A math and shape intersection library for Lua.

• Usage
• Functions

Using MLib and all of its modules is simple. Simply copy the director to the desired location, then require either mlib/init.lua, or the directory mlib that contains init.lua. The latter method is the preferred method, though both are acceptable.

local mlib = require( 'path.to.mlib' )
-- OR
local mlib = require( 'path.to.mlib.init' )

Alternatively, if you only wish to use one aspect of MLib, simply require that desired module.

local Line = require( 'path.to.mlib.line' )

• mlib.line
  • line.areLinesParallel
  • line.checkPoint
  • line.getClosestPoint
  • line.getLineIntersection
  • line.getSlope
  • line.getPerpendicularSope
  • line.getYIntercept
  • line.isVertical
• mlib.segment
  • segment.checkPoint
  • segment.getDistance
  • segment.getDistance2
  • segment.getMidpoint
  • segment.getLineIntersection
  • segment.getSegmentIntersection

Checks if lines two lines are parallel.

• Synopsis: parallel = mlib.line.areLinesParallel( line1, line2 )

• Parameters:

  • table line1: A table in one of the following formats:
    • { m }: Contains just the slope of the line.
      • m:
        • number: The slope of the line.
        • boolean (false): The slope if the line is vertical.
    • { m, x, y }: Contains the slope and a point on the line.
      • m:
        • number: The slope of the line.
        • boolean (false): The slope if the line is vertical.
      • number x: The position on the x-axis of a point on the line.
      • number y: The position on the y-axis of a point on the line.
    • { x1, y1, x2, y2 }:
      • number x1: The position on the x-axis of a point on the line.
      • number y1: The position on the y-axis of a point on the line.
      • number x2: The position on the x-axis of another point on the line.
      • number y2: The position on the y-axis of another point on the line.
  • table line2: A table in one of the above formats (see line1).

• Returns:

  • boolean parallel: Whether the lines are parallel (true) or not (false).

Checks if a point is on a line.

• Synopsis: onLine = mlib.line.checkPoint( px, py, m, b )

• Parameters:

  • number px: The position on the x-axis of a point to check.
  • number py: The position on the y-axis of a point to check.
  • m:
    • number: The slope of the line.
    • boolean (false): The slope if the line is vertical.
  • b:
    • number: The y-intercept of the line.
    • boolean (false): The y-itnercept if the line is vertical.

• Returns:

  • boolean onLine: Whether the point is on the line (true) or not (false).

• Synopsis: onLine = mlib.line.checkPoint( px, py, m, x, y )

• Parameters:

  • number px: The position on the x-axis of a point to check.
  • number py: The position on the y-axis of a point to check.
  • m:
    • number: The slope of the line.
    • boolean (false): The slope if the line is vertical.
  • number x: The position on the x-axis of a point on the line.
  • number y: The position on the y-axis of a point on the line.

• Returns:

  • boolean onLine: Whether the point is on the line (true) or not (false).

• Synopsis: onLine = mlib.line.checkPoint( px, py, x1, y1, x2, y2 )

• Parameters:

  • number px: The position on the x-axis of a point to check.
  • number py: The position on the y-axis of a point to check.
  • m:
    • number: The slope of the line.
    • boolean (false): The slope if the line is vertical.
  • number x1: The position on the x-axis of a point on the line.
  • number y1: The position on the y-axis of a point on the line.
  • number x2: The position on the x-axis of another point on the line.
  • number y2: The position on the y-axis of another point on the line.

• Returns:

  • boolean onLine: Whether the point is on the line (true) or not (false).

Checks if a point is on a line.

• Synopsis: x, y = mlib.line.getClosestPoint( px, py, m, x, y )

• Parameters:

  • number px: The position on the x-axis of a point to check.
  • number py: The position on the y-axis of a point to check.
  • m:
    • number: The slope of the line.
    • boolean (false): The slope if the line is vertical.
  • number x: The position on the x-axis of a point on the line.
  • number y: The position on the y-axis of a point on the line.

• Returns:

  • number x: The position on the x-axis of the closest point on the line.
  • number y: The position on the y-axis of the closest point on the line.

