libGDX Math Utilities

Quick reference for com.badlogic.gdx.math.*. Covers vectors, matrices, quaternion, interpolation, intersection/collision, shapes, and math helpers.

CRITICAL: Vectors Mutate In Place

Almost every Vector2/Vector3 method mutates `this` and returns this for chaining. This is the #1 source of bugs.

Vector2 a = new Vector2(1, 2);
Vector2 b = new Vector2(3, 4);

a.add(b);            // a is now (4, 6) — b unchanged
a.cpy().add(b);      // returns new (4, 6) — a unchanged
a.sub(b).nor();      // a mutated TWICE — subtracted then normalized

This applies to: set(), add(), sub(), scl(), nor(), lerp(), rotate*(), limit(), clamp(), setLength(), mulAdd(), setZero(), setToRandomDirection().

Vector2

new Vector2()                    // (0, 0)
new Vector2(float x, float y)
new Vector2(Vector2 v)           // copy constructor EXISTS

// Static constants (WARNING: mutable — treat as read-only)
Vector2.X   // (1, 0)
Vector2.Y   // (0, 1)
Vector2.Zero // (0, 0)

Key methods beyond the obvious (set, add, sub, scl, nor, lerp, setZero, cpy — all mutating, return this):

• limit(float) / limit2(float) — cap magnitude (limit2 avoids sqrt)
• clamp(float min, float max) — clamp magnitude
• setLength(float) / setLength2(float) — set magnitude
• mulAdd(Vector2, float) — this += vec * scalar
• mul(Matrix3) — transform by Matrix3 only, NOT Matrix4
• crs(Vector2) — returns float (2D cross product is a scalar)
• len2(), dst2() — squared versions (prefer for comparisons, avoids sqrt)

Angle & Rotation (Vector2 only)

Use `Deg` suffix methods. Non-suffixed versions are deprecated:

• angleDeg() / angleDeg(Vector2 ref) — degrees 0–360
• angleRad() / angleRad(Vector2 ref) — radians
• rotateDeg(float) / rotateRad(float) — rotate vector
• rotateAroundDeg(Vector2 ref, float deg) — rotate around point
• setAngleDeg(float) / setAngleRad(float) — set direction
• rotate90(int dir) — dir >= 0 = CCW, dir < 0 = CW
• DEPRECATED: angle(), rotate(float), setAngle(float), rotateAround(Vector2, float) — use Deg versions

Vector3

new Vector3()
new Vector3(float x, float y, float z)
new Vector3(Vector3 other)              // copy constructor EXISTS
new Vector3(float[] values)             // uses [0], [1], [2]
new Vector3(Vector2 v, float z)

// Static constants (WARNING: mutable — treat as read-only)
Vector3.X, Vector3.Y, Vector3.Z, Vector3.Zero

Same methods as Vector2, plus key differences:

• crs(Vector3) — MUTATES `this` with 3D cross product (unlike Vector2's crs() which returns float). Use a.cpy().crs(b) to preserve a.
• slerp(Vector3 target, float alpha) — spherical lerp (Vector2 lacks this)
• rotate(Vector3 axis, float degrees) — NOT deprecated (unlike Vector2's rotate)
• mul(Matrix4), mul(Matrix3), mul(Quaternion) — transform by matrix/quaternion
• prj(Matrix4) — project (divide by w) — for projection matrices
• rot(Matrix4) — rotate only (ignores translation)

Matrix4

Column-major 4x4 matrix. public final float[] val = new float[16].

Matrix4 mat = new Matrix4();        // identity by default
mat.idt();                          // reset to identity

// "setTo" methods — reset matrix, then apply ONE transform
mat.setToTranslation(x, y, z);     // or (Vector3)
mat.setToRotation(axis, degrees);   // Vector3 + float, or (ax,ay,az, degrees)
mat.setToScaling(x, y, z);         // or (Vector3)
mat.setToLookAt(direction, up);    // or (position, target, up)

// Post-multiply methods — compose onto existing matrix
mat.translate(x, y, z);            // mat = mat * T
mat.rotate(axis, degrees);         // mat = mat * R (also Quaternion overload)
mat.scale(sx, sy, sz);             // mat = mat * S

mat.mul(other);                    // mat = mat * other (post-multiply)
mat.inv();                         // invert in place
mat.tra();                         // transpose in place
float d = mat.det();               // determinant

// Extraction
Vector3 pos = mat.getTranslation(new Vector3());
Quaternion rot = mat.getRotation(new Quaternion());  // also (Quaternion, boolean normalizeAxes)

// Compose from components
mat.set(position, rotation, scale);  // Vector3, Quaternion, Vector3
mat.set(quaternion);                 // rotation only

There is NO `setToRotation(Quaternion)` — use set(Quaternion) instead.

