mirror of https://github.com/axmolengine/axmol.git
721 lines
16 KiB
C++
721 lines
16 KiB
C++
/*
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* Copyright (c) 2006-2009 Erin Catto http://www.box2d.org
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*
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* This software is provided 'as-is', without any express or implied
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* warranty. In no event will the authors be held liable for any damages
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* arising from the use of this software.
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* Permission is granted to anyone to use this software for any purpose,
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* including commercial applications, and to alter it and redistribute it
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* freely, subject to the following restrictions:
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* 1. The origin of this software must not be misrepresented; you must not
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* claim that you wrote the original software. If you use this software
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* in a product, an acknowledgment in the product documentation would be
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* appreciated but is not required.
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* 2. Altered source versions must be plainly marked as such, and must not be
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* misrepresented as being the original software.
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* 3. This notice may not be removed or altered from any source distribution.
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*/
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#ifndef B2_MATH_H
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#define B2_MATH_H
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#include <Box2D/Common/b2Settings.h>
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#include <math.h>
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/// This function is used to ensure that a floating point number is not a NaN or infinity.
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inline bool b2IsValid(float32 x)
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{
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int32 ix = *reinterpret_cast<int32*>(&x);
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return (ix & 0x7f800000) != 0x7f800000;
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}
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/// This is a approximate yet fast inverse square-root.
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inline float32 b2InvSqrt(float32 x)
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{
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union
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{
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float32 x;
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int32 i;
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} convert;
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convert.x = x;
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float32 xhalf = 0.5f * x;
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convert.i = 0x5f3759df - (convert.i >> 1);
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x = convert.x;
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x = x * (1.5f - xhalf * x * x);
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return x;
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}
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#define b2Sqrt(x) sqrtf(x)
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#define b2Atan2(y, x) atan2f(y, x)
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/// A 2D column vector.
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struct b2Vec2
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{
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/// Default constructor does nothing (for performance).
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b2Vec2() {}
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/// Construct using coordinates.
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b2Vec2(float32 x, float32 y) : x(x), y(y) {}
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/// Set this vector to all zeros.
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void SetZero() { x = 0.0f; y = 0.0f; }
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/// Set this vector to some specified coordinates.
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void Set(float32 x_, float32 y_) { x = x_; y = y_; }
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/// Negate this vector.
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b2Vec2 operator -() const { b2Vec2 v; v.Set(-x, -y); return v; }
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/// Read from and indexed element.
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float32 operator () (int32 i) const
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{
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return (&x)[i];
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}
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/// Write to an indexed element.
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float32& operator () (int32 i)
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{
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return (&x)[i];
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}
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/// Add a vector to this vector.
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void operator += (const b2Vec2& v)
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{
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x += v.x; y += v.y;
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}
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/// Subtract a vector from this vector.
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void operator -= (const b2Vec2& v)
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{
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x -= v.x; y -= v.y;
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}
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/// Multiply this vector by a scalar.
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void operator *= (float32 a)
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{
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x *= a; y *= a;
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}
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/// Get the length of this vector (the norm).
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float32 Length() const
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{
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return b2Sqrt(x * x + y * y);
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}
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/// Get the length squared. For performance, use this instead of
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/// b2Vec2::Length (if possible).
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float32 LengthSquared() const
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{
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return x * x + y * y;
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}
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/// Convert this vector into a unit vector. Returns the length.
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float32 Normalize()
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{
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float32 length = Length();
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if (length < b2_epsilon)
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{
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return 0.0f;
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}
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float32 invLength = 1.0f / length;
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x *= invLength;
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y *= invLength;
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return length;
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}
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/// Does this vector contain finite coordinates?
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bool IsValid() const
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{
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return b2IsValid(x) && b2IsValid(y);
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}
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/// Get the skew vector such that dot(skew_vec, other) == cross(vec, other)
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b2Vec2 Skew() const
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{
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return b2Vec2(-y, x);
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}
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float32 x, y;
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};
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/// A 2D column vector with 3 elements.
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struct b2Vec3
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{
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/// Default constructor does nothing (for performance).
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b2Vec3() {}
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/// Construct using coordinates.
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b2Vec3(float32 x, float32 y, float32 z) : x(x), y(y), z(z) {}
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/// Set this vector to all zeros.
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void SetZero() { x = 0.0f; y = 0.0f; z = 0.0f; }
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/// Set this vector to some specified coordinates.
