/* * Copyright (c) 2007-2009 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. */ #include <Box2D/Common/b2Math.h> const b2Vec2 b2Vec2_zero(0.0f, 0.0f); /// Solve A * x = b, where b is a column vector. This is more efficient /// than computing the inverse in one-shot cases. b2Vec3 b2Mat33::Solve33(const b2Vec3& b) const { float32 det = b2Dot(ex, b2Cross(ey, ez)); if (det != 0.0f) { det = 1.0f / det; } b2Vec3 x; x.x = det * b2Dot(b, b2Cross(ey, ez)); x.y = det * b2Dot(ex, b2Cross(b, ez)); x.z = det * b2Dot(ex, b2Cross(ey, b)); return x; } /// Solve A * x = b, where b is a column vector. This is more efficient /// than computing the inverse in one-shot cases. b2Vec2 b2Mat33::Solve22(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; } /// void b2Mat33::GetInverse22(b2Mat33* M) const { float32 a = ex.x, b = ey.x, c = ex.y, d = ey.y; float32 det = a * d - b * c; if (det != 0.0f) { det = 1.0f / det; } M->ex.x = det * d; M->ey.x = -det * b; M->ex.z = 0.0f; M->ex.y = -det * c; M->ey.y = det * a; M->ey.z = 0.0f; M->ez.x = 0.0f; M->ez.y = 0.0f; M->ez.z = 0.0f; } /// Returns the zero matrix if singular. void b2Mat33::GetSymInverse33(b2Mat33* M) const { float32 det = b2Dot(ex, b2Cross(ey, ez)); if (det != 0.0f) { det = 1.0f / det; } float32 a11 = ex.x, a12 = ey.x, a13 = ez.x; float32 a22 = ey.y, a23 = ez.y; float32 a33 = ez.z; M->ex.x = det * (a22 * a33 - a23 * a23); M->ex.y = det * (a13 * a23 - a12 * a33); M->ex.z = det * (a12 * a23 - a13 * a22); M->ey.x = M->ex.y; M->ey.y = det * (a11 * a33 - a13 * a13); M->ey.z = det * (a13 * a12 - a11 * a23); M->ez.x = M->ex.z; M->ez.y = M->ey.z; M->ez.z = det * (a11 * a22 - a12 * a12); }