Use this skill when using Phaser 4 math and geometry utilities. Covers vectors, rectangles, circles, triangles, polygons, random number generation, angles, distance, interpolation, and snapping. Triggers on: Vector2, Rectangle, Circle, math, distance, angle, random, lerp.

Phaser 4 — Geometry and Math Geom classes (Circle, Ellipse, Line, Polygon, Rectangle, Triangle), intersection tests, and Math utilities (Vector2, Vector3, Matrix4, angles, distances, interpolation, easing, random, snap, clamp). Related skills: graphics and shapes.md, physics arcade.md Quick Start Core Concepts Geometry objects are pure data containers holding coordinates and dimensions. They are NOT game objects and cannot be added to the display list. To render geometry, use the Graphics game object or Shape game objects (see graphics and shapes.md). Every geom class has a type property set to a Phaser.Geom constant for fast type checks. All geom classes share a common instance method pattern: contains(x, y) point in shape test getPoint(position, output?) point at normalized position (0 1) on perimeter getPoints(quantity, stepRate?, output?) evenly spaced points on perimeter getRandomPoint(output?) random point inside the shape setTo(...) reset all properties setEmpty() zero out the shape setPosition(x, y) move origin/center Each geom type also has a folder of static helper functions (e.g., Phaser.Geom.Rectangle.Contains , Phaser.Geom.Circle.Area ). Geometry Classes Class Namespace Constructor Key Properties Circle Phaser.Geom.Circle (x, y, radius) x , y , radius , diameter , left , right , top , bottom Ellipse Phaser.Geom.Ellipse (x, y, width, height) x , y , width , height , left , right , top , bottom Line Phaser.Geom.Line (x1, y1, x2, y2) x1 , y1 , x2 , y2 , left , right , top , bottom Polygon Phaser.Geom.Polygon (points) area , points (array of Vector2Like) Rectangle Phaser.Geom.Rectangle (x, y, width, height) x , y , width , height , left , right , top , bottom , centerX , centerY Triangle Phaser.Geom.Triangle (x1, y1, x2, y2, x3, y3) x1 , y1 , x2 , y2 , x3 , y3 Rectangle Static Helpers Phaser.Geom.Rectangle. : Area, Ceil, CeilAll, CenterOn, Clone, Contains, ContainsPoint, ContainsRect, CopyFrom, Decompose, Equals, FitInside, FitOutside, Floor, FloorAll, FromPoints, FromXY, GetAspectRatio, GetCenter, GetPoint, GetPoints, GetSize, Inflate, Intersection, MarchingAnts, MergePoints, MergeRect, MergeXY, Offset, OffsetPoint, Overlaps, Perimeter, PerimeterPoint, Random, RandomOutside, SameDimensions, Scale, Union. Circle Static Helpers Phaser.Geom.Circle. : Area, Circumference, CircumferencePoint, Clone, Contains, ContainsPoint, ContainsRect, CopyFrom, Equals, GetBounds, GetPoint, GetPoints, Offset, OffsetPoint, Random. Line Static Helpers Phaser.Geom.Line. : Angle, BresenhamPoints, CenterOn, Clone, CopyFrom, Equals, Extend, GetEasedPoints, GetMidPoint, GetNearestPoint, GetNormal, GetPoint, GetPoints, GetShortestDistance, Height, Length, NormalAngle, NormalX, NormalY, Offset, PerpSlope, Random, ReflectAngle, Rotate, RotateAroundPoint, RotateAroundXY, SetToAngle, Slope, Width. Triangle Static Helpers Phaser.Geom.Triangle. : Area, BuildEquilateral, BuildFromPolygon, BuildRight, CenterOn, Centroid, CircumCenter, CircumCircle, Clone, Contains, ContainsArray, ContainsPoint, CopyFrom, Decompose, Equals, GetPoint, GetPoints, InCenter, Offset, Perimeter, Random, Rotate, RotateAroundPoint, RotateAroundXY. Polygon Input Formats The Polygon constructor accepts multiple formats for the points argument: Space separated string: '40 0 40 20 100 20 100 80' Array of {x, y} objects Flat number array: [x1, y1, x2, y2, ...] Array