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void Set(float32 x_, float32 y_, float32 z_) { x = x_; y = y_; z = z_; }
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/// Negate this vector.
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b2Vec3 operator -() const { b2Vec3 v; v.Set(-x, -y, -z); return v; }
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/// Add a vector to this vector.
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void operator += (const b2Vec3& v)
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{
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x += v.x; y += v.y; z += v.z;
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}
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/// Subtract a vector from this vector.
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void operator -= (const b2Vec3& v)
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{
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x -= v.x; y -= v.y; z -= v.z;
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}
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/// Multiply this vector by a scalar.
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void operator *= (float32 s)
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{
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x *= s; y *= s; z *= s;
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}
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float32 x, y, z;
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};
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/// A 2-by-2 matrix. Stored in column-major order.
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struct b2Mat22
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{
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/// The default constructor does nothing (for performance).
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b2Mat22() {}
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/// Construct this matrix using columns.
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b2Mat22(const b2Vec2& c1, const b2Vec2& c2)
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{
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ex = c1;
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ey = c2;
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}
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/// Construct this matrix using scalars.
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b2Mat22(float32 a11, float32 a12, float32 a21, float32 a22)
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{
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ex.x = a11; ex.y = a21;
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ey.x = a12; ey.y = a22;
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}
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/// Initialize this matrix using columns.
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void Set(const b2Vec2& c1, const b2Vec2& c2)
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{
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ex = c1;
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ey = c2;
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}
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/// Set this to the identity matrix.
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void SetIdentity()
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{
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ex.x = 1.0f; ey.x = 0.0f;
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ex.y = 0.0f; ey.y = 1.0f;
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}
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/// Set this matrix to all zeros.
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void SetZero()
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{
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ex.x = 0.0f; ey.x = 0.0f;
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ex.y = 0.0f; ey.y = 0.0f;
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}
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b2Mat22 GetInverse() const
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{
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float32 a = ex.x, b = ey.x, c = ex.y, d = ey.y;
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b2Mat22 B;
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float32 det = a * d - b * c;
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if (det != 0.0f)
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{
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det = 1.0f / det;
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}
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B.ex.x = det * d; B.ey.x = -det * b;
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B.ex.y = -det * c; B.ey.y = det * a;
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return B;
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}
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/// Solve A * x = b, where b is a column vector. This is more efficient
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/// than computing the inverse in one-shot cases.
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b2Vec2 Solve(const b2Vec2& b) const
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{
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float32 a11 = ex.x, a12 = ey.x, a21 = ex.y, a22 = ey.y;
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float32 det = a11 * a22 - a12 * a21;
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if (det != 0.0f)
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{
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det = 1.0f / det;
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}
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b2Vec2 x;
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x.x = det * (a22 * b.x - a12 * b.y);
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x.y = det * (a11 * b.y - a21 * b.x);
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return x;
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}
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b2Vec2 ex, ey;
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};
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/// A 3-by-3 matrix. Stored in column-major order.
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struct b2Mat33
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{
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/// The default constructor does nothing (for performance).
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b2Mat33() {}
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/// Construct this matrix using columns.
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b2Mat33(const b2Vec3& c1, const b2Vec3& c2, const b2Vec3& c3)
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{
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ex = c1;
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ey = c2;
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ez = c3;
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}
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/// Set this matrix to all zeros.
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void SetZero()
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{
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ex.SetZero();
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ey.SetZero();
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ez.SetZero();
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}
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/// Solve A * x = b, where b is a column vector. This is more efficient
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/// than computing the inverse in one-shot cases.
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b2Vec3 Solve33(const b2Vec3& b) const;
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/// Solve A * x = b, where b is a column vector. This is more efficient
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/// than computing the inverse in one-shot cases. Solve only the upper
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/// 2-by-2 matrix equation.
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b2Vec2 Solve22(const b2Vec2& b) const;
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/// Get the inverse of this matrix as a 2-by-2.
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/// Returns the zero matrix if singular.
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void GetInverse22(b2Mat33* M) const;
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/// Get the symmetric inverse of this matrix as a 3-by-3.
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/// Returns the zero matrix if singular.
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void GetSymInverse33(b2Mat33* M) const;
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b2Vec3 ex, ey, ez;
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};
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/// Rotation
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struct b2Rot
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{
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b2Rot() {}
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/// Initialize from an angle in radians
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explicit b2Rot(float32 angle)
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{
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/// TODO_ERIN optimize
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s = sinf(angle);
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c = cosf(angle);
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}
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/// Set using an angle in radians.
