math_functions.h

// SPDX-FileCopyrightText: 2023 Erin Catto
// SPDX-License-Identifier: MIT
 
#pragma once
 
#include "base.h"
 
#include <float.h>
#include <math.h>
#include <stdbool.h>
 
#define b2_pi 3.14159265359f
 
typedef struct b2Vec2
{
    float x, y;
} b2Vec2;
 
typedef struct b2Rot
{
    float c, s;
} b2Rot;
 
typedef struct b2Transform
{
    b2Vec2 p;
    b2Rot q;
} b2Transform;
 
typedef struct b2Mat22
{
    b2Vec2 cx, cy;
} b2Mat22;
 
typedef struct b2AABB
{
    b2Vec2 lowerBound;
    b2Vec2 upperBound;
} b2AABB;
 
static const b2Vec2 b2Vec2_zero = { 0.0f, 0.0f };
static const b2Rot b2Rot_identity = { 1.0f, 0.0f };
static const b2Transform b2Transform_identity = { { 0.0f, 0.0f }, { 1.0f, 0.0f } };
static const b2Mat22 b2Mat22_zero = { { 0.0f, 0.0f }, { 0.0f, 0.0f } };
 
B2_API float b2Atan2( float y, float x );
 
B2_INLINE float b2MinFloat( float a, float b )
{
    return a < b ? a : b;
}
 
B2_INLINE float b2MaxFloat( float a, float b )
{
    return a > b ? a : b;
}
 
B2_INLINE float b2AbsFloat( float a )
{
    return a < 0 ? -a : a;
}
 
B2_INLINE float b2ClampFloat( float a, float lower, float upper )
{
    return a < lower ? lower : ( a > upper ? upper : a );
}
 
B2_INLINE int b2MinInt( int a, int b )
{
    return a < b ? a : b;
}
 
B2_INLINE int b2MaxInt( int a, int b )
{
    return a > b ? a : b;
}
 
B2_INLINE int b2AbsInt( int a )
{
    return a < 0 ? -a : a;
}
 
B2_INLINE int b2ClampInt( int a, int lower, int upper )
{
    return a < lower ? lower : ( a > upper ? upper : a );
}
 
B2_INLINE float b2Dot( b2Vec2 a, b2Vec2 b )
{
    return a.x * b.x + a.y * b.y;
}
 
B2_INLINE float b2Cross( b2Vec2 a, b2Vec2 b )
{
    return a.x * b.y - a.y * b.x;
}
 
B2_INLINE b2Vec2 b2CrossVS( b2Vec2 v, float s )
{
    return B2_LITERAL( b2Vec2 ){ s * v.y, -s * v.x };
}
 
B2_INLINE b2Vec2 b2CrossSV( float s, b2Vec2 v )
{
    return B2_LITERAL( b2Vec2 ){ -s * v.y, s * v.x };
}
 
B2_INLINE b2Vec2 b2LeftPerp( b2Vec2 v )
{
    return B2_LITERAL( b2Vec2 ){ -v.y, v.x };
}
 
B2_INLINE b2Vec2 b2RightPerp( b2Vec2 v )
{
    return B2_LITERAL( b2Vec2 ){ v.y, -v.x };
}
 
B2_INLINE b2Vec2 b2Add( b2Vec2 a, b2Vec2 b )
{
    return B2_LITERAL( b2Vec2 ){ a.x + b.x, a.y + b.y };
}
 
B2_INLINE b2Vec2 b2Sub( b2Vec2 a, b2Vec2 b )
{
    return B2_LITERAL( b2Vec2 ){ a.x - b.x, a.y - b.y };
}
 
B2_INLINE b2Vec2 b2Neg( b2Vec2 a )
{
    return B2_LITERAL( b2Vec2 ){ -a.x, -a.y };
}
 
B2_INLINE b2Vec2 b2Lerp( b2Vec2 a, b2Vec2 b, float t )
{
    return B2_LITERAL( b2Vec2 ){ ( 1.0f - t ) * a.x + t * b.x, ( 1.0f - t ) * a.y + t * b.y };
}
 
B2_INLINE b2Vec2 b2Mul( b2Vec2 a, b2Vec2 b )
{
    return B2_LITERAL( b2Vec2 ){ a.x * b.x, a.y * b.y };
}
 
B2_INLINE b2Vec2 b2MulSV( float s, b2Vec2 v )
{
    return B2_LITERAL( b2Vec2 ){ s * v.x, s * v.y };
}
 
B2_INLINE b2Vec2 b2MulAdd( b2Vec2 a, float s, b2Vec2 b )
{
    return B2_LITERAL( b2Vec2 ){ a.x + s * b.x, a.y + s * b.y };
}
 
