1 /* 2 * Copyright (c) 2007-2009 Erin Catto http://www.box2d.org 3 * 4 * This software is provided 'as-is', without any express or implied 5 * warranty. In no event will the authors be held liable for any damages 6 * arising from the use of this software. 7 * Permission is granted to anyone to use this software for any purpose, 8 * including commercial applications, and to alter it and redistribute it 9 * freely, subject to the following restrictions: 10 * 1. The origin of this software must not be misrepresented; you must not 11 * claim that you wrote the original software. If you use this software 12 * in a product, an acknowledgment in the product documentation would be 13 * appreciated but is not required. 14 * 2. Altered source versions must be plainly marked as such, and must not be 15 * misrepresented as being the original software. 16 * 3. This notice may not be removed or altered from any source distribution. 17 */ 18 19 #include <Box2D/Common/b2Math.h> 20 21 const b2Vec2 b2Vec2_zero(0.0f, 0.0f); 22 23 /// Solve A * x = b, where b is a column vector. This is more efficient 24 /// than computing the inverse in one-shot cases. 25 b2Vec3 b2Mat33::Solve33(const b2Vec3& b) const 26 { 27 float32 det = b2Dot(ex, b2Cross(ey, ez)); 28 if (det != 0.0f) 29 { 30 det = 1.0f / det; 31 } 32 b2Vec3 x; 33 x.x = det * b2Dot(b, b2Cross(ey, ez)); 34 x.y = det * b2Dot(ex, b2Cross(b, ez)); 35 x.z = det * b2Dot(ex, b2Cross(ey, b)); 36 return x; 37 } 38 39 /// Solve A * x = b, where b is a column vector. This is more efficient 40 /// than computing the inverse in one-shot cases. 41 b2Vec2 b2Mat33::Solve22(const b2Vec2& b) const 42 { 43 float32 a11 = ex.x, a12 = ey.x, a21 = ex.y, a22 = ey.y; 44 float32 det = a11 * a22 - a12 * a21; 45 if (det != 0.0f) 46 { 47 det = 1.0f / det; 48 } 49 b2Vec2 x; 50 x.x = det * (a22 * b.x - a12 * b.y); 51 x.y = det * (a11 * b.y - a21 * b.x); 52 return x; 53 } 54 55 /// 56 void b2Mat33::GetInverse22(b2Mat33* M) const 57 { 58 float32 a = ex.x, b = ey.x, c = ex.y, d = ey.y; 59 float32 det = a * d - b * c; 60 if (det != 0.0f) 61 { 62 det = 1.0f / det; 63 } 64 65 M->ex.x = det * d; M->ey.x = -det * b; M->ex.z = 0.0f; 66 M->ex.y = -det * c; M->ey.y = det * a; M->ey.z = 0.0f; 67 M->ez.x = 0.0f; M->ez.y = 0.0f; M->ez.z = 0.0f; 68 } 69 70 /// Returns the zero matrix if singular. 71 void b2Mat33::GetSymInverse33(b2Mat33* M) const 72 { 73 float32 det = b2Dot(ex, b2Cross(ey, ez)); 74 if (det != 0.0f) 75 { 76 det = 1.0f / det; 77 } 78 79 float32 a11 = ex.x, a12 = ey.x, a13 = ez.x; 80 float32 a22 = ey.y, a23 = ez.y; 81 float32 a33 = ez.z; 82 83 M->ex.x = det * (a22 * a33 - a23 * a23); 84 M->ex.y = det * (a13 * a23 - a12 * a33); 85 M->ex.z = det * (a12 * a23 - a13 * a22); 86 87 M->ey.x = M->ex.y; 88 M->ey.y = det * (a11 * a33 - a13 * a13); 89 M->ey.z = det * (a13 * a12 - a11 * a23); 90 91 M->ez.x = M->ex.z; 92 M->ez.y = M->ey.z; 93 M->ez.z = det * (a11 * a22 - a12 * a12); 94 } 95
