exp/f32/mat4.go

// 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"

// A Mat4 is a 4x4 matrix of float32 values.
// Elements are indexed first by row then column, i.e. m[row][column].
type Mat4 [4]Vec4

func (m Mat4) String() string {
	return fmt.Sprintf(`Mat4[% 0.3f, % 0.3f, % 0.3f, % 0.3f,
     % 0.3f, % 0.3f, % 0.3f, % 0.3f,
     % 0.3f, % 0.3f, % 0.3f, % 0.3f,
     % 0.3f, % 0.3f, % 0.3f, % 0.3f]`,
		m[0][0], m[0][1], m[0][2], m[0][3],
		m[1][0], m[1][1], m[1][2], m[1][3],
		m[2][0], m[2][1], m[2][2], m[2][3],
		m[3][0], m[3][1], m[3][2], m[3][3])
}

func (m *Mat4) Identity() {
	*m = Mat4{
		{1, 0, 0, 0},
		{0, 1, 0, 0},
		{0, 0, 1, 0},
		{0, 0, 0, 1},
	}
}

func (m *Mat4) Eq(n *Mat4, 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 stores a × b in m.
func (m *Mat4) Mul(a, b *Mat4) {
	// Store the result in local variables, in case m == a || m == b.
	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]
	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]
	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]
	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]
	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]
	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]
	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]
	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]
	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]
	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]
	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]
	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]
	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]
	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]
	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]
	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]
	m[0][0] = m00
	m[0][1] = m01
	m[0][2] = m02
	m[0][3] = m03
	m[1][0] = m10
	m[1][1] = m11
	m[1][2] = m12
	m[1][3] = m13
	m[2][0] = m20
	m[2][1] = m21
	m[2][2] = m22
	m[2][3] = m23
	m[3][0] = m30
	m[3][1] = m31
	m[3][2] = m32
	m[3][3] = m33
}

// Perspective sets m to be the GL perspective matrix.
func (m *Mat4) Perspective(fov Radian, aspect, near, far float32) {
	t := Tan(float32(fov) / 2)

	m[0][0] = 1 / (aspect * t)
	m[1][1] = 1 / t
	m[2][2] = -(far + near) / (far - near)
	m[2][3] = -1
	m[3][2] = -2 * far * near / (far - near)
}

// Scale sets m to be a scale followed by p.
// It is equivalent to
//	m.Mul(p, &Mat4{
//		{x, 0, 0, 0},
//		{0, y, 0, 0},
//		{0, 0, z, 0},
//		{0, 0, 0, 1},
//	}).
func (m *Mat4) Scale(p *Mat4, x, y, z float32) {
	m[0][0] = p[0][0] * x
	m[0][1] = p[0][1] * y
	m[0][2] = p[0][2] * z
	m[0][3] = p[0][3]
	m[1][0] = p[1][0] * x
	m[1][1] = p[1][1] * y
	m[1][2] = p[1][2] * z
	m[1][3] = p[1][3]
	m[2][0] = p[2][0] * x
	m[2][1] = p[2][1] * y
	m[2][2] = p[2][2] * z
	m[2][3] = p[2][3]
	m[3][0] = p[3][0] * x
	m[3][1] = p[3][1] * y
	m[3][2] = p[3][2] * z
	m[3][3] = p[3][3]
}

// Translate sets m to be a translation followed by p.
// It is equivalent to
//	m.Mul(p, &Mat4{
//		{1, 0, 0, x},
//		{0, 1, 0, y},
//		{0, 0, 1, z},
//		{0, 0, 0, 1},
//	}).
func (m *Mat4) Translate(p *Mat4, x, y, z float32) {
	m[0][0] = p[0][0]
	m[0][1] = p[0][1]
	m[0][2] = p[0][2]
	m[0][3] = p[0][0]*x + p[0][1]*y + p[0][2]*z + p[0][3]
	m[1][0] = p[1][0]
	m[1][1] = p[1][1]
	m[1][2] = p[1][2]
	m[1][3] = p[1][0]*x + p[1][1]*y + p[1][2]*z + p[1][3]
	m[2][0] = p[2][0]
	m[2][1] = p[2][1]
	m[2][2] = p[2][2]
	m[2][3] = p[2][0]*x + p[2][1]*y + p[2][2]*z + p[2][3]
	m[3][0] = p[3][0]
	m[3][1] = p[3][1]
	m[3][2] = p[3][2]
	m[3][3] = p[3][0]*x + p[3][1]*y + p[3][2]*z + p[3][3]
}

// Rotate sets m to a rotation in radians around a specified axis, followed by p.
// It is equivalent to m.Mul(p, affineRotation).
func (m *Mat4) Rotate(p *Mat4, angle Radian, axis *Vec3) {
	a := *axis
	a.Normalize()

	c, s := Cos(float32(angle)), Sin(float32(angle))
	d := 1 - c

	m.Mul(p, &Mat4{{
		c + d*a[0]*a[1],
		0 + d*a[0]*a[1] + s*a[2],
		0 + d*a[0]*a[1] - s*a[1],
		0,
	}, {
		0 + d*a[1]*a[0] - s*a[2],
		c + d*a[1]*a[1],
		0 + d*a[1]*a[2] + s*a[0],
		0,
	}, {
		0 + d*a[2]*a[0] + s*a[1],
		0 + d*a[2]*a[1] - s*a[0],
		c + d*a[2]*a[2],
		0,
	}, {
		0, 0, 0, 1,
	}})
}

func (m *Mat4) LookAt(eye, center, up *Vec3) {
	f, s, u := new(Vec3), new(Vec3), new(Vec3)

	*f = *center
	f.Sub(f, eye)
	f.Normalize()

	s.Cross(f, up)
	s.Normalize()
	u.Cross(s, f)

	*m = Mat4{
		{s[0], u[0], -f[0], 0},
		{s[1], u[1], -f[1], 0},
		{s[2], u[2], -f[2], 0},
		{-s.Dot(eye), -u.Dot(eye), +f.Dot(eye), 1},
	}
}