b2_math.h

// MIT License
 
// Copyright (c) 2019 Erin Catto
 
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
 
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
 
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
 
#ifndef B2_MATH_H
#define B2_MATH_H
 
#include <math.h>
 
#include "b2_api.h"
#include "b2_settings.h"
 
inline bool b2IsValid(float x)
{
    return isfinite(x);
}
 
#define b2Sqrt(x)   sqrtf(x)
#define b2Atan2(y, x)   atan2f(y, x)
 
struct B2_API b2Vec2
{
    b2Vec2() = default;
 
    b2Vec2(float xIn, float yIn) : x(xIn), y(yIn) {}
 
    void SetZero() { x = 0.0f; y = 0.0f; }
 
    void Set(float x_, float y_) { x = x_; y = y_; }
 
    b2Vec2 operator -() const { b2Vec2 v; v.Set(-x, -y); return v; }
 
    float operator () (int32 i) const
    {
        return (&x)[i];
    }
 
    float& operator () (int32 i)
    {
        return (&x)[i];
    }
 
    void operator += (const b2Vec2& v)
    {
        x += v.x; y += v.y;
    }
 
    void operator -= (const b2Vec2& v)
    {
        x -= v.x; y -= v.y;
    }
 
    void operator *= (float a)
    {
        x *= a; y *= a;
    }
 
    float Length() const
    {
        return b2Sqrt(x * x + y * y);
    }
 
    float LengthSquared() const
    {
        return x * x + y * y;
    }
 
    float Normalize()
    {
        float length = Length();
        if (length < b2_epsilon)
        {
            return 0.0f;
        }
        float invLength = 1.0f / length;
        x *= invLength;
        y *= invLength;
 
        return length;
    }
 
    bool IsValid() const
    {
        return b2IsValid(x) && b2IsValid(y);
    }
 
    b2Vec2 Skew() const
    {
        return b2Vec2(-y, x);
    }
 
    float x, y;
};
 
struct B2_API b2Vec3
{
    b2Vec3() = default;
 
    b2Vec3(float xIn, float yIn, float zIn) : x(xIn), y(yIn), z(zIn) {}
 
    void SetZero() { x = 0.0f; y = 0.0f; z = 0.0f; }
 
    void Set(float x_, float y_, float z_) { x = x_; y = y_; z = z_; }
 
    b2Vec3 operator -() const { b2Vec3 v; v.Set(-x, -y, -z); return v; }
 
    void operator += (const b2Vec3& v)
    {
        x += v.x; y += v.y; z += v.z;
    }
 
    void operator -= (const b2Vec3& v)
    {
        x -= v.x; y -= v.y; z -= v.z;
    }
 
    void operator *= (float s)
    {
        x *= s; y *= s; z *= s;
    }
 
    float x, y, z;
};
 
struct B2_API b2Mat22
{
    b2Mat22() = default;
 
    b2Mat22(const b2Vec2& c1, const b2Vec2& c2)
    {
        ex = c1;
        ey = c2;
    }
 
    b2Mat22(float a11, float a12, float a21, float a22)
    {
        ex.x = a11; ex.y = a21;
        ey.x = a12; ey.y = a22;
    }
 
    void Set(const b2Vec2& c1, const b2Vec2& c2)
    {
        ex = c1;
        ey = c2;
    }
 
    void SetIdentity()
    {
        ex.x = 1.0f; ey.x = 0.0f;
        ex.y = 0.0f; ey.y = 1.0f;
    }
 
    void SetZero()
    {
        ex.x = 0.0f; ey.x = 0.0f;
        ex.y = 0.0f; ey.y = 0.0f;
    }
 
    b2Mat22 GetInverse() const
    {
        float a = ex.x, b = ey.x, c = ex.y, d = ey.y;
        b2Mat22 B;
        float det = a * d - b * c;
        if (det != 0.0f)
        {
            det = 1.0f / det;
        }
        B.ex.x =  det * d;  B.ey.x = -det * b;
        B.ex.y = -det * c;  B.ey.y =  det * a;
        return B;
    }
 