of [x, y] sub arrays Intersection Tests All under Phaser.Geom.Intersects . Boolean Tests (return true / false ) Function Description CircleToCircle(circleA, circleB) Two circles overlap CircleToRectangle(circle, rect) Circle overlaps rectangle LineToCircle(line, circle) Line segment intersects circle LineToLine(line1, line2, out?) Two line segments cross; writes point to out LineToRectangle(line, rect) Line segment intersects rectangle PointToLine(point, line, lineThickness?) Point lies on/near line PointToLineSegment(point, line) Point lies on finite line segment RectangleToRectangle(rectA, rectB) Two rectangles overlap RectangleToTriangle(rect, triangle) Rectangle overlaps triangle RectangleToValues(rect, left, right, top, bottom, tolerance?) Rectangle overlaps LRTB bounds TriangleToCircle(triangle, circle) Triangle overlaps circle TriangleToLine(triangle, line) Triangle intersects line TriangleToTriangle(triA, triB) Two triangles overlap Get Intersection Points (return Vector2[] ) Function Description GetCircleToCircle(circleA, circleB, out?) Intersection points of two circles GetCircleToRectangle(circle, rect, out?) Points where circle meets rectangle edges GetLineToCircle(line, circle, out?) Points where line crosses circle GetLineToLine(line1, line2, out?) Single intersection point of two lines GetLineToPoints(line, points, out?) Intersection with a series of points forming edges GetLineToPolygon(line, polygon, out?) Closest intersection with polygon edges GetLineToRectangle(line, rect, out?) Points where line crosses rectangle GetRaysFromPointToPolygon(x, y, polygon) Ray cast from point to polygon edges GetRectangleIntersection(rectA, rectB, out?) Overlapping rectangle region GetRectangleToRectangle(rectA, rectB, out?) Edge intersection points GetRectangleToTriangle(rect, triangle, out?) Edge intersection points GetTriangleToCircle(triangle, circle, out?) Edge intersection points GetTriangleToLine(triangle, line, out?) Edge intersection points GetTriangleToTriangle(triA, triB, out?) Edge intersection points Math Functions by Category All under Phaser.Math unless noted. Constants Constant Value Phaser.Math.TAU PI 2 (v4 addition) Phaser.Math.PI OVER 2 PI / 2 Phaser.Math.EPSILON 1.0e 6 Phaser.Math.DEG TO RAD PI / 180 Phaser.Math.RAD TO DEG 180 / PI Phaser.Math.RND Global RandomDataGenerator instance (seeded via game config seed ) Angle Functions ( Phaser.Math.Angle. ) Function Description Between(x1, y1, x2, y2) Angle in radians between two points BetweenPoints(point1, point2) Same, taking {x,y} objects BetweenY(x1, y1, x2, y2) Angle from vertical axis BetweenPointsY(point1, point2) Same, taking objects CounterClockwise(angle) Convert to counter clockwise GetClockwiseDistance(from, to) Clockwise angular distance GetCounterClockwiseDistance(from, to) Counter clockwise angular distance GetShortestDistance(from, to) Shortest angular distance (signed) Normalize(angle) Normalize to [0, 2PI) Random() Random angle in radians RandomDegrees() Random angle in degrees Reverse(angle) Reverse (add PI) RotateTo(currentAngle, targetAngle, lerp?) Step toward target angle ShortestBetween(angle1, angle2) Shortest difference in degrees Wrap(angle) Wrap to ( PI, PI] WrapDegrees(angle) Wrap to ( 180, 180] Distance Functions ( Phaser.Math.Distance. ) Function Description Between(x1, y1, x2, y2) Euclidean distance BetweenPoints(a, b) Same, taking {x,y} objects BetweenPointsSquared(a, b) Squared distance (avoids sqrt) Chebyshev(x1, y1, x2, y2) Chebyshev (chessboard) distance Power(x1, y1, x2, y2, pow) Minkowski distance with custom power Snake(x1, y1, x2, y2) Manhattan/taxicab