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Math2D

Based on game build 714014 | Last updated: 2026-03-10

Overview​

math2d is a pure utility module containing a collection of static, side-effect-free 2D geometry functions. It is used for hitbox detection and spatial queries where performance is critical—avoiding sqrt, trig, and division operations in favor of fast arithmetic. All functions operate on coordinate pairs or geometric primitives (points, lines, circles, triangles, axis-aligned rectangles) and return boolean or numeric values. This module has no ECS component semantics; it is a standalone collection of mathematical helpers, typically imported and used directly in other scripts (e.g., local math2d = require("math2d")).

Usage example​

local math2d = require("math2d")

-- Distance squared between two points (avoids expensive sqrt)
local dist_sq = math2d.DistSq(0, 0, 3, 4)  -- returns 25

-- Check if a point lies within a circle
local inside = math2d.IsPointInCircle(1, 1, 0, 0, 5)  -- returns true

-- Line intersection test
local intersects = math2d.LineIntersectsLine(0, 0, 1, 1, 0, 1, 1, 0)  -- returns true

Dependencies & tags​

Components used: None identified
Tags: None identified

Properties​

No public properties

Main functions​

DistSq(Ax, Ay, Bx, By)​

  • Description: Computes the squared Euclidean distance between two points A and B. Avoids costly sqrt operations for performance.
  • Parameters:
    Ax, Ay (numbers) - Coordinates of point A.
    Bx, By (numbers) - Coordinates of point B.
  • Returns: Number - squared distance ((Bx-Ax)^2 + (By-Ay)^2).

DistSqPointToLine(Px, Py, Ax, Ay, Bx, By)​

  • Description: Computes the squared distance from point P to the line segment AB (not the infinite line). Handles endpoints via clamping.
  • Parameters:
    Px, Py (numbers) - Coordinates of point P.
    Ax, Ay, Bx, By (numbers) - Endpoints of line segment AB.
  • Returns: Number - squared distance from P to segment AB.

IsPointOnLine(Px, Py, Ax, Ay, Bx, By)​

  • Description: Tests whether point P lies exactly on the line segment AB (including endpoints). Degenerate cases (A = B) are handled.
  • Parameters:
    Px, Py, Ax, Ay, Bx, By (numbers) - As above.
  • Returns: Boolean - true if P is collinear with AB and within the segment bounds.

IsPointInCircle(Px, Py, Cx, Cy, Cr)​

  • Description: Tests whether point P lies inside or on the boundary of the circle centered at C with radius Cr.
  • Parameters:
    Px, Py (numbers) - Coordinates of point P.
    Cx, Cy (numbers) - Circle center.
    Cr (number) - Circle radius (non-negative).
  • Returns: Boolean - true if point is inside or on the circle.

IsPointInTriangle(Px, Py, Ax, Ay, Bx, By, Cx, Cy)​

  • Description: Tests whether point P lies inside or on the boundary of triangle ABC. Handles degenerate (collinear) triangles by falling back to line segment containment.
  • Parameters:
    Px, Py (numbers) - Point coordinates.
    Ax, Ay, Bx, By, Cx, Cy (numbers) - Triangle vertex coordinates.
  • Returns: Boolean - true if point is inside or on the triangle.

LineIntersectsLine(Ax, Ay, Bx, By, Cx, Cy, Dx, Dy)​

  • Description: Tests whether line segment AB intersects line segment CD (including endpoint touches and partial/full overlap).
  • Parameters:
    Segment endpoints for AB and CD as numbers.
  • Returns: Boolean - true if segments intersect (including at endpoints or overlapping).

LineIntersectsCircle(Ax, Ay, Bx, By, Cx, Cy, Cr)​

  • Description: Tests whether line segment AB intersects circle centered at C with radius Cr.
  • Parameters:
    Segment endpoints Ax,Ay,Bx,By; circle center Cx,Cy; radius Cr (numbers).
  • Returns: Boolean - true if segment and circle intersect.

LineIntersectsTriangle(Ax, Ay, Bx, By, Dx, Dy, Ex, Ey, Fx, Fy)​

  • Description: Tests whether line segment AB intersects triangle DEF. Handles degenerate triangles (collinear vertices) via fallback to LineIntersectsLine.
  • Parameters:
    Segment endpoints Ax,Ay,Bx,By; triangle vertices Dx,Dy,Ex,Ey,Fx,Fy (numbers).
  • Returns: Boolean - true if segment and triangle intersect.

CircleIntersectsCircle(Ax, Ay, Ar, Bx, By, Br)​

  • Description: Tests whether circle A (center (Ax,Ay), radius Ar) intersects circle B (center (Bx,By), radius Br). Includes tangency and containment cases.
  • Parameters:
    Centers and radii for both circles as numbers.
  • Returns: Boolean - true if circles intersect (including touching or one inside the other).

TriangleIntersectsCircle(Ax, Ay, Bx, By, Cx, Cy, Ex, Ey, Er)​

  • Description: Tests whether triangle ABC intersects circle centered at E with radius Er. Handles degenerate triangles.
  • Parameters:
    Triangle vertices Ax,Ay,Bx,By,Cx,Cy; circle center Ex,Ey; radius Er (numbers).
  • Returns: Boolean - true if triangle and circle intersect.

TriangleIntersectsTriangle(Ax, Ay, Bx, By, Cx, Cy, Ex, Ey, Fx, Fy, Gx, Gy)​

  • Description: Tests whether triangle ABC intersects triangle EFG. Handles degenerate triangles.
  • Parameters:
    Triangle vertices for ABC and EFG as numbers.
  • Returns: Boolean - true if triangles intersect.

RectIntersectsRect(Al, At, Ar, Ab, Bl, Bt, Br, Bb)​

  • Description: Tests whether two axis-aligned rectangles intersect. Parameters define rectangle edges: left/right (Al, Ar) and top/bottom (At, Ab) for each rect.
  • Parameters:
    Al, At, Ar, Ab, Bl, Bt, Br, Bb (numbers) - Edge coordinates.
  • Returns: Boolean - true if rectangles overlap (including edge contact).

Events & listeners​

Not applicable