• Synopsis: x, y = mlib.line.getClosestPoint( px, py, x1, y1, x2, y2 )

• Parameters:

  • number px: The position on the x-axis of a point to check.
  • number py: The position on the y-axis of a point to check.
  • m:
    • number: The slope of the line.
    • boolean (false): The slope if the line is vertical.
  • number x1: The position on the x-axis of a point on the line.
  • number y1: The position on the y-axis of a point on the line.
  • number x2: The position on the x-axis of another point on the line.
  • number y2: The position on the y-axis of another point on the line.

• Returns:

  • number x: The position on the x-axis of the closest point on the line.
  • number y: The position on the y-axis of the closest point on the line.

Checks if lines two lines are parallel.

• Synopsis: x, y = mlib.line.areLinesParallel( line1, line2 )

• Parameters:

  • table line1: A table in one of the following formats:
    • { m, x, y }: Contains the slope and a point on the line.
      • m:
        • number: The slope of the line.
        • boolean (false): The slope if the line is vertical.
      • number x: The position on the x-axis of a point on the line.
      • number y: The position on the y-axis of a point on the line.
    • { x1, y1, x2, y2 }:
      • number x1: The position on the x-axis of a point on the line.
      • number y1: The position on the y-axis of a point on the line.
      • number x2: The position on the x-axis of another point on the line.
      • number y2: The position on the y-axis of another point on the line.
  • table line2: A table in one of the above formats (see line1).

• Returns:

  • x:
    • number: The position on the x-axis of where the lines intersect.
    • boolean (false): The lines do not intersect anywhere
  • number y: The position on the y-axis of where the lines intersect.

Gets the perpendicular slope to a line.

• Synopsis: pm = mlib.line.getPerpendicularSlope( m )

• Parameters:

  • m:
    • number: The slope of the line.
    • boolean (false): The slope if the line is vertical.

• Returns:

  • pm:
    • number: The slope of the perpendicular line.
    • boolean (false): The slope if the perpendicular line is vertical.

• Synopsis: pm = mlib.line.getPerpendicularSlope( x1, y1, x2, y2 )

• Parameters:

  • number x1: The position on the x-axis of a point on the line.
  • number y1: The position on the y-axis of a point on the line.
  • number x2: The position on the x-axis of another point on the line.
  • number y2: The position on the y-axis of another point on the line.

• Returns:

  • pm:
    • number: The slope of the perpendicular line.
    • boolean (false): The slope if the perpendicular line is vertical.

Gets the slope of a line.

• Synopsis: m = mlib.line.getSlope( x1, y1, x2, y2 )

• Parameters:

  • number x1: The position on the x-axis of a point on the line.
  • number y1: The position on the y-axis of a point on the line.
  • number x2: The position on the x-axis of another point on the line.
  • number y2: The position on the y-axis of another point on the line.

• Returns

  • m:
    • number: The slope of the line.
    • boolean (false): The slope if the line is vertical.

Gets the y-intercept of a line.

• Synopsis: b = mlib.line.getYIntercept( m, x, y )

• Parameters:

  • m:
    • number: The slope of the line.
    • boolean (false): The slope if the line is vertical.
  • number x: The position on the x-axis of a point on the line.
  • number y: The position on the y-axis of a point on the line.

• Returns:

  • b:
    • number: The y-intercept of the line.
    • boolean (false): The y-intercept if the line is vertical.

• Synopsis: b = mlib.line.getYIntercept( x1, y1, x2, y2 )

• Parameters:

  • number x1: The position on the x-axis of a point on the line.
  • number y1: The position on the y-axis of a point on the line.
  • number x2: The position on the x-axis of another point on the line.
  • number y2: The position on the y-axis of another point on the line.

• Returns:

  • b:
    • number: The y-intercept of the line.
    • boolean (false): The y-intercept if the line is vertical.

Checks if the line is vertical

• Synopsis: vertical = mlib.line.isVertical( m, x, y )

• Parameters:

  • m:
    • number: The slope of the line.
    • boolean (false): The slope if the line is vertical.
  • number x: The position on the x-axis of a point on the line.
  • number y: The position on the y-axis of a point on the line.

