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| 1 // Copyright 2014 The Go Authors. All rights reserved. | |
| 2 // Use of this source code is governed by a BSD-style | |
| 3 // license that can be found in the LICENSE file. | |
| 4 | |
| 5 package f32 | |
| 6 | |
| 7 import "fmt" | |
| 8 | |
| 9 // An Affine is a 3x3 matrix of float32 values for which the bottom row is | |
| 10 // implicitly always equal to [0 0 1]. | |
| 11 // Elements are indexed first by row then column, i.e. m[row][column]. | |
| 12 type Affine [2]Vec3 | |
| 13 | |
| 14 func (m Affine) String() string { | |
| 15 return fmt.Sprintf(`Affine[% 0.3f, % 0.3f, % 0.3f, | |
| 16 % 0.3f, % 0.3f, % 0.3f]`, | |
| 17 m[0][0], m[0][1], m[0][2], | |
| 18 m[1][0], m[1][1], m[1][2]) | |
| 19 } | |
| 20 | |
| 21 // Identity sets m to be the identity transform. | |
| 22 func (m *Affine) Identity() { | |
| 23 *m = Affine{ | |
| 24 {1, 0, 0}, | |
| 25 {0, 1, 0}, | |
| 26 } | |
| 27 } | |
| 28 | |
| 29 // Eq reports whether each component of m is within epsilon of the same | |
| 30 // component in n. | |
| 31 func (m *Affine) Eq(n *Affine, epsilon float32) bool { | |
| 32 for i := range m { | |
| 33 for j := range m[i] { | |
| 34 diff := m[i][j] - n[i][j] | |
| 35 if diff < -epsilon || +epsilon < diff { | |
| 36 return false | |
| 37 } | |
| 38 } | |
| 39 } | |
| 40 return true | |
| 41 } | |
| 42 | |
| 43 // Mul sets m to be p × q. | |
| 44 func (m *Affine) Mul(p, q *Affine) { | |
| 45 // Store the result in local variables, in case m == a || m == b. | |
| 46 m00 := p[0][0]*q[0][0] + p[0][1]*q[1][0] | |
| 47 m01 := p[0][0]*q[0][1] + p[0][1]*q[1][1] | |
| 48 m02 := p[0][0]*q[0][2] + p[0][1]*q[1][2] + p[0][2] | |
| 49 m10 := p[1][0]*q[0][0] + p[1][1]*q[1][0] | |
| 50 m11 := p[1][0]*q[0][1] + p[1][1]*q[1][1] | |
| 51 m12 := p[1][0]*q[0][2] + p[1][1]*q[1][2] + p[1][2] | |
| 52 m[0][0] = m00 | |
| 53 m[0][1] = m01 | |
| 54 m[0][2] = m02 | |
| 55 m[1][0] = m10 | |
| 56 m[1][1] = m11 | |
| 57 m[1][2] = m12 | |
| 58 } | |
| 59 | |
| 60 // Inverse sets m to be the inverse of p. | |
| 61 func (m *Affine) Inverse(p *Affine) { | |
| 62 m00 := p[1][1] | |
| 63 m01 := -p[0][1] | |
| 64 m02 := p[1][2]*p[0][1] - p[1][1]*p[0][2] | |
| 65 m10 := -p[1][0] | |
| 66 m11 := p[0][0] | |
| 67 m12 := p[1][0]*p[0][2] - p[1][2]*p[0][0] | |
| 68 | |
| 69 det := m00*m11 - m10*m01 | |
| 70 | |
| 71 m[0][0] = m00 / det | |
| 72 m[0][1] = m01 / det | |
| 73 m[0][2] = m02 / det | |
| 74 m[1][0] = m10 / det | |
| 75 m[1][1] = m11 / det | |
| 76 m[1][2] = m12 / det | |
| 77 } | |
| 78 | |
| 79 // Scale sets m to be a scale followed by p. | |
| 80 // It is equivalent to m.Mul(p, &Affine{{x,0,0}, {0,y,0}}). | |
| 81 func (m *Affine) Scale(p *Affine, x, y float32) { | |
| 82 m[0][0] = p[0][0] * x | |
| 83 m[0][1] = p[0][1] * y | |
| 84 m[0][2] = p[0][2] | |
| 85 m[1][0] = p[1][0] * x | |
| 86 m[1][1] = p[1][1] * y | |
| 87 m[1][2] = p[1][2] | |
| 88 } | |
| 89 | |
| 90 // Translate sets m to be a translation followed by p. | |
| 91 // It is equivalent to m.Mul(p, &Affine{{1,0,x}, {0,1,y}}). | |
| 92 func (m *Affine) Translate(p *Affine, x, y float32) { | |
| 93 m[0][0] = p[0][0] | |
| 94 m[0][1] = p[0][1] | |
| 95 m[0][2] = p[0][0]*x + p[0][1]*y + p[0][2] | |
| 96 m[1][0] = p[1][0] | |
| 97 m[1][1] = p[1][1] | |
| 98 m[1][2] = p[1][0]*x + p[1][1]*y + p[1][2] | |
| 99 } | |
| 100 | |
| 101 // Rotate sets m to a rotation in radians followed by p. | |
| 102 // It is equivalent to m.Mul(p, affineRotation). | |
| 103 func (m *Affine) Rotate(p *Affine, radians float32) { | |
| 104 s, c := Sin(radians), Cos(radians) | |
| 105 m.Mul(p, &Affine{ | |
| 106 {+c, +s, 0}, | |
| 107 {-s, +c, 0}, | |
| 108 }) | |
| 109 } | |
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