Math

Vector math types and functions More...

Data Structures
struct	b2Vec2
	2D vector This can be used to represent a point or free vector More...
struct	b2Rot
	2D rotation This is similar to using a complex number for rotation More...
struct	b2Transform
	A 2D rigid transform. More...
struct	b2Mat22
	A 2-by-2 Matrix. More...
struct	b2AABB
	Axis-aligned bounding box. More...

Macros
#define	b2_pi   3.14159265359f
	https://en.wikipedia.org/wiki/Pi

Functions
float	b2Atan2 (float y, float x)
	Compute an approximate arctangent in the range [-pi, pi] This is hand coded for cross platform determinism.
float	b2MinFloat (float a, float b)
float	b2MaxFloat (float a, float b)
float	b2AbsFloat (float a)
float	b2ClampFloat (float a, float lower, float upper)
int	b2MinInt (int a, int b)
int	b2MaxInt (int a, int b)
int	b2AbsInt (int a)
int	b2ClampInt (int a, int lower, int upper)
float	b2Dot (b2Vec2 a, b2Vec2 b)
	Vector dot product.
float	b2Cross (b2Vec2 a, b2Vec2 b)
	Vector cross product. In 2D this yields a scalar.
b2Vec2	b2CrossVS (b2Vec2 v, float s)
	Perform the cross product on a vector and a scalar. In 2D this produces a vector.
b2Vec2	b2CrossSV (float s, b2Vec2 v)
	Perform the cross product on a scalar and a vector. In 2D this produces a vector.
b2Vec2	b2LeftPerp (b2Vec2 v)
	Get a left pointing perpendicular vector. Equivalent to b2CrossSV(1.0f, v)
b2Vec2	b2RightPerp (b2Vec2 v)
	Get a right pointing perpendicular vector. Equivalent to b2CrossVS(v, 1.0f)
b2Vec2	b2Add (b2Vec2 a, b2Vec2 b)
	Vector addition.
b2Vec2	b2Sub (b2Vec2 a, b2Vec2 b)
	Vector subtraction.
b2Vec2	b2Neg (b2Vec2 a)
	Vector negation.
b2Vec2	b2Lerp (b2Vec2 a, b2Vec2 b, float t)
	Vector linear interpolation https://fgiesen.wordpress.com/2012/08/15/linear-interpolation-past-present-and-future/.
b2Vec2	b2Mul (b2Vec2 a, b2Vec2 b)
	Component-wise multiplication.
b2Vec2	b2MulSV (float s, b2Vec2 v)
	Multiply a scalar and vector.
b2Vec2	b2MulAdd (b2Vec2 a, float s, b2Vec2 b)
	a + s * b
b2Vec2	b2MulSub (b2Vec2 a, float s, b2Vec2 b)
	a - s * b
b2Vec2	b2Abs (b2Vec2 a)
	Component-wise absolute vector.
b2Vec2	b2Min (b2Vec2 a, b2Vec2 b)
	Component-wise minimum vector.
b2Vec2	b2Max (b2Vec2 a, b2Vec2 b)
	Component-wise maximum vector.
b2Vec2	b2Clamp (b2Vec2 v, b2Vec2 a, b2Vec2 b)
	Component-wise clamp vector v into the range [a, b].
float	b2Length (b2Vec2 v)
	Get the length of this vector (the norm)
float	b2Distance (b2Vec2 a, b2Vec2 b)
	Get the distance between two points.
b2Vec2	b2Normalize (b2Vec2 v)
	Convert a vector into a unit vector if possible, otherwise returns the zero vector.
b2Vec2	b2GetLengthAndNormalize (float *length, b2Vec2 v)
	Convert a vector into a unit vector if possible, otherwise returns the zero vector.
b2Rot	b2NormalizeRot (b2Rot q)
	Normalize rotation.
b2Rot	b2IntegrateRotation (b2Rot q1, float deltaAngle)
	Integration rotation from angular velocity.
float	b2LengthSquared (b2Vec2 v)
	Get the length squared of this vector.
float	b2DistanceSquared (b2Vec2 a, b2Vec2 b)
	Get the distance squared between points.
b2Rot	b2MakeRot (float angle)
	Make a rotation using an angle in radians.
bool	b2IsNormalized (b2Rot q)
	Is this rotation normalized?
b2Rot	b2NLerp (b2Rot q1, b2Rot q2, float t)
	Normalized linear interpolation https://fgiesen.wordpress.com/2012/08/15/linear-interpolation-past-present-and-future/.
float	b2ComputeAngularVelocity (b2Rot q1, b2Rot q2, float inv_h)
	Compute the angular velocity necessary to rotate between two rotations over a give time.
float	b2Rot_GetAngle (b2Rot q)
	Get the angle in radians in the range [-pi, pi].
b2Vec2	b2Rot_GetXAxis (b2Rot q)
	Get the x-axis.
b2Vec2	b2Rot_GetYAxis (b2Rot q)
	Get the y-axis.
b2Rot	b2MulRot (b2Rot q, b2Rot r)
	Multiply two rotations: q * r.
b2Rot	b2InvMulRot (b2Rot q, b2Rot r)
	Transpose multiply two rotations: qT * r.
float	b2RelativeAngle (b2Rot b, b2Rot a)
	relative angle between b and a (rot_b * inv(rot_a))
float	b2UnwindAngle (float angle)
	Convert an angle in the range [-2*pi, 2*pi] into the range [-pi, pi].
float	b2UnwindLargeAngle (float angle)
	Convert any into the range [-pi, pi] (slow)
b2Vec2	b2RotateVector (b2Rot q, b2Vec2 v)
	Rotate a vector.
b2Vec2	b2InvRotateVector (b2Rot q, b2Vec2 v)
	Inverse rotate a vector.
b2Vec2	b2TransformPoint (b2Transform t, const b2Vec2 p)
	Transform a point (e.g. local space to world space)
b2Vec2	b2InvTransformPoint (b2Transform t, const b2Vec2 p)
	Inverse transform a point (e.g. world space to local space)
b2Transform	b2MulTransforms (b2Transform A, b2Transform B)
	v2 = A.q.Rot(B.q.Rot(v1) + B.p) + A.p = (A.q * B.q).Rot(v1) + A.q.Rot(B.p) + A.p
b2Transform	b2InvMulTransforms (b2Transform A, b2Transform B)
	v2 = A.q' * (B.q * v1 + B.p - A.p) = A.q' * B.q * v1 + A.q' * (B.p - A.p)
b2Vec2	b2MulMV (b2Mat22 A, b2Vec2 v)
	Multiply a 2-by-2 matrix times a 2D vector.
b2Mat22	b2GetInverse22 (b2Mat22 A)
	Get the inverse of a 2-by-2 matrix.
b2Vec2	b2Solve22 (b2Mat22 A, b2Vec2 b)
	Solve A * x = b, where b is a column vector.
bool	b2AABB_Contains (b2AABB a, b2AABB b)
	Does a fully contain b.
b2Vec2	b2AABB_Center (b2AABB a)
	Get the center of the AABB.
b2Vec2	b2AABB_Extents (b2AABB a)
	Get the extents of the AABB (half-widths).
b2AABB	b2AABB_Union (b2AABB a, b2AABB b)
	Union of two AABBs.
bool	b2IsValid (float a)
	Is this a valid number? Not NaN or infinity.
bool	b2Vec2_IsValid (b2Vec2 v)
	Is this a valid vector? Not NaN or infinity.
bool	b2Rot_IsValid (b2Rot q)
	Is this a valid rotation? Not NaN or infinity. Is normalized.
bool	b2AABB_IsValid (b2AABB aabb)
	Is this a valid bounding box? Not Nan or infinity. Upper bound greater than or equal to lower bound.
void	b2SetLengthUnitsPerMeter (float lengthUnits)
	Box2D bases all length units on meters, but you may need different units for your game.
float	b2GetLengthUnitsPerMeter (void)
	Get the current length units per meter.