• Returns:

  • boolean vertical: Whether the line is vertical (true) or not (false).

• Synopsis: vertical = mlib.line.isVertical( x1, y1, x2, y2 )

• Parameters:

  • number x1: The position on the x-axis of a point on the line.
  • number y1: The position on the y-axis of a point on the line.
  • number x2: The position on the x-axis of another point on the line.
  • number y2: The position on the y-axis of another point on the line.

• Returns:

  • boolean vertical: Whether the line is vertical (true) or not (false).

Checks if a point is on a line segment.

• Synopsis: onSegment = mlib.segment.checkPoint( px, py, x1, y1, x2, y2 )

• Parameters:

  • number px: The position on the x-axis of the point to check.
  • number py: The position on the y-axis of the point to check.
  • number x1: The position on the x-axis of a point on the line.
  • number y1: The position on the y-axis of a point on the line.
  • number x2: The position on the x-axis of another point on the line.
  • number y2: The position on the y-axis of another point on the line.

• Returns

  • boolean onPoint: Whether the given point is on the line segment (true) or not (false).

Gets the squared distance between two points.

• Synopsis: dist = mlib.segment.getDistance( x1, y1, x2, y2 )

• Parameters:

  • number x1: The position on the x-axis of a point on the segment.
  • number y1: The position on the y-axis of a point on the segment.
  • number x2: The position on the x-axis of another point on the segment.
  • number y2: The position on the y-axis of another point on the segment.

• Returns:

  • number dist: The distance between the two points.

Gets the squared distance between two points.

• Synopsis: dist2 = mlib.segment.getDistance2( x1, y1, x2, y2 )

• Parameters:

  • number x1: The position on the x-axis of a point on the segment.
  • number y1: The position on the y-axis of a point on the segment.
  • number x2: The position on the x-axis of another point on the segment.
  • number y2: The position on the y-axis of another point on the segment.

• Returns:

  • number dist2: The squared distance between the two points.

Gets the midpoint of a segment.

• Synopsis: mx, my = mlib.segment.getDistance2( x1, y1, x2, y2 )

• Parameters:

  • number x1: The position on the x-axis of a point on the segment.
  • number y1: The position on the y-axis of a point on the segment.
  • number x2: The position on the x-axis of another point on the segment.
  • number y2: The position on the y-axis of another point on the segment.

• Returns:

  • number mx: The position on the x-axis of the midpoint.
  • number my: The position on the y-axis of the midpoint.

Gets the intersection of a line and a segment.

• Synopsis: x, y = mlib.segment.getLineIntersection( segment, line )

• Parameters:

  • table segment: The two points that define the line segment in the form { x1, y1, x2, y2 }.
  • table line: A table in one of the following formats:
    • { m, x, y }: Contains the slope and a point on the line.
      • m:
        • number: The slope of the line.
        • boolean (false): The slope if the line is vertical.
      • number x: The position on the x-axis of a point on the line.
      • number y: The position on the y-axis of a point on the line.
    • { x1, y1, x2, y2 }:
      • number x1: The position on the x-axis of a point on the line.
      • number y1: The position on the y-axis of a point on the line.
      • number x2: The position on the x-axis of another point on the line.
      • number y2: The position on the y-axis of another point on the line.

• Returns:

  • x:
    • number: The position on the x-axis of where the line and segment intersect.
    • boolean (false): The lines do not intersect anywhere
  • number y: The position on the y-axis of where the line and segment intersect.

Gets the intersection of two line segments.

• Synopsis: x, y = mlib.segment.getSegmentIntersection( segment1, segment2 )

• Parameters:

  • table segment1: The two points that define the first line segment in the form { x1, y1, x2, y2 }.
  • table segment2: The two points that define the second line segment in the form { x1, y1, x2, y2 }.

• Returns:

  • x:
    • number: The position on the x-axis of where the two segments intersect.
    • boolean (false): The lines do not intersect anywhere
  • number y: The position on the y-axis of where the two segments intersect.