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 // Copyright 2014 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package f32 import "fmt" // An Affine is a 3x3 matrix of float32 values for which the bottom row is // implicitly always equal to [0 0 1]. // Elements are indexed first by row then column, i.e. m[row][column]. type Affine [2]Vec3 func (m Affine) String() string { return fmt.Sprintf(`Affine[% 0.3f, % 0.3f, % 0.3f, % 0.3f, % 0.3f, % 0.3f]`, m[0][0], m[0][1], m[0][2], m[1][0], m[1][1], m[1][2]) } // Identity sets m to be the identity transform. func (m *Affine) Identity() { *m = Affine{ {1, 0, 0}, {0, 1, 0}, } } // Eq reports whether each component of m is within epsilon of the same // component in n. func (m *Affine) Eq(n *Affine, epsilon float32) bool { for i := range m { for j := range m[i] { diff := m[i][j] - n[i][j] if diff < -epsilon || +epsilon < diff { return false } } } return true } // Mul sets m to be p × q. func (m *Affine) Mul(p, q *Affine) { // Store the result in local variables, in case m == a || m == b. m00 := p[0][0]*q[0][0] + p[0][1]*q[1][0] m01 := p[0][0]*q[0][1] + p[0][1]*q[1][1] m02 := p[0][0]*q[0][2] + p[0][1]*q[1][2] + p[0][2] m10 := p[1][0]*q[0][0] + p[1][1]*q[1][0] m11 := p[1][0]*q[0][1] + p[1][1]*q[1][1] m12 := p[1][0]*q[0][2] + p[1][1]*q[1][2] + p[1][2] m[0][0] = m00 m[0][1] = m01 m[0][2] = m02 m[1][0] = m10 m[1][1] = m11 m[1][2] = m12 } // Inverse sets m to be the inverse of p. func (m *Affine) Inverse(p *Affine) { m00 := p[1][1] m01 := -p[0][1] m02 := p[1][2]*p[0][1] - p[1][1]*p[0][2] m10 := -p[1][0] m11 := p[0][0] m12 := p[1][0]*p[0][2] - p[1][2]*p[0][0] det := m00*m11 - m10*m01 m[0][0] = m00 / det m[0][1] = m01 / det m[0][2] = m02 / det m[1][0] = m10 / det m[1][1] = m11 / det m[1][2] = m12 / det } // Scale sets m to be a scale followed by p. // It is equivalent to m.Mul(p, &Affine{{x,0,0}, {0,y,0}}). func (m *Affine) Scale(p *Affine, x, y float32) { m[0][0] = p[0][0] * x m[0][1] = p[0][1] * y m[0][2] = p[0][2] m[1][0] = p[1][0] * x m[1][1] = p[1][1] * y m[1][2] = p[1][2] } // Translate sets m to be a translation followed by p. // It is equivalent to m.Mul(p, &Affine{{1,0,x}, {0,1,y}}). func (m *Affine) Translate(p *Affine, x, y float32) { m[0][0] = p[0][0] m[0][1] = p[0][1] m[0][2] = p[0][0]*x + p[0][1]*y + p[0][2] m[1][0] = p[1][0] m[1][1] = p[1][1] m[1][2] = p[1][0]*x + p[1][1]*y + p[1][2] } // Rotate sets m to a rotation in radians followed by p. // It is equivalent to m.Mul(p, affineRotation). func (m *Affine) Rotate(p *Affine, radians float32) { s, c := Sin(radians), Cos(radians) m.Mul(p, &Affine{ {+c, +s, 0}, {-s, +c, 0}, }) }