Detailed Description

Vector math types and functions

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Data Structure Documentation

b2Vec2

struct b2Vec2

2D vector This can be used to represent a point or free vector

Data Fields
float	x	coordinates
float	y

b2Rot

struct b2Rot

2D rotation This is similar to using a complex number for rotation

Data Fields
float	c	cosine and sine
float	s

b2Transform

struct b2Transform

A 2D rigid transform.

Collaboration diagram for b2Transform:

Data Fields
b2Vec2	p
b2Rot	q

b2Mat22

struct b2Mat22

A 2-by-2 Matrix.

Collaboration diagram for b2Mat22:

Data Fields
b2Vec2	cx	columns
b2Vec2	cy

b2AABB

struct b2AABB

Axis-aligned bounding box.

Collaboration diagram for b2AABB:

Data Fields
b2Vec2	lowerBound
b2Vec2	upperBound

Function Documentation

b2AbsFloat()

float b2AbsFloat

(

float

a

)

Returns

the absolute value of a float

b2AbsInt()

int b2AbsInt

(

int

a

)

Returns

the absolute value of an integer

b2Atan2()

float b2Atan2	(	float	y,
		float	x )

Compute an approximate arctangent in the range [-pi, pi] This is hand coded for cross platform determinism.

The atan2f function in the standard library is not cross platform deterministic.

b2ClampFloat()

float b2ClampFloat	(	float	a,
		float	lower,
		float	upper )

Returns

a float clamped between a lower and upper bound

b2ClampInt()

int b2ClampInt	(	int	a,
		int	lower,
		int	upper )

Returns

an integer clamped between a lower and upper bound

b2ComputeAngularVelocity()

float b2ComputeAngularVelocity	(	b2Rot	q1,
		b2Rot	q2,
		float	inv_h )

Compute the angular velocity necessary to rotate between two rotations over a give time.

Parameters

q1	initial rotation
q2	final rotation
inv_h	inverse time step

b2GetLengthAndNormalize()

b2Vec2 b2GetLengthAndNormalize	(	float *	length,
		b2Vec2	v )

Convert a vector into a unit vector if possible, otherwise returns the zero vector.

Also outputs the length.

b2IntegrateRotation()

b2Rot b2IntegrateRotation	(	b2Rot	q1,
		float	deltaAngle )

Integration rotation from angular velocity.

Parameters

q1	initial rotation
deltaAngle	the angular displacement in radians

b2MaxFloat()

float b2MaxFloat	(	float	a,
		float	b )

Returns

the maximum of two floats

b2MaxInt()

int b2MaxInt	(	int	a,
		int	b )

Returns

the maximum of two integers

b2MinFloat()

float b2MinFloat	(	float	a,
		float	b )

Returns

the minimum of two floats

b2MinInt()

int b2MinInt	(	int	a,
		int	b )

Returns

the minimum of two integers

b2SetLengthUnitsPerMeter()

void b2SetLengthUnitsPerMeter

(

float

lengthUnits

)

Box2D bases all length units on meters, but you may need different units for your game.

You can set this value to use different units. This should be done at application startup and only modified once. Default value is 1.

Warning

This must be modified before any calls to Box2D

b2Solve22()

b2Vec2 b2Solve22	(	b2Mat22	A,
		b2Vec2	b )

Solve A * x = b, where b is a column vector.

This is more efficient than computing the inverse in one-shot cases.