math_functions.h

// SPDX-FileCopyrightText: 2025 Erin Catto
// SPDX-License-Identifier: MIT
 
#pragma once
 
#include "base.h"
 
#include <float.h>
 
// for sqrtf and remainderf
#include <math.h>
#include <stdbool.h>


#define B3_PI 3.14159265359f

#define B3_DEG_TO_RAD 0.01745329251f

#define B3_RAD_TO_DEG 57.2957795131f

#define B3_MIN_SCALE 0.01f

typedef struct b3Vec2
{
    float x;
    float y;
} b3Vec2;

typedef struct b3Vec3
{
    float x;
    float y;
    float z;
} b3Vec3;

typedef struct b3CosSin
{
    float cosine;
    float sine;
} b3CosSin;

typedef struct b3Quat
{
    b3Vec3 v;
    float s;
} b3Quat;

typedef struct b3Transform
{
    b3Vec3 p;
    b3Quat q;
} b3Transform;
 
#if defined( BOX3D_DOUBLE_PRECISION )

typedef struct b3Pos
{
    double x, y, z;
} b3Pos;

typedef struct b3WorldTransform
{
    b3Pos p;
    b3Quat q;
} b3WorldTransform;
 
#else

typedef b3Vec3 b3Pos;

typedef b3Transform b3WorldTransform;
 
#endif

typedef struct b3Matrix3
{
    b3Vec3 cx, cy, cz;
} b3Matrix3;

typedef struct b3AABB
{
    b3Vec3 lowerBound;
    b3Vec3 upperBound;
} b3AABB;

typedef struct b3Plane
{
    b3Vec3 normal;
    float offset;
} b3Plane;
 
static const b3Vec3 b3Vec3_zero = { 0.0f, 0.0f, 0.0f };
static const b3Vec3 b3Vec3_one = { 1.0f, 1.0f, 1.0f };
static const b3Vec3 b3Vec3_axisX = { 1.0f, 0.0f, 0.0f };
static const b3Vec3 b3Vec3_axisY = { 0.0f, 1.0f, 0.0f };
static const b3Vec3 b3Vec3_axisZ = { 0.0f, 0.0f, 1.0f };
static const b3Quat b3Quat_identity = { { 0.0f, 0.0f, 0.0f }, 1.0f };
static const b3Transform b3Transform_identity = { { 0.0f, 0.0f, 0.0f }, { { 0.0f, 0.0f, 0.0f }, 1.0f } };
static const b3Matrix3 b3Mat3_zero = {
    { 0.0f, 0.0f, 0.0f },
    { 0.0f, 0.0f, 0.0f },
    { 0.0f, 0.0f, 0.0f },
};
static const b3Matrix3 b3Mat3_identity = {
    { 1.0f, 0.0f, 0.0f },
    { 0.0f, 1.0f, 0.0f },
    { 0.0f, 0.0f, 1.0f },
};
 
// Valid in both modes: 0.0f promotes to double, the identity rotation stays float
static const b3Pos b3Pos_zero = { 0.0f, 0.0f, 0.0f };
static const b3WorldTransform b3WorldTransform_identity = { { 0.0f, 0.0f, 0.0f }, { { 0.0f, 0.0f, 0.0f }, 1.0f } };

B3_INLINE int b3MinInt( int a, int b )
{
    return a < b ? a : b;
}

B3_INLINE int b3MaxInt( int a, int b )
{
    return a > b ? a : b;
}

B3_INLINE int b3ClampInt( int a, int lower, int upper )
{
    return a < lower ? lower : ( upper < a ? upper : a );
}

B3_INLINE float b3AbsFloat( float a )
{
    return a < 0 ? -a : a;
}

B3_INLINE float b3MinFloat( float a, float b )
{
    return a < b ? a : b;
}

B3_INLINE float b3MaxFloat( float a, float b )
{
    return a > b ? a : b;
}

B3_INLINE float b3ClampFloat( float a, float lower, float upper )
{
    return a < lower ? lower : ( upper < a ? upper : a );
}

B3_INLINE float b3LerpFloat( float a, float b, float alpha )
{
    return ( 1.0f - alpha ) * a + alpha * b;
}

B3_API float b3Atan2( float y, float x );

B3_API b3CosSin b3ComputeCosSin( float radians );

B3_INLINE float b3Sin( float radians )
{
    b3CosSin cs = b3ComputeCosSin( radians );
    return cs.sine;
}

B3_INLINE float b3Cos( float radians )
{
    b3CosSin cs = b3ComputeCosSin( radians );
    return cs.cosine;
}

B3_INLINE float b3UnwindAngle( float radians )
{
    // Assuming this is deterministic
    return remainderf( radians, 2.0f * B3_PI );
}