B2_INLINE b2Vec2 b2MulSub( b2Vec2 a, float s, b2Vec2 b )
{
    return B2_LITERAL( b2Vec2 ){ a.x - s * b.x, a.y - s * b.y };
}
 
B2_INLINE b2Vec2 b2Abs( b2Vec2 a )
{
    b2Vec2 b;
    b.x = b2AbsFloat( a.x );
    b.y = b2AbsFloat( a.y );
    return b;
}
 
B2_INLINE b2Vec2 b2Min( b2Vec2 a, b2Vec2 b )
{
    b2Vec2 c;
    c.x = b2MinFloat( a.x, b.x );
    c.y = b2MinFloat( a.y, b.y );
    return c;
}
 
B2_INLINE b2Vec2 b2Max( b2Vec2 a, b2Vec2 b )
{
    b2Vec2 c;
    c.x = b2MaxFloat( a.x, b.x );
    c.y = b2MaxFloat( a.y, b.y );
    return c;
}
 
B2_INLINE b2Vec2 b2Clamp( b2Vec2 v, b2Vec2 a, b2Vec2 b )
{
    b2Vec2 c;
    c.x = b2ClampFloat( v.x, a.x, b.x );
    c.y = b2ClampFloat( v.y, a.y, b.y );
    return c;
}
 
B2_INLINE float b2Length( b2Vec2 v )
{
    return sqrtf( v.x * v.x + v.y * v.y );
}
 
B2_INLINE float b2Distance( b2Vec2 a, b2Vec2 b )
{
    float dx = b.x - a.x;
    float dy = b.y - a.y;
    return sqrtf( dx * dx + dy * dy );
}
 
B2_INLINE b2Vec2 b2Normalize( b2Vec2 v )
{
    float length = sqrtf( v.x * v.x + v.y * v.y );
    if ( length < FLT_EPSILON )
    {
        return b2Vec2_zero;
    }
 
    float invLength = 1.0f / length;
    b2Vec2 n = { invLength * v.x, invLength * v.y };
    return n;
}
 
B2_INLINE b2Vec2 b2GetLengthAndNormalize( float* length, b2Vec2 v )
{
    *length = b2Length( v );
    if ( *length < FLT_EPSILON )
    {
        return b2Vec2_zero;
    }
 
    float invLength = 1.0f / *length;
    b2Vec2 n = { invLength * v.x, invLength * v.y };
    return n;
}
 
B2_INLINE b2Rot b2NormalizeRot( b2Rot q )
{
    float mag = sqrtf( q.s * q.s + q.c * q.c );
    float invMag = mag > 0.0 ? 1.0f / mag : 0.0f;
    b2Rot qn = { q.c * invMag, q.s * invMag };
    return qn;
}
 
B2_INLINE b2Rot b2IntegrateRotation( b2Rot q1, float deltaAngle )
{
    // dc/dt = -omega * sin(t)
    // ds/dt = omega * cos(t)
    // c2 = c1 - omega * h * s1
    // s2 = s1 + omega * h * c1
    b2Rot q2 = { q1.c - deltaAngle * q1.s, q1.s + deltaAngle * q1.c };
    float mag = sqrtf( q2.s * q2.s + q2.c * q2.c );
    float invMag = mag > 0.0 ? 1.0f / mag : 0.0f;
    b2Rot qn = { q2.c * invMag, q2.s * invMag };
    return qn;
}
 
B2_INLINE float b2LengthSquared( b2Vec2 v )
{
    return v.x * v.x + v.y * v.y;
}
 
B2_INLINE float b2DistanceSquared( b2Vec2 a, b2Vec2 b )
{
    b2Vec2 c = { b.x - a.x, b.y - a.y };
    return c.x * c.x + c.y * c.y;
}
 
B2_API b2Rot b2MakeRot( float angle );
 
B2_INLINE bool b2IsNormalized( b2Rot q )
{
    // larger tolerance due to failure on mingw 32-bit
    float qq = q.s * q.s + q.c * q.c;
    return 1.0f - 0.0006f < qq && qq < 1.0f + 0.0006f;
}
 
B2_INLINE b2Rot b2NLerp( b2Rot q1, b2Rot q2, float t )
{
    float omt = 1.0f - t;
    b2Rot q = {
        omt * q1.c + t * q2.c,
        omt * q1.s + t * q2.s,
    };
 
    return b2NormalizeRot( q );
}
 
 
B2_INLINE float b2ComputeAngularVelocity( b2Rot q1, b2Rot q2, float inv_h )
{
    // ds/dt = omega * cos(t)
    // dc/dt = -omega * sin(t)
    // s2 = s1 + omega * h * c1
    // c2 = c1 - omega * h * s1
 
