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.
Solve33(const b2Vec3 & b) const25 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.
Solve22(const b2Vec2 & b) const41 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 ///
GetInverse22(b2Mat33 * M) const56 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.
GetSymInverse33(b2Mat33 * M) const71 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