Matrix3

9-float 2D transform / normal matrix. public float[] val = new float[9] (NOT final).

Matrix3 m3 = new Matrix3();
m3.set(matrix4);     // extract top-left 3x3 (for normal matrix)
m3.inv();            // invert in place
m3.mul(other);       // m3 = m3 * other
float d = m3.det();

Quaternion

new Quaternion()                           // identity (0,0,0,1)
new Quaternion(float x, float y, float z, float w)
new Quaternion(Quaternion other)           // copy
new Quaternion(Vector3 axis, float degrees)

q.idt();                                   // reset to identity (0,0,0,1)
q.set(other);                              // copy
q.setFromAxis(axis, degrees);              // or (ax,ay,az, degrees)
q.setFromAxisRad(axis, radians);           // or (ax,ay,az, radians)

// Euler angles — DEGREES, order is yaw/pitch/roll
q.setEulerAngles(yaw, pitch, roll);        // yaw=Y, pitch=X, roll=Z
q.setEulerAnglesRad(yaw, pitch, roll);     // same order, radians

q.getYaw();     // degrees (-180 to 180), rotation around Y
q.getPitch();   // degrees (-90 to 90), rotation around X
q.getRoll();    // degrees (-180 to 180), rotation around Z
// Also: getYawRad(), getPitchRad(), getRollRad()

q.slerp(endQuat, alpha);     // mutates this, alpha [0,1]
q.mul(other);                // this = this * other (Hamilton product)
q.mulLeft(other);            // this = other * this
q.nor();                     // normalize
q.conjugate();               // negate x,y,z (leave w)
q.transform(vector3);        // MUTATES the vector, returns the vector
q.toMatrix(float[16]);       // fills 16-float array, returns VOID (not this)
q.cpy();                     // new copy

Gotchas:

• setEulerAngles parameter order is (yaw, pitch, roll), not (pitch, yaw, roll). Other engines differ.
• transform(Vector3) mutates the input vector — not the quaternion.
• toMatrix() returns void, not the Quaternion.
• Quaternion must be normalized for getYaw/getPitch/getRoll to be accurate.

MathUtils

Constants

Random

MathUtils.random()                    // float [0, 1)
MathUtils.random(int range)           // int [0, range] INCLUSIVE both ends
MathUtils.random(int start, int end)  // int [start, end] INCLUSIVE both ends
MathUtils.random(float range)         // float [0, range) EXCLUSIVE end
MathUtils.random(float start, float end)  // float [start, end) EXCLUSIVE end
MathUtils.randomSign()                // int: -1 or 1
MathUtils.randomBoolean()             // boolean
MathUtils.randomBoolean(float chance) // true if random() < chance

int overloads are INCLUSIVE on both bounds. float overloads are EXCLUSIVE on the upper bound. This catches people constantly.

Trig (lookup-table — faster than Math.sin/cos)

Utility

MathUtils.clamp(value, min, max)   // float, int, long, short, double overloads
MathUtils.lerp(from, to, progress) // float
MathUtils.norm(rangeStart, rangeEnd, value)  // inverse lerp (NOT clamped)
MathUtils.map(inStart, inEnd, outStart, outEnd, value)  // remap (NOT clamped)
MathUtils.isZero(float)            // within FLOAT_ROUNDING_ERROR
MathUtils.isZero(float, tolerance) // within tolerance
MathUtils.isEqual(a, b)            // within FLOAT_ROUNDING_ERROR
MathUtils.isEqual(a, b, tolerance) // within tolerance
MathUtils.log2(float value)        // returns FLOAT (not int!)
MathUtils.lerpAngle(fromRad, toRad, progress)     // handles wrapping at 2π
MathUtils.lerpAngleDeg(fromDeg, toDeg, progress)  // handles wrapping at 360°
// Also: floor(float), ceil(float), round(float) — return int
// Also: nextPowerOfTwo(int), isPowerOfTwo(int)

Interpolation

Usage: Interpolation.NAME.apply(alpha) where alpha in [0,1]. Also: apply(start, end, alpha).

