194 lines
5.0 KiB
Go
194 lines
5.0 KiB
Go
// Copyright 2014 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package f32
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import "fmt"
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// A Mat4 is a 4x4 matrix of float32 values.
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// Elements are indexed first by row then column, i.e. m[row][column].
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type Mat4 [4]Vec4
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func (m Mat4) String() string {
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return fmt.Sprintf(`Mat4[% 0.3f, % 0.3f, % 0.3f, % 0.3f,
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% 0.3f, % 0.3f, % 0.3f, % 0.3f,
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% 0.3f, % 0.3f, % 0.3f, % 0.3f,
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% 0.3f, % 0.3f, % 0.3f, % 0.3f]`,
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m[0][0], m[0][1], m[0][2], m[0][3],
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m[1][0], m[1][1], m[1][2], m[1][3],
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m[2][0], m[2][1], m[2][2], m[2][3],
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m[3][0], m[3][1], m[3][2], m[3][3])
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}
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func (m *Mat4) Identity() {
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*m = Mat4{
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{1, 0, 0, 0},
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{0, 1, 0, 0},
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{0, 0, 1, 0},
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{0, 0, 0, 1},
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}
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}
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func (m *Mat4) Eq(n *Mat4, epsilon float32) bool {
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for i := range m {
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for j := range m[i] {
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diff := m[i][j] - n[i][j]
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if diff < -epsilon || +epsilon < diff {
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return false
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}
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}
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}
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return true
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}
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// Mul stores a × b in m.
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func (m *Mat4) Mul(a, b *Mat4) {
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// Store the result in local variables, in case m == a || m == b.
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m00 := a[0][0]*b[0][0] + a[0][1]*b[1][0] + a[0][2]*b[2][0] + a[0][3]*b[3][0]
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m01 := a[0][0]*b[0][1] + a[0][1]*b[1][1] + a[0][2]*b[2][1] + a[0][3]*b[3][1]
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m02 := a[0][0]*b[0][2] + a[0][1]*b[1][2] + a[0][2]*b[2][2] + a[0][3]*b[3][2]
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m03 := a[0][0]*b[0][3] + a[0][1]*b[1][3] + a[0][2]*b[2][3] + a[0][3]*b[3][3]
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m10 := a[1][0]*b[0][0] + a[1][1]*b[1][0] + a[1][2]*b[2][0] + a[1][3]*b[3][0]
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m11 := a[1][0]*b[0][1] + a[1][1]*b[1][1] + a[1][2]*b[2][1] + a[1][3]*b[3][1]
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m12 := a[1][0]*b[0][2] + a[1][1]*b[1][2] + a[1][2]*b[2][2] + a[1][3]*b[3][2]
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m13 := a[1][0]*b[0][3] + a[1][1]*b[1][3] + a[1][2]*b[2][3] + a[1][3]*b[3][3]
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m20 := a[2][0]*b[0][0] + a[2][1]*b[1][0] + a[2][2]*b[2][0] + a[2][3]*b[3][0]
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m21 := a[2][0]*b[0][1] + a[2][1]*b[1][1] + a[2][2]*b[2][1] + a[2][3]*b[3][1]
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m22 := a[2][0]*b[0][2] + a[2][1]*b[1][2] + a[2][2]*b[2][2] + a[2][3]*b[3][2]
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m23 := a[2][0]*b[0][3] + a[2][1]*b[1][3] + a[2][2]*b[2][3] + a[2][3]*b[3][3]
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m30 := a[3][0]*b[0][0] + a[3][1]*b[1][0] + a[3][2]*b[2][0] + a[3][3]*b[3][0]
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m31 := a[3][0]*b[0][1] + a[3][1]*b[1][1] + a[3][2]*b[2][1] + a[3][3]*b[3][1]
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m32 := a[3][0]*b[0][2] + a[3][1]*b[1][2] + a[3][2]*b[2][2] + a[3][3]*b[3][2]
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m33 := a[3][0]*b[0][3] + a[3][1]*b[1][3] + a[3][2]*b[2][3] + a[3][3]*b[3][3]
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m[0][0] = m00
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m[0][1] = m01
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m[0][2] = m02
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m[0][3] = m03
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m[1][0] = m10
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m[1][1] = m11
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m[1][2] = m12
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m[1][3] = m13
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m[2][0] = m20
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m[2][1] = m21
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m[2][2] = m22
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m[2][3] = m23
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m[3][0] = m30
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m[3][1] = m31
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m[3][2] = m32
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m[3][3] = m33
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}
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// Perspective sets m to be the GL perspective matrix.
