File indexing completed on 2024-05-19 14:56:23

 /*
 * Copyright (c) 2006-2009 Erin Catto http://www.box2d.org
 *
 * This software is provided 'as-is', without any express or implied
 * warranty.  In no event will the authors be held liable for any damages
 * arising from the use of this software.
 * Permission is granted to anyone to use this software for any purpose,
 * including commercial applications, and to alter it and redistribute it
 * freely, subject to the following restrictions:
 * 1. The origin of this software must not be misrepresented; you must not
 * claim that you wrote the original software. If you use this software
 * in a product, an acknowledgment in the product documentation would be
 * appreciated but is not required.
 * 2. Altered source versions must be plainly marked as such, and must not be
 * misrepresented as being the original software.
 * 3. This notice may not be removed or altered from any source distribution.
 */
 
 #ifndef B2_MATH_H
 #define B2_MATH_H
 
 #include <Box2D/Common/b2Settings.h>
 #include <math.h>
 
 /// This function is used to ensure that a floating point number is not a NaN or infinity.
 inline bool b2IsValid(float32 x)
 {
     int32 ix = *reinterpret_cast<int32*>(&x);
     return (ix & 0x7f800000) != 0x7f800000;
 }
 
 /// This is a approximate yet fast inverse square-root.
 inline float32 b2InvSqrt(float32 x)
 {
     union
     {
         float32 x;
         int32 i;
     } convert;
 
     convert.x = x;
     float32 xhalf = 0.5f * x;
     convert.i = 0x5f3759df - (convert.i >> 1);
     x = convert.x;
     x = x * (1.5f - xhalf * x * x);
     return x;
 }
 
 #define b2Sqrt(x)   sqrtf(x)
 #define b2Atan2(y, x)   atan2f(y, x)
 
 /// A 2D column vector.
 struct b2Vec2
 {
     /// Default constructor does nothing (for performance).
     b2Vec2() {}
 
     /// Construct using coordinates.
     b2Vec2(float32 x, float32 y) : x(x), y(y) {}
 
     /// Set this vector to all zeros.
     void SetZero() { x = 0.0f; y = 0.0f; }
 
     /// Set this vector to some specified coordinates.
     void Set(float32 x_, float32 y_) { x = x_; y = y_; }
 
     /// Negate this vector.
     b2Vec2 operator -() const { b2Vec2 v; v.Set(-x, -y); return v; }
     
     /// Read from and indexed element.
     float32 operator () (int32 i) const
     {
         return (&x)[i];
     }
 
     /// Write to an indexed element.
     float32& operator () (int32 i)
     {
         return (&x)[i];
     }
 
     /// Add a vector to this vector.
     void operator += (const b2Vec2& v)
     {
         x += v.x; y += v.y;
     }
     
     /// Subtract a vector from this vector.
     void operator -= (const b2Vec2& v)
     {
         x -= v.x; y -= v.y;
     }
 
     /// Multiply this vector by a scalar.
     void operator *= (float32 a)
     {
         x *= a; y *= a;
     }
 
     /// Get the length of this vector (the norm).
     float32 Length() const
     {
         return b2Sqrt(x * x + y * y);
     }
 
     /// Get the length squared. For performance, use this instead of
     /// b2Vec2::Length (if possible).
     float32 LengthSquared() const
     {
         return x * x + y * y;
     }
 
     /// Convert this vector into a unit vector. Returns the length.
     float32 Normalize()
     {
         float32 length = Length();
         if (length < b2_epsilon)
         {
             return 0.0f;
         }
         float32 invLength = 1.0f / length;
         x *= invLength;
         y *= invLength;
 
         return length;
     }
 
     /// Does this vector contain finite coordinates?
     bool IsValid() const
     {
         return b2IsValid(x) && b2IsValid(y);
     }
 
     /// Get the skew vector such that dot(skew_vec, other) == cross(vec, other)
     b2Vec2 Skew() const
     {
         return b2Vec2(-y, x);
     }
 
     float32 x, y;
 };
 