Naming pattern: {category}, {category}In (slow-to-fast), {category}Out (fast-to-slow). Categories: pow2–pow5, sine, exp5, exp10, circle, elastic, swing, bounce.

Standalone: linear, smooth (smoothstep), smooth2, smoother (Perlin smootherstep).

Aliases: fade = smoother (NOT smooth), slowFast = pow2In, fastSlow = pow2Out.

Inverses exist ONLY for pow2 and pow3: pow2InInverse, pow2OutInverse, pow3InInverse, pow3OutInverse.

DO NOT use quadIn, cubicOut, easeIn, easeOut, easeInOut, linear_in, quad — none exist. Convention is pow2, pow3, etc.

Custom: new Interpolation.Pow(6), new Interpolation.Elastic(2, 10, 7, 1), new Interpolation.Swing(2.5f).

Intersector

Static utility — all methods are public static.

Key methods (all return boolean unless noted):

• overlaps(Circle, Circle), overlaps(Circle, Rectangle), overlaps(Rectangle, Rectangle)
• overlapConvexPolygons(Polygon, Polygon) — optional MinimumTranslationVector param for MTV
• isPointInTriangle(...), isPointInPolygon(...) — Vector2 or float overloads
• intersectSegments(x1,y1, x2,y2, x3,y3, x4,y4, Vector2 intersection) — populates intersection
• intersectRayTriangle(Ray, Vector3, Vector3, Vector3, Vector3 intersection)
• intersectLinePlane(...) — returns FLOAT (distance), NOT boolean
• intersectRayBounds(Ray, BoundingBox, Vector3), intersectRaySphere(Ray, Vector3, float, Vector3)
• nearestSegmentPoint(...) — returns Vector2; distanceSegmentPoint(...) — returns float

Common Mistakes

1. Mutating vectors unintentionally — a.add(b) changes a. Use a.cpy().add(b) to create a new vector. This applies to nearly every Vector method.
2. Mutating Vector3.X/Y/Z/Zero constants — These are mutable static fields, not true constants. Vector3.Zero.set(1,0,0) corrupts the constant globally. Never pass them to methods that mutate.
3. Using invented Interpolation names — There is no quadIn, cubicOut, easeIn, easeInOut. Use pow2In, pow3Out, etc. Use fade or smoother for smooth acceleration.
4. Confusing `fade` with `smooth` — fade is an alias for smoother (Perlin smootherstep), NOT for smooth (classic smoothstep).
5. Wrong random bounds assumption — MathUtils.random(int start, int end) is INCLUSIVE on both ends. MathUtils.random(float start, float end) is EXCLUSIVE on the upper bound.
6. Calling `Intersector.overlap()` (singular) — The method is overlaps (plural). There is no overlap().
7. Expecting `intersectLinePlane` to return boolean — It returns float (distance from first point to plane), not boolean.
8. Forgetting `Vector3.crs()` mutates — Unlike Vector2's crs() which returns a float scalar, Vector3's crs() overwrites this with the cross product. Use a.cpy().crs(b).
9. Using deprecated Vector2 angle/rotate methods — angle(), rotate(float), setAngle(float), rotateAround(Vector2, float) are all deprecated. Use angleDeg(), rotateDeg(), setAngleDeg(), rotateAroundDeg().
10. Allocating vectors in hot loops — new Vector2() in render/update creates GC pressure. Declare reusable private static final Vector2 tmp = new Vector2() fields and call tmp.set(...).
11. Using `Matrix4.setToRotation(quaternion)` — This method does not exist. Use mat.set(quaternion) or mat.rotate(quaternion) instead.
12. Not calling `cpy()` before passing vectors to physics/AI — Many libraries store references. If you reuse a temp vector, the stored reference silently changes value.