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void Set(float32 angle)
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{
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/// TODO_ERIN optimize
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s = sinf(angle);
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c = cosf(angle);
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}
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/// Set to the identity rotation
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void SetIdentity()
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{
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s = 0.0f;
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c = 1.0f;
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}
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/// Get the angle in radians
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float32 GetAngle() const
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{
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return b2Atan2(s, c);
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}
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/// Get the x-axis
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b2Vec2 GetXAxis() const
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{
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return b2Vec2(c, s);
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}
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/// Get the u-axis
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b2Vec2 GetYAxis() const
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{
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return b2Vec2(-s, c);
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}
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/// Sine and cosine
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float32 s, c;
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};
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/// A transform contains translation and rotation. It is used to represent
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/// the position and orientation of rigid frames.
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struct b2Transform
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{
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/// The default constructor does nothing.
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b2Transform() {}
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/// Initialize using a position vector and a rotation.
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b2Transform(const b2Vec2& position, const b2Rot& rotation) : p(position), q(rotation) {}
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/// Set this to the identity transform.
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void SetIdentity()
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{
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p.SetZero();
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q.SetIdentity();
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}
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/// Set this based on the position and angle.
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void Set(const b2Vec2& position, float32 angle)
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{
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p = position;
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q.Set(angle);
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}
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b2Vec2 p;
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b2Rot q;
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};
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/// This describes the motion of a body/shape for TOI computation.
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/// Shapes are defined with respect to the body origin, which may
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/// no coincide with the center of mass. However, to support dynamics
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/// we must interpolate the center of mass position.
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struct b2Sweep
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{
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/// Get the interpolated transform at a specific time.
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/// @param beta is a factor in [0,1], where 0 indicates alpha0.
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void GetTransform(b2Transform* xfb, float32 beta) const;
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/// Advance the sweep forward, yielding a new initial state.
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/// @param alpha the new initial time.
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void Advance(float32 alpha);
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/// Normalize the angles.
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void Normalize();
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b2Vec2 localCenter; ///< local center of mass position
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b2Vec2 c0, c; ///< center world positions
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float32 a0, a; ///< world angles
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/// Fraction of the current time step in the range [0,1]
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/// c0 and a0 are the positions at alpha0.
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float32 alpha0;
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};
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/// Useful constant
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extern const b2Vec2 b2Vec2_zero;
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/// Perform the dot product on two vectors.
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inline float32 b2Dot(const b2Vec2& a, const b2Vec2& b)
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{
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return a.x * b.x + a.y * b.y;
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}
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/// Perform the cross product on two vectors. In 2D this produces a scalar.
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inline float32 b2Cross(const b2Vec2& a, const b2Vec2& b)
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{
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return a.x * b.y - a.y * b.x;
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}
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/// Perform the cross product on a vector and a scalar. In 2D this produces
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/// a vector.
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inline b2Vec2 b2Cross(const b2Vec2& a, float32 s)
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{
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return b2Vec2(s * a.y, -s * a.x);
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}
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/// Perform the cross product on a scalar and a vector. In 2D this produces
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/// a vector.
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inline b2Vec2 b2Cross(float32 s, const b2Vec2& a)
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{
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return b2Vec2(-s * a.y, s * a.x);
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}
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/// Multiply a matrix times a vector. If a rotation matrix is provided,
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/// then this transforms the vector from one frame to another.
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inline b2Vec2 b2Mul(const b2Mat22& A, const b2Vec2& v)
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{
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return b2Vec2(A.ex.x * v.x + A.ey.x * v.y, A.ex.y * v.x + A.ey.y * v.y);
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}
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/// Multiply a matrix transpose times a vector. If a rotation matrix is provided,
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/// then this transforms the vector from one frame to another (inverse transform).
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inline b2Vec2 b2MulT(const b2Mat22& A, const b2Vec2& v)
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{
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return b2Vec2(b2Dot(v, A.ex), b2Dot(v, A.ey));
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}
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/// Add two vectors component-wise.
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inline b2Vec2 operator + (const b2Vec2& a, const b2Vec2& b)
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{
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return b2Vec2(a.x + b.x, a.y + b.y);
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}
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/// Subtract two vectors component-wise.