 /// A 2D column vector with 3 elements.
 struct b2Vec3
 {
     /// Default constructor does nothing (for performance).
     b2Vec3() {}
 
     /// Construct using coordinates.
     b2Vec3(float32 x, float32 y, float32 z) : x(x), y(y), z(z) {}
 
     /// Set this vector to all zeros.
     void SetZero() { x = 0.0f; y = 0.0f; z = 0.0f; }
 
     /// Set this vector to some specified coordinates.
     void Set(float32 x_, float32 y_, float32 z_) { x = x_; y = y_; z = z_; }
 
     /// Negate this vector.
     b2Vec3 operator -() const { b2Vec3 v; v.Set(-x, -y, -z); return v; }
 
     /// Add a vector to this vector.
     void operator += (const b2Vec3& v)
     {
         x += v.x; y += v.y; z += v.z;
     }
 
     /// Subtract a vector from this vector.
     void operator -= (const b2Vec3& v)
     {
         x -= v.x; y -= v.y; z -= v.z;
     }
 
     /// Multiply this vector by a scalar.
     void operator *= (float32 s)
     {
         x *= s; y *= s; z *= s;
     }
 
     float32 x, y, z;
 };
 
 /// A 2-by-2 matrix. Stored in column-major order.
 struct b2Mat22
 {
     /// The default constructor does nothing (for performance).
     b2Mat22() {}
 
     /// Construct this matrix using columns.
     b2Mat22(const b2Vec2& c1, const b2Vec2& c2)
     {
         ex = c1;
         ey = c2;
     }
 
     /// Construct this matrix using scalars.
     b2Mat22(float32 a11, float32 a12, float32 a21, float32 a22)
     {
         ex.x = a11; ex.y = a21;
         ey.x = a12; ey.y = a22;
     }
 
     /// Initialize this matrix using columns.
     void Set(const b2Vec2& c1, const b2Vec2& c2)
     {
         ex = c1;
         ey = c2;
     }
 
     /// Set this to the identity matrix.
     void SetIdentity()
     {
         ex.x = 1.0f; ey.x = 0.0f;
         ex.y = 0.0f; ey.y = 1.0f;
     }
 
     /// Set this matrix to all zeros.
     void SetZero()
     {
         ex.x = 0.0f; ey.x = 0.0f;
         ex.y = 0.0f; ey.y = 0.0f;
     }
 
     b2Mat22 GetInverse() const
     {
         float32 a = ex.x, b = ey.x, c = ex.y, d = ey.y;
         b2Mat22 B;
         float32 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;
     }
 
     /// Solve A * x = b, where b is a column vector. This is more efficient
     /// than computing the inverse in one-shot cases.
     b2Vec2 Solve(const b2Vec2& b) const
     {
         float32 a11 = ex.x, a12 = ey.x, a21 = ex.y, a22 = ey.y;
         float32 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;
 };
 
 /// A 3-by-3 matrix. Stored in column-major order.
 struct b2Mat33
 {
     /// The default constructor does nothing (for performance).
     b2Mat33() {}
 
     /// Construct this matrix using columns.
     b2Mat33(const b2Vec3& c1, const b2Vec3& c2, const b2Vec3& c3)
     {
         ex = c1;
         ey = c2;
         ez = c3;
     }
 
     /// Set this matrix to all zeros.
     void SetZero()
     {
         ex.SetZero();
         ey.SetZero();
         ez.SetZero();
     }
 
     /// Solve A * x = b, where b is a column vector. This is more efficient
     /// than computing the inverse in one-shot cases.
     b2Vec3 Solve33(const b2Vec3& b) const;
 
     /// Solve A * x = b, where b is a column vector. This is more efficient
     /// than computing the inverse in one-shot cases. Solve only the upper
     /// 2-by-2 matrix equation.
     b2Vec2 Solve22(const b2Vec2& b) const;
 
     /// Get the inverse of this matrix as a 2-by-2.
     /// Returns the zero matrix if singular.
     void GetInverse22(b2Mat33* M) const;
 
     /// Get the symmetric inverse of this matrix as a 3-by-3.
     /// Returns the zero matrix if singular.
     void GetSymInverse33(b2Mat33* M) const;
 
     b2Vec3 ex, ey, ez;
 };
 