    b2Vec2 Solve(const b2Vec2& b) const
    {
        float a11 = ex.x, a12 = ey.x, a21 = ex.y, a22 = ey.y;
        float det = a11 * a22 - a12 * a21;
        if (det != 0.0f)
        {
            det = 1.0f / det;
        }
        b2Vec2 x;
        x.x = det * (a22 * b.x - a12 * b.y);
        x.y = det * (a11 * b.y - a21 * b.x);
        return x;
    }
 
    b2Vec2 ex, ey;
};
 
struct B2_API b2Mat33
{
    b2Mat33() = default;
 
    b2Mat33(const b2Vec3& c1, const b2Vec3& c2, const b2Vec3& c3)
    {
        ex = c1;
        ey = c2;
        ez = c3;
    }
 
    void SetZero()
    {
        ex.SetZero();
        ey.SetZero();
        ez.SetZero();
    }
 
    b2Vec3 Solve33(const b2Vec3& b) const;
 
    b2Vec2 Solve22(const b2Vec2& b) const;
 
    void GetInverse22(b2Mat33* M) const;
 
    void GetSymInverse33(b2Mat33* M) const;
 
    b2Vec3 ex, ey, ez;
};
 
struct B2_API b2Rot
{
    b2Rot() = default;
 
    explicit b2Rot(float angle)
    {
        s = sinf(angle);
        c = cosf(angle);
    }
 
    void Set(float angle)
    {
        s = sinf(angle);
        c = cosf(angle);
    }
 
    void SetIdentity()
    {
        s = 0.0f;
        c = 1.0f;
    }
 
    float GetAngle() const
    {
        return b2Atan2(s, c);
    }
 
    b2Vec2 GetXAxis() const
    {
        return b2Vec2(c, s);
    }
 
    b2Vec2 GetYAxis() const
    {
        return b2Vec2(-s, c);
    }
 
    float s, c;
};
 
struct B2_API b2Transform
{
    b2Transform() = default;
 
    b2Transform(const b2Vec2& position, const b2Rot& rotation) : p(position), q(rotation) {}
 
    void SetIdentity()
    {
        p.SetZero();
        q.SetIdentity();
    }
 
    void Set(const b2Vec2& position, float angle)
    {
        p = position;
        q.Set(angle);
    }
 
    b2Vec2 p;
    b2Rot q;
};
 
struct B2_API b2Sweep
{
    b2Sweep() = default;
 
    void GetTransform(b2Transform* transform, float beta) const;
 
    void Advance(float alpha);
 
    void Normalize();
 
    b2Vec2 localCenter; 
    b2Vec2 c0, c;       
    float a0, a;        
 
    float alpha0;
};
 
extern B2_API const b2Vec2 b2Vec2_zero;
 
inline float b2Dot(const b2Vec2& a, const b2Vec2& b)
{
    return a.x * b.x + a.y * b.y;
}
 
inline float b2Cross(const b2Vec2& a, const b2Vec2& b)
{
    return a.x * b.y - a.y * b.x;
}
 
inline b2Vec2 b2Cross(const b2Vec2& a, float s)
{
    return b2Vec2(s * a.y, -s * a.x);
}
 
inline b2Vec2 b2Cross(float s, const b2Vec2& a)
{
    return b2Vec2(-s * a.y, s * a.x);
}
 
inline b2Vec2 b2Mul(const b2Mat22& A, const b2Vec2& v)
{
    return b2Vec2(A.ex.x * v.x + A.ey.x * v.y, A.ex.y * v.x + A.ey.y * v.y);
}
 
inline b2Vec2 b2MulT(const b2Mat22& A, const b2Vec2& v)
{
    return b2Vec2(b2Dot(v, A.ex), b2Dot(v, A.ey));
}
 
