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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"
// 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},
}
}
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