 /// Rotation
 struct b2Rot
 {
     b2Rot() {}
 
     /// Initialize from an angle in radians
     explicit b2Rot(float32 angle)
     {
         /// TODO_ERIN optimize
         s = sinf(angle);
         c = cosf(angle);
     }
 
     /// Set using an angle in radians.
     void Set(float32 angle)
     {
         /// TODO_ERIN optimize
         s = sinf(angle);
         c = cosf(angle);
     }
 
     /// Set to the identity rotation
     void SetIdentity()
     {
         s = 0.0f;
         c = 1.0f;
     }
 
     /// Get the angle in radians
     float32 GetAngle() const
     {
         return b2Atan2(s, c);
     }
 
     /// Get the x-axis
     b2Vec2 GetXAxis() const
     {
         return b2Vec2(c, s);
     }
 
     /// Get the u-axis
     b2Vec2 GetYAxis() const
     {
         return b2Vec2(-s, c);
     }
 
     /// Sine and cosine
     float32 s, c;
 };
 
 /// A transform contains translation and rotation. It is used to represent
 /// the position and orientation of rigid frames.
 struct b2Transform
 {
     /// The default constructor does nothing.
     b2Transform() {}
 
     /// Initialize using a position vector and a rotation.
     b2Transform(const b2Vec2& position, const b2Rot& rotation) : p(position), q(rotation) {}
 
     /// Set this to the identity transform.
     void SetIdentity()
     {
         p.SetZero();
         q.SetIdentity();
     }
 
     /// Set this based on the position and angle.
     void Set(const b2Vec2& position, float32 angle)
     {
         p = position;
         q.Set(angle);
     }
 
     b2Vec2 p;
     b2Rot q;
 };
 
 /// This describes the motion of a body/shape for TOI computation.
 /// Shapes are defined with respect to the body origin, which may
 /// no coincide with the center of mass. However, to support dynamics
 /// we must interpolate the center of mass position.
 struct b2Sweep
 {
     /// Get the interpolated transform at a specific time.
     /// @param beta is a factor in [0,1], where 0 indicates alpha0.
     void GetTransform(b2Transform* xfb, float32 beta) const;
 
     /// Advance the sweep forward, yielding a new initial state.
     /// @param alpha the new initial time.
     void Advance(float32 alpha);
 
     /// Normalize the angles.
     void Normalize();
 
     b2Vec2 localCenter; ///< local center of mass position
     b2Vec2 c0, c;       ///< center world positions
     float32 a0, a;      ///< world angles
 
     /// Fraction of the current time step in the range [0,1]
     /// c0 and a0 are the positions at alpha0.
     float32 alpha0;
 };
 
 /// Useful constant
 extern const b2Vec2 b2Vec2_zero;
 
 /// Perform the dot product on two vectors.
 inline float32 b2Dot(const b2Vec2& a, const b2Vec2& b)
 {
     return a.x * b.x + a.y * b.y;
 }
 
 /// Perform the cross product on two vectors. In 2D this produces a scalar.
 inline float32 b2Cross(const b2Vec2& a, const b2Vec2& b)
 {
     return a.x * b.y - a.y * b.x;
 }
 
 /// Perform the cross product on a vector and a scalar. In 2D this produces
 /// a vector.
 inline b2Vec2 b2Cross(const b2Vec2& a, float32 s)
 {
     return b2Vec2(s * a.y, -s * a.x);
 }
 
 /// Perform the cross product on a scalar and a vector. In 2D this produces
 /// a vector.
 inline b2Vec2 b2Cross(float32 s, const b2Vec2& a)
 {
     return b2Vec2(-s * a.y, s * a.x);
 }
 
 /// Multiply a matrix times a vector. If a rotation matrix is provided,
 /// then this transforms the vector from one frame to another.
 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);
 }
 