inline b2Vec2 operator + (const b2Vec2& a, const b2Vec2& b)
{
    return b2Vec2(a.x + b.x, a.y + b.y);
}
 
inline b2Vec2 operator - (const b2Vec2& a, const b2Vec2& b)
{
    return b2Vec2(a.x - b.x, a.y - b.y);
}
 
inline b2Vec2 operator * (float s, const b2Vec2& a)
{
    return b2Vec2(s * a.x, s * a.y);
}
 
inline bool operator == (const b2Vec2& a, const b2Vec2& b)
{
    return a.x == b.x && a.y == b.y;
}
 
inline bool operator != (const b2Vec2& a, const b2Vec2& b)
{
    return a.x != b.x || a.y != b.y;
}
 
inline float b2Distance(const b2Vec2& a, const b2Vec2& b)
{
    b2Vec2 c = a - b;
    return c.Length();
}
 
inline float b2DistanceSquared(const b2Vec2& a, const b2Vec2& b)
{
    b2Vec2 c = a - b;
    return b2Dot(c, c);
}
 
inline b2Vec3 operator * (float s, const b2Vec3& a)
{
    return b2Vec3(s * a.x, s * a.y, s * a.z);
}
 
inline b2Vec3 operator + (const b2Vec3& a, const b2Vec3& b)
{
    return b2Vec3(a.x + b.x, a.y + b.y, a.z + b.z);
}
 
inline b2Vec3 operator - (const b2Vec3& a, const b2Vec3& b)
{
    return b2Vec3(a.x - b.x, a.y - b.y, a.z - b.z);
}
 
inline float b2Dot(const b2Vec3& a, const b2Vec3& b)
{
    return a.x * b.x + a.y * b.y + a.z * b.z;
}
 
inline b2Vec3 b2Cross(const b2Vec3& a, const b2Vec3& b)
{
    return b2Vec3(a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x);
}
 
inline b2Mat22 operator + (const b2Mat22& A, const b2Mat22& B)
{
    return b2Mat22(A.ex + B.ex, A.ey + B.ey);
}
 
// A * B
inline b2Mat22 b2Mul(const b2Mat22& A, const b2Mat22& B)
{
    return b2Mat22(b2Mul(A, B.ex), b2Mul(A, B.ey));
}
 
// A^T * B
inline b2Mat22 b2MulT(const b2Mat22& A, const b2Mat22& B)
{
    b2Vec2 c1(b2Dot(A.ex, B.ex), b2Dot(A.ey, B.ex));
    b2Vec2 c2(b2Dot(A.ex, B.ey), b2Dot(A.ey, B.ey));
    return b2Mat22(c1, c2);
}
 
inline b2Vec3 b2Mul(const b2Mat33& A, const b2Vec3& v)
{
    return v.x * A.ex + v.y * A.ey + v.z * A.ez;
}
 
inline b2Vec2 b2Mul22(const b2Mat33& A, const b2Vec2& v)
{
    return b2Vec2(A.ex.x * v.x + A.ey.x * v.y, A.ex.y * v.x + A.ey.y * v.y);
}
 
inline b2Rot b2Mul(const b2Rot& q, const 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 = qs * rc + qc * rs
    // c = 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;
}
 
inline b2Rot b2MulT(const b2Rot& q, const 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 = qc * rs - qs * rc
    // c = 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;
}
 
inline b2Vec2 b2Mul(const b2Rot& q, const b2Vec2& v)
{
    return b2Vec2(q.c * v.x - q.s * v.y, q.s * v.x + q.c * v.y);
}
 
inline b2Vec2 b2MulT(const b2Rot& q, const b2Vec2& v)
{
    return b2Vec2(q.c * v.x + q.s * v.y, -q.s * v.x + q.c * v.y);
}
 
inline b2Vec2 b2Mul(const b2Transform& T, const b2Vec2& v)
{
    float x = (T.q.c * v.x - T.q.s * v.y) + T.p.x;
    float y = (T.q.s * v.x + T.q.c * v.y) + T.p.y;
 