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func (m *Mat4) Perspective(fov Radian, aspect, near, far float32) {
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t := Tan(float32(fov) / 2)
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m[0][0] = 1 / (aspect * t)
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m[1][1] = 1 / t
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m[2][2] = -(far + near) / (far - near)
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m[2][3] = -1
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m[3][2] = -2 * far * near / (far - near)
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}
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// Scale sets m to be a scale followed by p.
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// It is equivalent to
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// m.Mul(p, &Mat4{
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// {x, 0, 0, 0},
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// {0, y, 0, 0},
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// {0, 0, z, 0},
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// {0, 0, 0, 1},
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// }).
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func (m *Mat4) Scale(p *Mat4, x, y, z float32) {
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m[0][0] = p[0][0] * x
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m[0][1] = p[0][1] * y
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m[0][2] = p[0][2] * z
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m[0][3] = p[0][3]
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m[1][0] = p[1][0] * x
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m[1][1] = p[1][1] * y
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m[1][2] = p[1][2] * z
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m[1][3] = p[1][3]
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m[2][0] = p[2][0] * x
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m[2][1] = p[2][1] * y
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m[2][2] = p[2][2] * z
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m[2][3] = p[2][3]
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m[3][0] = p[3][0] * x
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m[3][1] = p[3][1] * y
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m[3][2] = p[3][2] * z
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m[3][3] = p[3][3]
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}
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// Translate sets m to be a translation followed by p.
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// It is equivalent to
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// m.Mul(p, &Mat4{
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// {1, 0, 0, x},
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// {0, 1, 0, y},
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// {0, 0, 1, z},
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// {0, 0, 0, 1},
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// }).
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func (m *Mat4) Translate(p *Mat4, x, y, z float32) {
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m[0][0] = p[0][0]
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m[0][1] = p[0][1]
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m[0][2] = p[0][2]
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m[0][3] = p[0][0]*x + p[0][1]*y + p[0][2]*z + p[0][3]
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m[1][0] = p[1][0]
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m[1][1] = p[1][1]
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m[1][2] = p[1][2]
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m[1][3] = p[1][0]*x + p[1][1]*y + p[1][2]*z + p[1][3]
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m[2][0] = p[2][0]
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m[2][1] = p[2][1]
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m[2][2] = p[2][2]
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m[2][3] = p[2][0]*x + p[2][1]*y + p[2][2]*z + p[2][3]
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m[3][0] = p[3][0]
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m[3][1] = p[3][1]
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m[3][2] = p[3][2]
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m[3][3] = p[3][0]*x + p[3][1]*y + p[3][2]*z + p[3][3]
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}
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// Rotate sets m to a rotation in radians around a specified axis, followed by p.
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// It is equivalent to m.Mul(p, affineRotation).
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func (m *Mat4) Rotate(p *Mat4, angle Radian, axis *Vec3) {
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a := *axis
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a.Normalize()
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c, s := Cos(float32(angle)), Sin(float32(angle))
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d := 1 - c
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m.Mul(p, &Mat4{{
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c + d*a[0]*a[1],
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0 + d*a[0]*a[1] + s*a[2],
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0 + d*a[0]*a[1] - s*a[1],
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0,
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}, {
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0 + d*a[1]*a[0] - s*a[2],
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c + d*a[1]*a[1],
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0 + d*a[1]*a[2] + s*a[0],
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0,
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}, {
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0 + d*a[2]*a[0] + s*a[1],
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0 + d*a[2]*a[1] - s*a[0],
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c + d*a[2]*a[2],
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0,
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}, {
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0, 0, 0, 1,
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}})
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}
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func (m *Mat4) LookAt(eye, center, up *Vec3) {
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f, s, u := new(Vec3), new(Vec3), new(Vec3)
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*f = *center
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f.Sub(f, eye)
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f.Normalize()
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s.Cross(f, up)
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s.Normalize()
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u.Cross(s, f)
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*m = Mat4{
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{s[0], u[0], -f[0], 0},
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{s[1], u[1], -f[1], 0},
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{s[2], u[2], -f[2], 0},
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{-s.Dot(eye), -u.Dot(eye), +f.Dot(eye), 1},
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}
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}
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