B3_INLINE b3Vec3 b3Add( b3Vec3 a, b3Vec3 b )
{
    return B3_LITERAL( b3Vec3 ){ a.x + b.x, a.y + b.y, a.z + b.z };
}

B3_INLINE b3Vec3 b3Sub( b3Vec3 a, b3Vec3 b )
{
    return B3_LITERAL( b3Vec3 ){ a.x - b.x, a.y - b.y, a.z - b.z };
}

B3_INLINE b3Vec3 b3Mul( b3Vec3 a, b3Vec3 b )
{
    return B3_LITERAL( b3Vec3 ){ a.x * b.x, a.y * b.y, a.z * b.z };
}

B3_INLINE b3Vec3 b3Neg( b3Vec3 a )
{
    return B3_LITERAL( b3Vec3 ){ -a.x, -a.y, -a.z };
}

B3_INLINE float b3Dot( b3Vec3 a, b3Vec3 b )
{
    return a.x * b.x + a.y * b.y + a.z * b.z;
}

B3_INLINE float b3Length( b3Vec3 v )
{
    return sqrtf( b3Dot( v, v ) );
}

B3_INLINE float b3LengthSquared( b3Vec3 a )
{
    return a.x * a.x + a.y * a.y + a.z * a.z;
}

B3_INLINE float b3Distance( b3Vec3 a, b3Vec3 b )
{
    b3Vec3 dv = { b.x - a.x, b.y - a.y, b.z - a.z };
    return b3Length( dv );
}

B3_INLINE float b3DistanceSquared( b3Vec3 a, b3Vec3 b )
{
    b3Vec3 dv = { b.x - a.x, b.y - a.y, b.z - a.z };
    return dv.x * dv.x + dv.y * dv.y + dv.z * dv.z;
}

B3_INLINE b3Vec3 b3Normalize( b3Vec3 a )
{
    float lengthSquared = a.x * a.x + a.y * a.y + a.z * a.z;
 
    if ( lengthSquared > 1000.0f * FLT_MIN )
    {
        float s = 1.0f / sqrtf( lengthSquared );
        b3Vec3 u = { s * a.x, s * a.y, s * a.z };
        return u;
    }
 
    return B3_LITERAL( b3Vec3 ){ 0.0f, 0.0f, 0.0f };
}

B3_INLINE b3Vec3 b3GetLengthAndNormalize( float* length, b3Vec3 a )
{
    *length = b3Length( a );
    if ( *length < FLT_EPSILON )
    {
        return b3Vec3_zero;
    }
 
    float invLength = 1.0f / *length;
    b3Vec3 n = { invLength * a.x, invLength * a.y, invLength * a.z };
    return n;
}

B3_INLINE b3Vec3 b3Perp( b3Vec3 a )
{
    // Suppose vector a has all equal components and is a unit vector: a = (s, s, s)
    // Then 3*s*s = 1, s = sqrt(1/3) = 0.57735. This means that at least one component
    // of a unit vector must be greater or equal to 0.57735.
    b3Vec3 p;
    if ( a.x < -0.5f || 0.5f < a.x )
    {
        p = B3_LITERAL( b3Vec3 ){ a.y, -a.x, 0.0f };
    }
    else
    {
        p = B3_LITERAL( b3Vec3 ){ 0.0f, a.z, -a.y };
    }
 
    return b3Normalize( p );
}

B3_INLINE bool b3IsNormalized( b3Vec3 a )
{
    float aa = b3Dot( a, a );
    return b3AbsFloat( 1.0f - aa ) < 100.0f * FLT_EPSILON;
}

B3_INLINE b3Vec3 b3MulAdd( b3Vec3 a, float s, b3Vec3 b )
{
    return B3_LITERAL( b3Vec3 ){ a.x + s * b.x, a.y + s * b.y, a.z + s * b.z };
}

B3_INLINE b3Vec3 b3MulSub( b3Vec3 a, float s, b3Vec3 b )
{
    return B3_LITERAL( b3Vec3 ){ a.x - s * b.x, a.y - s * b.y, a.z - s * b.z };
}

B3_INLINE b3Vec3 b3MulSV( float s, b3Vec3 a )
{
    return B3_LITERAL( b3Vec3 ){ s * a.x, s * a.y, s * a.z };
}

B3_INLINE b3Vec3 b3Cross( b3Vec3 a, b3Vec3 b )
{
    b3Vec3 c;
    c.x = a.y * b.z - a.z * b.y;
    c.y = a.z * b.x - a.x * b.z;
    c.z = a.x * b.y - a.y * b.x;
    return c;
}