distance Squared(x1, y1, x2, y2) Squared Euclidean distance Interpolation ( Phaser.Math.Interpolation. ) Function Description BezierInterpolation(v, k) Bezier curve through control points CatmullRomInterpolation(v, k) Catmull Rom spline through points CubicBezierInterpolation(t, p0, p1, p2, p3) Cubic Bezier between four values LinearInterpolation(v, k) Linear through array of values QuadraticBezierInterpolation(t, p0, p1, p2) Quadratic Bezier SmoothStepInterpolation(t, min, max) Hermite smooth step SmootherStepInterpolation(t, min, max) Ken Perlin's smoother step Snap Functions ( Phaser.Math.Snap. ) Function Description To(value, gap, start?, divide?) Snap to nearest increment Floor(value, gap, start?, divide?) Snap down to increment Ceil(value, gap, start?, divide?) Snap up to increment Fuzzy Comparison ( Phaser.Math.Fuzzy. ) Function Description Equal(a, b, epsilon?) a approximately equals b LessThan(a, b, epsilon?) a < b within epsilon GreaterThan(a, b, epsilon?) a b within epsilon Ceil(value, epsilon?) Fuzzy ceiling Floor(value, epsilon?) Fuzzy floor Easing Functions ( Phaser.Math.Easing. ) Each type has .In , .Out , .InOut variants. Used primarily by tweens (pass string names like 'Sine.easeOut' ). Type String Keys Back Back.easeIn , Back.easeOut , Back.easeInOut Bounce Bounce.easeIn , Bounce.easeOut , Bounce.easeInOut Circular Circ.easeIn , Circ.easeOut , Circ.easeInOut Cubic Cubic.easeIn , Cubic.easeOut , Cubic.easeInOut Elastic Elastic.easeIn , Elastic.easeOut , Elastic.easeInOut Expo Expo.easeIn , Expo.easeOut , Expo.easeInOut Linear Linear (no variants) Quadratic Quad.easeIn , Quad.easeOut , Quad.easeInOut Quartic Quart.easeIn , Quart.easeOut , Quart.easeInOut Quintic Quint.easeIn , Quint.easeOut , Quint.easeInOut Sine Sine.easeIn , Sine.easeOut , Sine.easeInOut Stepped Stepped (no variants) Power aliases: Power0 = Linear, Power1 = Quad.Out, Power2 = Cubic.Out, Power3 = Quart.Out, Power4 = Quint.Out. Short names also work: 'Quad' = Quad.Out, 'Sine' = Sine.Out, etc. Core Math Helpers (directly on Phaser.Math ) Function Description Between(min, max) Random integer in [min, max] FloatBetween(min, max) Random float in [min, max] Clamp(value, min, max) Constrain value to range Wrap(value, min, max) Wrap value within range Within(a, b, tolerance) Check if a is within tolerance of b Percent(value, min, max, upperMax?) Value as percentage of range FromPercent(percent, min, max) Value from percentage of range DegToRad(degrees) Convert degrees to radians RadToDeg(radians) Convert radians to degrees Linear(p0, p1, t) Lerp between two values LinearXY(v1, v2, t, out?) Lerp between two Vector2Like objects SmoothStep(x, min, max) Hermite smooth step SmootherStep(x, min, max) Perlin smoother step Average(values) Mean of number array Median(values) Median of number array CeilTo(value, place?, base?) Ceil to decimal place FloorTo(value, place?, base?) Floor to decimal place RoundTo(value, place?, base?) Round to decimal place RoundAwayFromZero(value) Round away from zero MaxAdd(value, amount, max) Add clamped to max MinSub(value, amount, min) Subtract clamped to min Difference(a, b) Absolute difference IsEven(value) Integer is even IsEvenStrict(value) Strictly even (not zero) Factorial(value) Factorial Rotate(point, angle) Rotate point around origin RotateAround(point, cx, cy, angle) Rotate point around custom center RotateAroundDistance(point, cx, cy, angle, dist) Rotate at fixed distance TransformXY(x, y, posX, posY, rotation, scaleX, scaleY, output?) Full 2D transform GetSpeed(distance, time) Speed from distance and time RandomXY(vector, scale?) Set vector to

geometry-and-math