    // omega * h * s1 = c1 - c2
    // omega * h * c1 = s2 - s1
    // omega * h = (c1 - c2) * s1 + (s2 - s1) * c1;
    // omega * h = s1 * c1 - c2 * s1 + s2 * c1 - s1 * c1
    // omega * h = s2 * c1 - c2 * s1 = sin(a2 - a1) ~= a2 - a1 for small delta
    float omega = inv_h * ( q2.s * q1.c - q2.c * q1.s );
    return omega;
}
 
B2_INLINE float b2Rot_GetAngle( b2Rot q )
{
    return b2Atan2( q.s, q.c );
}
 
B2_INLINE b2Vec2 b2Rot_GetXAxis( b2Rot q )
{
    b2Vec2 v = { q.c, q.s };
    return v;
}
 
B2_INLINE b2Vec2 b2Rot_GetYAxis( b2Rot q )
{
    b2Vec2 v = { -q.s, q.c };
    return v;
}
 
B2_INLINE b2Rot b2MulRot( b2Rot q, b2Rot r )
{
    // [qc -qs] * [rc -rs] = [qc*rc-qs*rs -qc*rs-qs*rc]
    // [qs  qc]   [rs  rc]   [qs*rc+qc*rs -qs*rs+qc*rc]
    // s(q + r) = qs * rc + qc * rs
    // c(q + r) = qc * rc - qs * rs
    b2Rot qr;
    qr.s = q.s * r.c + q.c * r.s;
    qr.c = q.c * r.c - q.s * r.s;
    return qr;
}
 
B2_INLINE b2Rot b2InvMulRot( b2Rot q, b2Rot r )
{
    // [ qc qs] * [rc -rs] = [qc*rc+qs*rs -qc*rs+qs*rc]
    // [-qs qc]   [rs  rc]   [-qs*rc+qc*rs qs*rs+qc*rc]
    // s(q - r) = qc * rs - qs * rc
    // c(q - r) = qc * rc + qs * rs
    b2Rot qr;
    qr.s = q.c * r.s - q.s * r.c;
    qr.c = q.c * r.c + q.s * r.s;
    return qr;
}
 
B2_INLINE float b2RelativeAngle( b2Rot b, b2Rot a )
{
    // sin(b - a) = bs * ac - bc * as
    // cos(b - a) = bc * ac + bs * as
    float s = b.s * a.c - b.c * a.s;
    float c = b.c * a.c + b.s * a.s;
    return b2Atan2( s, c );
}
 
B2_INLINE float b2UnwindAngle( float angle )
{
    if ( angle < -b2_pi )
    {
        return angle + 2.0f * b2_pi;
    }
    else if ( angle > b2_pi )
    {
        return angle - 2.0f * b2_pi;
    }
 
    return angle;
}
 
B2_INLINE float b2UnwindLargeAngle( float angle )
{
    while ( angle > b2_pi )
    {
        angle -= 2.0f * b2_pi;
    }
 
    while ( angle < -b2_pi )
    {
        angle += 2.0f * b2_pi;
    }
 
    return angle;
}
 
B2_INLINE b2Vec2 b2RotateVector( b2Rot q, b2Vec2 v )
{
    return B2_LITERAL( b2Vec2 ){ q.c * v.x - q.s * v.y, q.s * v.x + q.c * v.y };
}
 
B2_INLINE b2Vec2 b2InvRotateVector( b2Rot q, b2Vec2 v )
{
    return B2_LITERAL( b2Vec2 ){ q.c * v.x + q.s * v.y, -q.s * v.x + q.c * v.y };
}
 
B2_INLINE b2Vec2 b2TransformPoint( b2Transform t, const b2Vec2 p )
{
    float x = ( t.q.c * p.x - t.q.s * p.y ) + t.p.x;
    float y = ( t.q.s * p.x + t.q.c * p.y ) + t.p.y;
 
    return B2_LITERAL( b2Vec2 ){ x, y };
}
 
B2_INLINE b2Vec2 b2InvTransformPoint( b2Transform t, const b2Vec2 p )
{
    float vx = p.x - t.p.x;
    float vy = p.y - t.p.y;
    return B2_LITERAL( b2Vec2 ){ t.q.c * vx + t.q.s * vy, -t.q.s * vx + t.q.c * vy };
}
 
B2_INLINE b2Transform b2MulTransforms( b2Transform A, b2Transform B )
{
    b2Transform C;
    C.q = b2MulRot( A.q, B.q );
    C.p = b2Add( b2RotateVector( A.q, B.p ), A.p );
    return C;
}
 