B3_INLINE b3Vec3 b3Lerp( b3Vec3 a, b3Vec3 b, float alpha )
{
    B3_ASSERT( 0.0f <= alpha && alpha <= 1.0f );
 
    b3Vec3 c = {
        ( 1.0f - alpha ) * a.x + alpha * b.x,
        ( 1.0f - alpha ) * a.y + alpha * b.y,
        ( 1.0f - alpha ) * a.z + alpha * b.z,
    };
    return c;
}

B3_INLINE b3Vec3 b3Blend2( float s, b3Vec3 a, float t, b3Vec3 b )
{
    b3Vec3 d = {
        s * a.x + t * b.x,
        s * a.y + t * b.y,
        s * a.z + t * b.z,
    };
    return d;
}

B3_INLINE b3Vec3 b3Abs( b3Vec3 a )
{
    return B3_LITERAL( b3Vec3 ){
        b3AbsFloat( a.x ),
        b3AbsFloat( a.y ),
        b3AbsFloat( a.z ),
    };
}

B3_INLINE b3Vec3 b3Sign( b3Vec3 a )
{
    return B3_LITERAL( b3Vec3 ){
        a.x >= 0.0f ? 1.0f : -1.0f,
        a.y >= 0.0f ? 1.0f : -1.0f,
        a.z >= 0.0f ? 1.0f : -1.0f,
    };
}

B3_INLINE b3Vec3 b3Min( b3Vec3 a, b3Vec3 b )
{
    return B3_LITERAL( b3Vec3 ){
        b3MinFloat( a.x, b.x ),
        b3MinFloat( a.y, b.y ),
        b3MinFloat( a.z, b.z ),
    };
}

B3_INLINE b3Vec3 b3Max( b3Vec3 a, b3Vec3 b )
{
    return B3_LITERAL( b3Vec3 ){
        b3MaxFloat( a.x, b.x ),
        b3MaxFloat( a.y, b.y ),
        b3MaxFloat( a.z, b.z ),
    };
}

B3_INLINE b3Vec3 b3Clamp( b3Vec3 a, b3Vec3 lower, b3Vec3 upper )
{
    b3Vec3 b;
    b.x = b3ClampFloat( a.x, lower.x, upper.x );
    b.y = b3ClampFloat( a.y, lower.y, upper.y );
    b.z = b3ClampFloat( a.z, lower.z, upper.z );
    return b;
}

B3_INLINE b3Vec3 b3SafeScale( b3Vec3 a )
{
    b3Vec3 absScale = b3Abs( a );
    b3Vec3 minScale = { B3_MIN_SCALE, B3_MIN_SCALE, B3_MIN_SCALE };
    b3Vec3 safeScale = b3Mul( b3Sign( a ), b3Max( absScale, minScale ) );
    return safeScale;
}

B3_INLINE bool b3IsNormalizedQuat( b3Quat q )
{
    float qq = q.v.x * q.v.x + q.v.y * q.v.y + q.v.z * q.v.z + q.s * q.s;
    return 1.0f - 20.0f * FLT_EPSILON < qq && qq < 1.0f + 20.0f * FLT_EPSILON;
}

B3_INLINE b3Vec3 b3RotateVector( b3Quat q, b3Vec3 v )
{
    // v + 2 * cross(q.v, cross(q.v, v) + q.s * v)
    // B3_ASSERT( b3IsNormalizedQuat( q ) );
    b3Vec3 t1 = b3Cross( q.v, v );
    b3Vec3 t2 = b3MulAdd( t1, q.s, v );
    b3Vec3 t3 = b3Cross( q.v, t2 );
    return b3MulAdd( v, 2.0f, t3 );
}

B3_INLINE b3Vec3 b3InvRotateVector( b3Quat q, b3Vec3 v )
{
    // v + 2 * cross(q.v, cross(q.v, v) - q.s * v)
    // B3_ASSERT( b3IsNormalizedQuat( q ) );
    b3Vec3 t1 = b3Cross( q.v, v );
    b3Vec3 t2 = b3MulSub( t1, q.s, v );
    b3Vec3 t3 = b3Cross( q.v, t2 );
    return b3MulAdd( v, 2.0f, t3 );
}

B3_INLINE float b3DotQuat( b3Quat a, b3Quat b )
{
    return a.v.x * b.v.x + a.v.y * b.v.y + a.v.z * b.v.z + a.s * b.s;
}

B3_INLINE b3Quat b3MulQuat( b3Quat q1, b3Quat q2 )
{
    b3Vec3 t1 = b3Cross( q1.v, q2.v );
    b3Vec3 t2 = b3MulAdd( t1, q1.s, q2.v );
    b3Vec3 t3 = b3MulAdd( t2, q2.s, q1.v );
    b3Quat q = { t3, q1.s * q2.s - b3Dot( q1.v, q2.v ) };
    return q;
}