 /// Multiply a matrix transpose times a vector. If a rotation matrix is provided,
 /// then this transforms the vector from one frame to another (inverse transform).
 inline b2Vec2 b2MulT(const b2Mat22& A, const b2Vec2& v)
 {
     return b2Vec2(b2Dot(v, A.ex), b2Dot(v, A.ey));
 }
 
 /// Add two vectors component-wise.
 inline b2Vec2 operator + (const b2Vec2& a, const b2Vec2& b)
 {
     return b2Vec2(a.x + b.x, a.y + b.y);
 }
 
 /// Subtract two vectors component-wise.
 inline b2Vec2 operator - (const b2Vec2& a, const b2Vec2& b)
 {
     return b2Vec2(a.x - b.x, a.y - b.y);
 }
 
 inline b2Vec2 operator * (float32 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 float32 b2Distance(const b2Vec2& a, const b2Vec2& b)
 {
     b2Vec2 c = a - b;
     return c.Length();
 }
 
 inline float32 b2DistanceSquared(const b2Vec2& a, const b2Vec2& b)
 {
     b2Vec2 c = a - b;
     return b2Dot(c, c);
 }
 
 inline b2Vec3 operator * (float32 s, const b2Vec3& a)
 {
     return b2Vec3(s * a.x, s * a.y, s * a.z);
 }
 
 /// Add two vectors component-wise.
 inline b2Vec3 operator + (const b2Vec3& a, const b2Vec3& b)
 {
     return b2Vec3(a.x + b.x, a.y + b.y, a.z + b.z);
 }
 
 /// Subtract two vectors component-wise.
 inline b2Vec3 operator - (const b2Vec3& a, const b2Vec3& b)
 {
     return b2Vec3(a.x - b.x, a.y - b.y, a.z - b.z);
 }
 
 /// Perform the dot product on two vectors.
 inline float32 b2Dot(const b2Vec3& a, const b2Vec3& b)
 {
     return a.x * b.x + a.y * b.y + a.z * b.z;
 }
 
 /// Perform the cross product on two vectors.
 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);
 }
 
 /// Multiply a matrix times a vector.
 inline b2Vec3 b2Mul(const b2Mat33& A, const b2Vec3& v)
 {
     return v.x * A.ex + v.y * A.ey + v.z * A.ez;
 }
 
 /// Multiply a matrix times a vector.
 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);
 }
 
 /// Multiply two rotations: q * r
 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;
 }
 
 /// Transpose multiply two rotations: qT * r
 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;
 }
 
 /// Rotate a vector
 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);
 }
 
 /// Inverse rotate a vector
 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)
 {
     float32 x = (T.q.c * v.x - T.q.s * v.y) + T.p.x;
     float32 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)
 {
     float32 px = v.x - T.p.x;
     float32 py = v.y - T.p.y;
     float32 x = (T.q.c * px + T.q.s * py);
     float32 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;
 }
 
 /// "Next Largest Power of 2
 /// Given a binary integer value x, the next largest power of 2 can be computed by a SWAR algorithm
 /// that recursively "folds" the upper bits into the lower bits. This process yields a bit vector with
 /// the same most significant 1 as x, but all 1's below it. Adding 1 to that value yields the next
 /// largest power of 2. For a 32-bit value:"
 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;
 }
 
 inline void b2Sweep::GetTransform(b2Transform* xf, float32 beta) const
 {
     xf->p = (1.0f - beta) * c0 + beta * c;
     float32 angle = (1.0f - beta) * a0 + beta * a;
     xf->q.Set(angle);
 
     // Shift to origin
     xf->p -= b2Mul(xf->q, localCenter);
 }
 
 inline void b2Sweep::Advance(float32 alpha)
 {
     b2Assert(alpha0 < 1.0f);
     float32 beta = (alpha - alpha0) / (1.0f - alpha0);
     c0 += beta * (c - c0);
     a0 += beta * (a - a0);
     alpha0 = alpha;
 }
 
 /// Normalize an angle in radians to be between -pi and pi
 inline void b2Sweep::Normalize()
 {
     float32 twoPi = 2.0f * b2_pi;
     float32 d =  twoPi * floorf(a0 / twoPi);
     a0 -= d;
     a -= d;
 }
 
 #endif