B2_INLINE b2Transform b2InvMulTransforms( b2Transform A, b2Transform B )
{
    b2Transform C;
    C.q = b2InvMulRot( A.q, B.q );
    C.p = b2InvRotateVector( A.q, b2Sub( B.p, A.p ) );
    return C;
}
 
B2_INLINE b2Vec2 b2MulMV( b2Mat22 A, b2Vec2 v )
{
    b2Vec2 u = {
        A.cx.x * v.x + A.cy.x * v.y,
        A.cx.y * v.x + A.cy.y * v.y,
    };
    return u;
}
 
B2_INLINE b2Mat22 b2GetInverse22( b2Mat22 A )
{
    float a = A.cx.x, b = A.cy.x, c = A.cx.y, d = A.cy.y;
    float det = a * d - b * c;
    if ( det != 0.0f )
    {
        det = 1.0f / det;
    }
 
    b2Mat22 B = {
        { det * d, -det * c },
        { -det * b, det * a },
    };
    return B;
}
 
B2_INLINE b2Vec2 b2Solve22( b2Mat22 A, b2Vec2 b )
{
    float a11 = A.cx.x, a12 = A.cy.x, a21 = A.cx.y, a22 = A.cy.y;
    float det = a11 * a22 - a12 * a21;
    if ( det != 0.0f )
    {
        det = 1.0f / det;
    }
    b2Vec2 x = { det * ( a22 * b.x - a12 * b.y ), det * ( a11 * b.y - a21 * b.x ) };
    return x;
}
 
B2_INLINE bool b2AABB_Contains( b2AABB a, b2AABB b )
{
    bool s = true;
    s = s && a.lowerBound.x <= b.lowerBound.x;
    s = s && a.lowerBound.y <= b.lowerBound.y;
    s = s && b.upperBound.x <= a.upperBound.x;
    s = s && b.upperBound.y <= a.upperBound.y;
    return s;
}
 
B2_INLINE b2Vec2 b2AABB_Center( b2AABB a )
{
    b2Vec2 b = { 0.5f * ( a.lowerBound.x + a.upperBound.x ), 0.5f * ( a.lowerBound.y + a.upperBound.y ) };
    return b;
}
 
B2_INLINE b2Vec2 b2AABB_Extents( b2AABB a )
{
    b2Vec2 b = { 0.5f * ( a.upperBound.x - a.lowerBound.x ), 0.5f * ( a.upperBound.y - a.lowerBound.y ) };
    return b;
}
 
B2_INLINE b2AABB b2AABB_Union( b2AABB a, b2AABB b )
{
    b2AABB c;
    c.lowerBound.x = b2MinFloat( a.lowerBound.x, b.lowerBound.x );
    c.lowerBound.y = b2MinFloat( a.lowerBound.y, b.lowerBound.y );
    c.upperBound.x = b2MaxFloat( a.upperBound.x, b.upperBound.x );
    c.upperBound.y = b2MaxFloat( a.upperBound.y, b.upperBound.y );
    return c;
}
 
B2_API bool b2IsValid( float a );
 
B2_API bool b2Vec2_IsValid( b2Vec2 v );
 
B2_API bool b2Rot_IsValid( b2Rot q );
 
B2_API bool b2AABB_IsValid( b2AABB aabb );
 
B2_API void b2SetLengthUnitsPerMeter( float lengthUnits );
 
B2_API float b2GetLengthUnitsPerMeter( void );
 
#ifdef __cplusplus
 
inline void operator+=( b2Vec2& a, b2Vec2 b )
{
    a.x += b.x;
    a.y += b.y;
}
 
inline void operator-=( b2Vec2& a, b2Vec2 b )
{
    a.x -= b.x;
    a.y -= b.y;
}
 
inline void operator*=( b2Vec2& a, float b )
{
    a.x *= b;
    a.y *= b;
}
 
inline b2Vec2 operator-( b2Vec2 a )
{
    return { -a.x, -a.y };
}
 
inline b2Vec2 operator+( b2Vec2 a, b2Vec2 b )
{
    return { a.x + b.x, a.y + b.y };
}
 
inline b2Vec2 operator-( b2Vec2 a, b2Vec2 b )
{
    return { a.x - b.x, a.y - b.y };
}
 
inline b2Vec2 operator*( float a, b2Vec2 b )
{
    return { a * b.x, a * b.y };
}
 
inline b2Vec2 operator*( b2Vec2 a, float b )
{
    return { a.x * b, a.y * b };
}
 
inline bool operator==( b2Vec2 a, b2Vec2 b )
{
    return a.x == b.x && a.y == b.y;
}
 
inline bool operator!=( b2Vec2 a, b2Vec2 b )
{
    return a.x != b.x || a.y != b.y;
}
 
#endif