B3_INLINE b3Quat b3InvMulQuat( b3Quat q1, b3Quat q2 )
{
    b3Vec3 t1 = b3Cross( q2.v, q1.v );
    b3Vec3 t2 = b3MulAdd( t1, q1.s, q2.v );
    b3Vec3 t3 = b3MulSub( t2, q2.s, q1.v );
    b3Quat q = { t3, q1.s * q2.s + b3Dot( q1.v, q2.v ) };
    return q;
}

B3_INLINE b3Quat b3Conjugate( b3Quat q )
{
    return B3_LITERAL( b3Quat ){ { -q.v.x, -q.v.y, -q.v.z }, q.s };
}

B3_INLINE b3Quat b3NegateQuat( b3Quat q )
{
    return B3_LITERAL( b3Quat ){ { -q.v.x, -q.v.y, -q.v.z }, -q.s };
}

B3_INLINE b3Quat b3NormalizeQuat( b3Quat q )
{
    float lengthSq = b3DotQuat( q, q );
    if ( lengthSq > 1000.0f * FLT_MIN )
    {
        float s = 1.0f / sqrtf( lengthSq );
        b3Quat qn = { { s * q.v.x, s * q.v.y, s * q.v.z }, s * q.s };
        return qn;
    }
 
    return b3Quat_identity;
}

B3_INLINE b3Quat b3MakeQuatFromAxisAngle( b3Vec3 axis, float radians )
{
    B3_ASSERT( b3IsNormalized( axis ) );
    b3CosSin cs = b3ComputeCosSin( 0.5f * radians );
    b3Quat q = { { cs.sine * axis.x, cs.sine * axis.y, cs.sine * axis.z }, cs.cosine };
    return q;
}

B3_INLINE b3Vec3 b3GetAxisAngle( float* radians, b3Quat q )
{
    float length = sqrtf( q.v.x * q.v.x + q.v.y * q.v.y + q.v.z * q.v.z );
    *radians = 2.0f * b3Atan2( length, q.s );
    if ( length > 0.0f )
    {
        float invLength = 1.0f / length;
        b3Vec3 axis = { invLength * q.v.x, invLength * q.v.y, invLength * q.v.z };
        return axis;
    }
 
    return b3Vec3_zero;
}

B3_INLINE float b3GetQuatAngle( b3Quat q )
{
    float length = sqrtf( q.v.x * q.v.x + q.v.y * q.v.y + q.v.z * q.v.z );
    return 2.0f * b3Atan2( length, q.s );
}

B3_API b3Quat b3MakeQuatFromMatrix( const b3Matrix3* m );

B3_API b3Quat b3ComputeQuatBetweenUnitVectors( b3Vec3 v1, b3Vec3 v2 );

B3_INLINE float b3GetTwistAngle( b3Quat q )
{
    // Account for polarity to keep the twist angle in range.
    // This is simpler than asking the user to check polarity or unwinding.
    float twist = q.s < 0.0f ? b3Atan2( -q.v.z, -q.s ) : b3Atan2( q.v.z, q.s );
    twist *= 2.0f;
    B3_ASSERT( -B3_PI <= twist && twist <= B3_PI );
    return twist;
}

B3_INLINE float b3GetSwingAngle( b3Quat q )
{
    // Polarity should not matter because all terms are squared.
    float x = sqrtf( q.v.z * q.v.z + q.s * q.s );
    float y = sqrtf( q.v.x * q.v.x + q.v.y * q.v.y );
    float swing = 2.0f * b3Atan2( y, x );
    B3_ASSERT( 0.0f <= swing && swing <= B3_PI );
    return swing;
}

B3_INLINE b3Quat b3NLerp( b3Quat q1, b3Quat q2, float alpha )
{
    B3_VALIDATE( 0.0f <= alpha && alpha <= 1.0f );
    if ( b3DotQuat( q1, q2 ) < 0.0f )
    {
        q1 = B3_LITERAL( b3Quat ){ { -q1.v.x, -q1.v.y, -q1.v.z }, -q1.s };
    }
 
    b3Quat q;
    q.v = b3Lerp( q1.v, q2.v, alpha );
    q.s = ( 1.0f - alpha ) * q1.s + alpha * q2.s;
 
    return b3NormalizeQuat( q );
}

B3_INLINE b3Transform b3MulTransforms( b3Transform a, b3Transform b )
{
    b3Transform out;
    out.p = b3Add( b3RotateVector( a.q, b.p ), a.p );
    out.q = b3MulQuat( a.q, b.q );
    return out;
}

B3_FORCE_INLINE b3Transform b3InvMulTransforms( b3Transform a, b3Transform b )
{
    b3Transform out;
    out.p = b3InvRotateVector( a.q, b3Sub( b.p, a.p ) );
    out.q = b3InvMulQuat( a.q, b.q );
    return out;
}

