyInsidePolygon = isCircleCompletelyInsidePolygon, + }, + polygon = { + getSignedArea = getSignedPolygonArea, + getArea = getPolygonArea, + getTriangleHeight = getTriangleHeight, + getCentroid = getCentroid, + getLineIntersection = getPolygonLineIntersection, + getSegmentIntersection = getPolygonSegmentIntersection, + checkPoint = checkPolygonPoint, + isSegmentInside = isSegmentInsidePolygon, + getPolygonIntersection = getPolygonPolygonIntersection, + getCircleIntersection = getPolygonCircleIntersection, + isCircleInside = isCircleInsidePolygon, + isPolygonInside = isPolygonInsidePolygon, + isCircleCompletelyInside = isCircleCompletelyInsidePolygon, + isSegmentCompletelyInside = isSegmentCompletelyInsidePolygon, + isPolygonCompletelyInside = isPolygonCompletelyInsidePolygon, + + -- Aliases + isCircleCompletelyOver = isPolygonCompletelyInsideCircle, + }, + statistics = { + getMean = getMean, + getMedian = getMedian, + getMode = getMode, + getRange = getRange, + getVariance = getVariance, + getStandardDeviation = getStandardDeviation, + getCentralTendency = getCentralTendency, + getVariationRatio = getVariationRatio, + getDispersion = getDispersion, + }, +} |