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inline b2Vec2 operator - (const b2Vec2& a, const b2Vec2& b)
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{
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return b2Vec2(a.x - b.x, a.y - b.y);
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}
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inline b2Vec2 operator * (float32 s, const b2Vec2& a)
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{
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return b2Vec2(s * a.x, s * a.y);
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}
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inline bool operator == (const b2Vec2& a, const b2Vec2& b)
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{
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return a.x == b.x && a.y == b.y;
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}
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inline float32 b2Distance(const b2Vec2& a, const b2Vec2& b)
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{
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b2Vec2 c = a - b;
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return c.Length();
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}
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inline float32 b2DistanceSquared(const b2Vec2& a, const b2Vec2& b)
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{
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b2Vec2 c = a - b;
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return b2Dot(c, c);
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}
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inline b2Vec3 operator * (float32 s, const b2Vec3& a)
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{
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return b2Vec3(s * a.x, s * a.y, s * a.z);
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}
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/// Add two vectors component-wise.
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inline b2Vec3 operator + (const b2Vec3& a, const b2Vec3& b)
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{
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return b2Vec3(a.x + b.x, a.y + b.y, a.z + b.z);
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}
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/// Subtract two vectors component-wise.
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inline b2Vec3 operator - (const b2Vec3& a, const b2Vec3& b)
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{
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return b2Vec3(a.x - b.x, a.y - b.y, a.z - b.z);
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}
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/// Perform the dot product on two vectors.
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inline float32 b2Dot(const b2Vec3& a, const b2Vec3& b)
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{
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return a.x * b.x + a.y * b.y + a.z * b.z;
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}
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/// Perform the cross product on two vectors.
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inline b2Vec3 b2Cross(const b2Vec3& a, const b2Vec3& b)
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{
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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);
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}
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inline b2Mat22 operator + (const b2Mat22& A, const b2Mat22& B)
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{
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return b2Mat22(A.ex + B.ex, A.ey + B.ey);
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}
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// A * B
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inline b2Mat22 b2Mul(const b2Mat22& A, const b2Mat22& B)
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{
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return b2Mat22(b2Mul(A, B.ex), b2Mul(A, B.ey));
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}
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// A^T * B
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inline b2Mat22 b2MulT(const b2Mat22& A, const b2Mat22& B)
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{
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b2Vec2 c1(b2Dot(A.ex, B.ex), b2Dot(A.ey, B.ex));
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b2Vec2 c2(b2Dot(A.ex, B.ey), b2Dot(A.ey, B.ey));
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return b2Mat22(c1, c2);
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}
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/// Multiply a matrix times a vector.
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inline b2Vec3 b2Mul(const b2Mat33& A, const b2Vec3& v)
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{
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return v.x * A.ex + v.y * A.ey + v.z * A.ez;
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}
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/// Multiply a matrix times a vector.
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inline b2Vec2 b2Mul22(const b2Mat33& A, const b2Vec2& v)
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|
{
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return b2Vec2(A.ex.x * v.x + A.ey.x * v.y, A.ex.y * v.x + A.ey.y * v.y);
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}
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/// Multiply two rotations: q * r
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inline b2Rot b2Mul(const b2Rot& q, const b2Rot& r)
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|
{
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// [qc -qs] * [rc -rs] = [qc*rc-qs*rs -qc*rs-qs*rc]
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// [qs qc] [rs rc] [qs*rc+qc*rs -qs*rs+qc*rc]
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// s = qs * rc + qc * rs
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// c = qc * rc - qs * rs
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b2Rot qr;
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qr.s = q.s * r.c + q.c * r.s;
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qr.c = q.c * r.c - q.s * r.s;
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return qr;
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}
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|
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/// Transpose multiply two rotations: qT * r
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inline b2Rot b2MulT(const b2Rot& q, const b2Rot& r)
|
|
{
|
|
// [ qc qs] * [rc -rs] = [qc*rc+qs*rs -qc*rs+qs*rc]
|
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// [-qs qc] [rs rc] [-qs*rc+qc*rs qs*rs+qc*rc]
|
|
// s = qc * rs - qs * rc
|
|
// c = qc * rc + qs * rs
|
|
b2Rot qr;
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|
qr.s = q.c * r.s - q.s * r.c;
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|
qr.c = q.c * r.c + q.s * r.s;
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return qr;
|
|
}
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|
|
|
/// 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
|