B3_INLINE b3Transform b3InvertTransform( b3Transform t )
{
    b3Transform out;
    out.p = b3InvRotateVector( t.q, b3Neg( t.p ) );
    out.q = b3Conjugate( t.q );
    return out;
}

B3_INLINE b3Vec3 b3TransformPoint( b3Transform t, b3Vec3 v )
{
    b3Vec3 rv = b3RotateVector( t.q, v );
    return b3Add( rv, t.p );
}

B3_INLINE b3Vec3 b3InvTransformPoint( b3Transform t, b3Vec3 v )
{
    return b3InvRotateVector( t.q, b3Sub( v, t.p ) );
}
 
// World position boundary. These cross between the double precision world space at the public
// boundary and the float interior. One set of bodies serves both modes: the typedefs collapse
// the types in float mode and the explicit float casts become no-ops.

B3_INLINE b3Pos b3ToPos( b3Vec3 v )
{
    return B3_LITERAL( b3Pos ){ v.x, v.y, v.z };
}

B3_INLINE b3Vec3 b3ToVec3( b3Pos p )
{
    return B3_LITERAL( b3Vec3 ){ (float)p.x, (float)p.y, (float)p.z };
}

B3_INLINE float b3RoundDownFloat( double x )
{
#if defined( BOX3D_DOUBLE_PRECISION )
    float f = (float)x;
    return (double)f > x ? nextafterf( f, -FLT_MAX ) : f;
#else
    return (float)x;
#endif
}

B3_INLINE float b3RoundUpFloat( double x )
{
#if defined( BOX3D_DOUBLE_PRECISION )
    float f = (float)x;
    return (double)f < x ? nextafterf( f, FLT_MAX ) : f;
#else
    return (float)x;
#endif
}

B3_INLINE b3Vec3 b3SubPos( b3Pos a, b3Pos b )
{
    return B3_LITERAL( b3Vec3 ){ (float)( a.x - b.x ), (float)( a.y - b.y ), (float)( a.z - b.z ) };
}

B3_INLINE b3Pos b3OffsetPos( b3Pos p, b3Vec3 d )
{
    return B3_LITERAL( b3Pos ){ p.x + d.x, p.y + d.y, p.z + d.z };
}

B3_INLINE b3Pos b3LerpPosition( b3Pos a, b3Pos b, float t )
{
    return B3_LITERAL( b3Pos ){
        ( 1.0f - t ) * a.x + t * b.x,
        ( 1.0f - t ) * a.y + t * b.y,
        ( 1.0f - t ) * a.z + t * b.z,
    };
}

B3_INLINE b3Pos b3TransformWorldPoint( b3WorldTransform t, b3Vec3 p )
{
    b3Vec3 r = b3RotateVector( t.q, p );
    return B3_LITERAL( b3Pos ){ t.p.x + r.x, t.p.y + r.y, t.p.z + r.z };
}

B3_INLINE b3Vec3 b3InvTransformWorldPoint( b3WorldTransform t, b3Pos p )
{
    b3Vec3 d = { (float)( p.x - t.p.x ), (float)( p.y - t.p.y ), (float)( p.z - t.p.z ) };
    return b3InvRotateVector( t.q, d );
}

B3_INLINE b3Transform b3InvMulWorldTransforms( b3WorldTransform A, b3WorldTransform B )
{
    b3Transform C;
    C.q = b3InvMulQuat( A.q, B.q );
    b3Vec3 d = { (float)( B.p.x - A.p.x ), (float)( B.p.y - A.p.y ), (float)( B.p.z - A.p.z ) };
    C.p = b3InvRotateVector( A.q, d );
    return C;
}

B3_INLINE b3WorldTransform b3MulWorldTransforms( b3WorldTransform A, b3Transform B )
{
    b3WorldTransform C;
    C.q = b3MulQuat( A.q, B.q );
    b3Vec3 r = b3RotateVector( A.q, B.p );
    C.p = B3_LITERAL( b3Pos ){ A.p.x + r.x, A.p.y + r.y, A.p.z + r.z };
    return C;
}

B3_INLINE b3Transform b3ToRelativeTransform( b3WorldTransform t, b3Pos base )
{
    b3Transform r;
    r.q = t.q;
    r.p = B3_LITERAL( b3Vec3 ){ (float)( t.p.x - base.x ), (float)( t.p.y - base.y ), (float)( t.p.z - base.z ) };
    return r;
}

B3_INLINE b3WorldTransform b3MakeWorldTransform( b3Transform t )
{
    b3WorldTransform w;
    w.p = b3ToPos( t.p );
    w.q = t.q;
    return w;
}