    return b2Vec2(x, y);
}
 
inline b2Vec2 b2MulT(const b2Transform& T, const b2Vec2& v)
{
    float px = v.x - T.p.x;
    float py = v.y - T.p.y;
    float x = (T.q.c * px + T.q.s * py);
    float y = (-T.q.s * px + T.q.c * py);
 
    return b2Vec2(x, y);
}
 
// 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
inline b2Transform b2Mul(const b2Transform& A, const b2Transform& B)
{
    b2Transform C;
    C.q = b2Mul(A.q, B.q);
    C.p = b2Mul(A.q, B.p) + A.p;
    return C;
}
 
// v2 = A.q' * (B.q * v1 + B.p - A.p)
//    = A.q' * B.q * v1 + A.q' * (B.p - A.p)
inline b2Transform b2MulT(const b2Transform& A, const b2Transform& B)
{
    b2Transform C;
    C.q = b2MulT(A.q, B.q);
    C.p = b2MulT(A.q, B.p - A.p);
    return C;
}
 
template <typename T>
inline T b2Abs(T a)
{
    return a > T(0) ? a : -a;
}
 
inline b2Vec2 b2Abs(const b2Vec2& a)
{
    return b2Vec2(b2Abs(a.x), b2Abs(a.y));
}
 
inline b2Mat22 b2Abs(const b2Mat22& A)
{
    return b2Mat22(b2Abs(A.ex), b2Abs(A.ey));
}
 
template <typename T>
inline T b2Min(T a, T b)
{
    return a < b ? a : b;
}
 
inline b2Vec2 b2Min(const b2Vec2& a, const b2Vec2& b)
{
    return b2Vec2(b2Min(a.x, b.x), b2Min(a.y, b.y));
}
 
template <typename T>
inline T b2Max(T a, T b)
{
    return a > b ? a : b;
}
 
inline b2Vec2 b2Max(const b2Vec2& a, const b2Vec2& b)
{
    return b2Vec2(b2Max(a.x, b.x), b2Max(a.y, b.y));
}
 
template <typename T>
inline T b2Clamp(T a, T low, T high)
{
    return b2Max(low, b2Min(a, high));
}
 
inline b2Vec2 b2Clamp(const b2Vec2& a, const b2Vec2& low, const b2Vec2& high)
{
    return b2Max(low, b2Min(a, high));
}
 
template<typename T> inline void b2Swap(T& a, T& b)
{
    T tmp = a;
    a = b;
    b = tmp;
}
 
inline uint32 b2NextPowerOfTwo(uint32 x)
{
    x |= (x >> 1);
    x |= (x >> 2);
    x |= (x >> 4);
    x |= (x >> 8);
    x |= (x >> 16);
    return x + 1;
}
 
inline bool b2IsPowerOfTwo(uint32 x)
{
    bool result = x > 0 && (x & (x - 1)) == 0;
    return result;
}
 
// https://fgiesen.wordpress.com/2012/08/15/linear-interpolation-past-present-and-future/
inline void b2Sweep::GetTransform(b2Transform* xf, float beta) const
{
    xf->p = (1.0f - beta) * c0 + beta * c;
    float angle = (1.0f - beta) * a0 + beta * a;
    xf->q.Set(angle);
 
    // Shift to origin
    xf->p -= b2Mul(xf->q, localCenter);
}
 
inline void b2Sweep::Advance(float alpha)
{
    b2Assert(alpha0 < 1.0f);
    float beta = (alpha - alpha0) / (1.0f - alpha0);
    c0 += beta * (c - c0);
    a0 += beta * (a - a0);
    alpha0 = alpha;
}
 
inline void b2Sweep::Normalize()
{
    float twoPi = 2.0f * b2_pi;
    float d =  twoPi * floorf(a0 / twoPi);
    a0 -= d;
    a -= d;
}
 
#endif