B3_INLINE b3AABB b3OffsetAABB( b3AABB localBox, b3Pos origin )
{
    b3AABB out;
    out.lowerBound.x = b3RoundDownFloat( origin.x + localBox.lowerBound.x );
    out.lowerBound.y = b3RoundDownFloat( origin.y + localBox.lowerBound.y );
    out.lowerBound.z = b3RoundDownFloat( origin.z + localBox.lowerBound.z );
    out.upperBound.x = b3RoundUpFloat( origin.x + localBox.upperBound.x );
    out.upperBound.y = b3RoundUpFloat( origin.y + localBox.upperBound.y );
    out.upperBound.z = b3RoundUpFloat( origin.z + localBox.upperBound.z );
    return out;
}

B3_INLINE float b3Det( b3Matrix3 m )
{
    return b3Dot( m.cx, b3Cross( m.cy, m.cz ) );
}

B3_INLINE b3Vec3 b3MulMV( b3Matrix3 m, b3Vec3 a )
{
    b3Vec3 b = {
        m.cx.x * a.x + m.cy.x * a.y + m.cz.x * a.z,
        m.cx.y * a.x + m.cy.y * a.y + m.cz.y * a.z,
        m.cx.z * a.x + m.cy.z * a.y + m.cz.z * a.z,
    };
    return b;
}

B3_INLINE b3Matrix3 b3NegateMat3( b3Matrix3 a )
{
    return B3_LITERAL( b3Matrix3 ){
        { -a.cx.x, -a.cx.y, -a.cx.z },
        { -a.cy.x, -a.cy.y, -a.cy.z },
        { -a.cz.x, -a.cz.y, -a.cz.z },
    };
}

B3_INLINE b3Matrix3 b3AddMM( b3Matrix3 a, b3Matrix3 b )
{
    return B3_LITERAL( b3Matrix3 ){
        { a.cx.x + b.cx.x, a.cx.y + b.cx.y, a.cx.z + b.cx.z },
        { a.cy.x + b.cy.x, a.cy.y + b.cy.y, a.cy.z + b.cy.z },
        { a.cz.x + b.cz.x, a.cz.y + b.cz.y, a.cz.z + b.cz.z },
    };
}

B3_INLINE b3Matrix3 b3SubMM( b3Matrix3 a, b3Matrix3 b )
{
    return B3_LITERAL( b3Matrix3 ){
        { a.cx.x - b.cx.x, a.cx.y - b.cx.y, a.cx.z - b.cx.z },
        { a.cy.x - b.cy.x, a.cy.y - b.cy.y, a.cy.z - b.cy.z },
        { a.cz.x - b.cz.x, a.cz.y - b.cz.y, a.cz.z - b.cz.z },
    };
}

B3_INLINE b3Matrix3 b3MulSM( float s, b3Matrix3 a )
{
    return B3_LITERAL( b3Matrix3 ){
        { s * a.cx.x, s * a.cx.y, s * a.cx.z },
        { s * a.cy.x, s * a.cy.y, s * a.cy.z },
        { s * a.cz.x, s * a.cz.y, s * a.cz.z },
    };
}

B3_INLINE b3Matrix3 b3MulMM( b3Matrix3 a, b3Matrix3 b )
{
    b3Matrix3 out;
    out.cx = b3MulMV( a, b.cx );
    out.cy = b3MulMV( a, b.cy );
    out.cz = b3MulMV( a, b.cz );
    return out;
}

B3_INLINE b3Matrix3 b3Transpose( b3Matrix3 m )
{
    b3Matrix3 out;
    out.cx = B3_LITERAL( b3Vec3 ){ m.cx.x, m.cy.x, m.cz.x };
    out.cy = B3_LITERAL( b3Vec3 ){ m.cx.y, m.cy.y, m.cz.y };
    out.cz = B3_LITERAL( b3Vec3 ){ m.cx.z, m.cy.z, m.cz.z };
 
    return out;
}

B3_INLINE b3Matrix3 b3InvertMatrix( b3Matrix3 m )
{
    float det = b3Det( m );
    if ( b3AbsFloat( det ) > 1000.0f * FLT_MIN )
    {
        float invDet = 1.0f / det;
        b3Matrix3 out;
        out.cx = b3MulSV( invDet, b3Cross( m.cy, m.cz ) );
        out.cy = b3MulSV( invDet, b3Cross( m.cz, m.cx ) );
        out.cz = b3MulSV( invDet, b3Cross( m.cx, m.cy ) );
 
        return b3Transpose( out );
    }
 
    return b3Mat3_zero;
}

B3_INLINE b3Vec3 b3Solve3( b3Matrix3 m, b3Vec3 a )
{
    float det = b3Det( m );
    if ( b3AbsFloat( det ) > 1000.0f * FLT_MIN )
    {
        float invDet = 1.0f / det;
        b3Matrix3 s;
        s.cx = b3Cross( m.cy, m.cz );
        s.cy = b3Cross( m.cz, m.cx );
        s.cz = b3Cross( m.cx, m.cy );
 
        b3Vec3 b = {
            invDet * b3Dot( s.cx, a ),
            invDet * b3Dot( s.cy, a ),
            invDet * b3Dot( s.cz, a ),
        };
 
        return b;
    }
 
    return b3Vec3_zero;
}

B3_INLINE b3Matrix3 b3InvertT( b3Matrix3 m )
{
    float det = b3Det( m );
    if ( b3AbsFloat( det ) > 1000.0f * FLT_MIN )
    {
        float invDet = 1.0f / det;
        b3Matrix3 out;
        out.cx = b3MulSV( invDet, b3Cross( m.cy, m.cz ) );
        out.cy = b3MulSV( invDet, b3Cross( m.cz, m.cx ) );
        out.cz = b3MulSV( invDet, b3Cross( m.cx, m.cy ) );
        return out;
    }
 
    return b3Mat3_zero;
}

B3_INLINE b3Matrix3 b3AbsMatrix3( b3Matrix3 m )
{
    b3Matrix3 out;
    out.cx = b3Abs( m.cx );
    out.cy = b3Abs( m.cy );
    out.cz = b3Abs( m.cz );
 
    return out;
}

B3_FORCE_INLINE b3Matrix3 b3MakeMatrixFromQuat( b3Quat q )
{
    float xx = q.v.x * q.v.x;
    float yy = q.v.y * q.v.y;
    float zz = q.v.z * q.v.z;
    float xy = q.v.x * q.v.y;
    float xz = q.v.x * q.v.z;
    float xw = q.v.x * q.s;
    float yz = q.v.y * q.v.z;
    float yw = q.v.y * q.s;
    float zw = q.v.z * q.s;
 
    return B3_LITERAL( b3Matrix3 ){
        { 1.0f - 2.0f * ( yy + zz ), 2.0f * ( xy + zw ), 2.0f * ( xz - yw ) },
        { 2.0f * ( xy - zw ), 1.0f - 2.0f * ( xx + zz ), 2.0f * ( yz + xw ) },
        { 2.0f * ( xz + yw ), 2.0f * ( yz - xw ), 1.0f - 2.0f * ( xx + yy ) },
    };
}

B3_API b3Matrix3 b3Steiner( float mass, b3Vec3 origin );

B3_INLINE b3AABB b3MakeAABB( const b3Vec3* points, int count, float radius )
{
    B3_ASSERT( count > 0 );
    b3AABB a = { points[0], points[0] };
    for ( int i = 1; i < count; ++i )
    {
        a.lowerBound = b3Min( a.lowerBound, points[i] );
        a.upperBound = b3Max( a.upperBound, points[i] );
    }
 
    b3Vec3 r = { radius, radius, radius };
    a.lowerBound = b3Sub( a.lowerBound, r );
    a.upperBound = b3Add( a.upperBound, r );
 
    return a;
}

B3_INLINE bool b3AABB_Contains( b3AABB a, b3AABB b )
{
    if ( a.lowerBound.x > b.lowerBound.x || b.upperBound.x > a.upperBound.x )
        return false;
    if ( a.lowerBound.y > b.lowerBound.y || b.upperBound.y > a.upperBound.y )
        return false;
    if ( a.lowerBound.z > b.lowerBound.z || b.upperBound.z > a.upperBound.z )
        return false;
 
    return true;
}

B3_INLINE float b3AABB_Area( b3AABB a )
{
    b3Vec3 delta = b3Sub( a.upperBound, a.lowerBound );
    return 2.0f * ( delta.x * delta.y + delta.y * delta.z + delta.z * delta.x );
}

B3_INLINE b3Vec3 b3AABB_Center( b3AABB a )
{
    return b3MulSV( 0.5f, b3Add( a.upperBound, a.lowerBound ) );
}

B3_INLINE b3Vec3 b3AABB_Extents( b3AABB a )
{
    return b3MulSV( 0.5f, b3Sub( a.upperBound, a.lowerBound ) );
}

B3_INLINE b3AABB b3AABB_Union( b3AABB a, b3AABB b )
{
    b3AABB out;
    out.lowerBound = b3Min( a.lowerBound, b.lowerBound );
    out.upperBound = b3Max( a.upperBound, b.upperBound );
    return out;
}

B3_INLINE b3AABB b3AABB_Inflate( b3AABB a, float extension )
{
    b3Vec3 radius = { extension, extension, extension };
 
    b3AABB out;
    out.lowerBound = b3Sub( a.lowerBound, radius );
    out.upperBound = b3Add( a.upperBound, radius );
    return out;
}

B3_INLINE bool b3AABB_Overlaps( b3AABB a, b3AABB b )
{
    // No intersection if separated along one axis
    if ( a.upperBound.x < b.lowerBound.x || a.lowerBound.x > b.upperBound.x )
        return false;
    if ( a.upperBound.y < b.lowerBound.y || a.lowerBound.y > b.upperBound.y )
        return false;
    if ( a.upperBound.z < b.lowerBound.z || a.lowerBound.z > b.upperBound.z )
        return false;
 
    // Overlapping on all axis means bounds are intersecting
    return true;
}

B3_INLINE b3AABB b3AABB_Transform( b3Transform transform, b3AABB a )
{
    b3Vec3 center = b3TransformPoint( transform, b3AABB_Center( a ) );
    b3Matrix3 m = b3MakeMatrixFromQuat( transform.q );
    b3Vec3 extent = b3MulMV( b3AbsMatrix3( m ), b3AABB_Extents( a ) );
    b3AABB out = { b3Sub( center, extent ), b3Add( center, extent ) };
    return out;
}

B3_INLINE b3Vec3 b3ClosestPointToAABB( b3Vec3 point, b3AABB a )
{
    return b3Clamp( point, a.lowerBound, a.upperBound );
}

typedef struct b3SegmentDistanceResult
{
    b3Vec3 point1;
    float fraction1;
    b3Vec3 point2;
    float fraction2;
} b3SegmentDistanceResult;

B3_API b3Vec3 b3PointToSegmentDistance( b3Vec3 a, b3Vec3 b, b3Vec3 q );

B3_API b3SegmentDistanceResult b3LineDistance( b3Vec3 p1, b3Vec3 d1, b3Vec3 p2, b3Vec3 d2 );

B3_API b3SegmentDistanceResult b3SegmentDistance( b3Vec3 p1, b3Vec3 q1, b3Vec3 p2, b3Vec3 q2 );

B3_API bool b3IsValidFloat( float a );

B3_API bool b3IsValidVec3( b3Vec3 a );

B3_API bool b3IsValidQuat( b3Quat q );

B3_API bool b3IsValidTransform( b3Transform a );

B3_API bool b3IsValidMatrix3( b3Matrix3 a );

B3_API bool b3IsValidAABB( b3AABB a );

B3_API bool b3IsBoundedAABB( b3AABB a );

B3_API bool b3IsSaneAABB( b3AABB a );

B3_API bool b3IsValidPlane( b3Plane a );

B3_API bool b3IsValidPosition( b3Pos p );

B3_API bool b3IsValidWorldTransform( b3WorldTransform t );
 // math

 
#ifdef __cplusplus

B3_FORCE_INLINE b3Vec3& operator+=( b3Vec3& a, b3Vec3 b )
{
    a.x += b.x;
    a.y += b.y;
    a.z += b.z;
    return a;
}

B3_FORCE_INLINE b3Vec3& operator-=( b3Vec3& a, b3Vec3 b )
{
    a.x -= b.x;
    a.y -= b.y;
    a.z -= b.z;
    return a;
}

B3_FORCE_INLINE b3Vec3& operator*=( b3Vec3& a, float s )
{
    a.x *= s;
    a.y *= s;
    a.z *= s;
    return a;
}

B3_FORCE_INLINE b3Vec3 operator-( b3Vec3 a )
{
    return { -a.x, -a.y, -a.z };
}

B3_FORCE_INLINE b3Vec3 operator*( float s, b3Vec3 a )
{
    return { s * a.x, s * a.y, s * a.z };
}

B3_FORCE_INLINE b3Vec3 operator*( b3Vec3 a, float s )
{
    return { s * a.x, s * a.y, s * a.z };
}

B3_FORCE_INLINE b3Vec3 operator*( b3Vec3 a, b3Vec3 b )
{
    return { a.x * b.x, a.y * b.y, a.z * b.z };
}

B3_FORCE_INLINE b3Vec3 operator+( b3Vec3 a, b3Vec3 b )
{
    return { a.x + b.x, a.y + b.y, a.z + b.z };
}

B3_FORCE_INLINE b3Vec3 operator-( b3Vec3 a, b3Vec3 b )
{
    return { a.x - b.x, a.y - b.y, a.z - b.z };
}
 
#if defined( BOX3D_DOUBLE_PRECISION )

B3_FORCE_INLINE b3Pos operator+( b3Pos a, b3Vec3 b )
{
    return { a.x + b.x, a.y + b.y, a.z + b.z };
}

B3_FORCE_INLINE b3Pos operator-( b3Pos a, b3Vec3 b )
{
    return { a.x - b.x, a.y - b.y, a.z - b.z };
}

B3_FORCE_INLINE b3Vec3 operator-( b3Pos a, b3Pos b )
{
    return { (float)( a.x - b.x ), (float)( a.y - b.y ), (float)( a.z - b.z ) };
}
 
#endif
 
#endif
 // math_cpp