/
matrix.go
179 lines (159 loc) · 6.64 KB
/
matrix.go
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package gl
import "math"
const deg = math.Pi / 180
// The type Mat4 represents a double precision 4x4 matrix.
type Mat4 [4][4]float64
// An identity matrix
var Identity Mat4 = [4][4]float64{[4]float64{1, 0, 0, 0}, [4]float64{0, 1, 0, 0}, [4]float64{0, 0, 1, 0}, [4]float64{0, 0, 0, 1}}
func mul4(a, b Mat4) Mat4 {
var r Mat4
for i := 0; i < 4; i++ {
for j := 0; j < 4; j++ {
for k := 0; k < 4; k++ {
r[i][k] += a[i][j] * b[j][k]
}
}
}
return r
}
// Mul4 multiplies an arbitrary number of Mat4 matrices.
func Mul4(a ...Mat4) Mat4 {
r := Identity
for i, j := range a {
if i == 0 {
r = j
} else {
r = mul4(r, j)
}
}
return r
}
// Apply4 applies the matrix to a 4-element vector
func (m Mat4) Apply4 (v [4]float64) [4]float64 {
var r [4]float64
for i := 0; i < 4; i++ {
for j := 0; j < 4; j++ {
r[i] += m[i][j] * v[j]
}
}
return r
}
// Apply3 applies the matrix to a 3-element vector
func (m Mat4) Apply3 (v [3]float64) [3]float64 {
r := [4]float64{m[0][3], m[1][3], m[2][3], m[3][3]}
for i := 0; i < 4; i++ {
for j := 0; j < 3; j++ {
r[i] += m[i][j] * v[j]
}
}
return [3]float64{r[0]/r[3], r[1]/r[3], r[2]/r[3]}
}
// RotZ returns a rotation matrix rotating r degrees around the z axis.
func RotZ(r float64) Mat4 {
r *= deg
return Mat4{[4]float64{math.Cos(r), -math.Sin(r), 0, 0},
[4]float64{math.Sin(r), math.Cos(r), 0, 0},
[4]float64{0, 0, 1, 0},
[4]float64{0, 0, 0, 1}}
}
// RotX returns a rotation matrix rotating r degrees around the x axis.
func RotX(r float64) Mat4 {
r *= deg
return Mat4{[4]float64{1, 0, 0, 0},
[4]float64{0, math.Cos(r), math.Sin(r), 0},
[4]float64{0, -math.Sin(r), math.Cos(r), 0},
[4]float64{0, 0, 0, 1}}
}
// RotY returns a rotation matrix rotating r degrees around the y axis.
func RotY(r float64) Mat4 {
r *= deg
return Mat4{[4]float64{math.Cos(r), 0, math.Sin(r), 0},
[4]float64{0, 1, 0, 0},
[4]float64{-math.Sin(r), 0, math.Cos(r), 0},
[4]float64{0, 0, 0, 1}}
}
// Translate returns a translation matrix
func Translate(x, y, z float64) Mat4 {
return Mat4{[4]float64{1, 0, 0, x},
[4]float64{0, 1, 0, y},
[4]float64{0, 0, 1, z},
[4]float64{0, 0, 0, 1}}
}
// Frustum returns a projection matrix similar to gluPerspective. The arguments are field of view angle in degrees, aspect ratio and near and far z clipping plane distance.
func Frustum(fov, aspect, zNear, zFar float64) Mat4 {
f := 1 / math.Tan(fov*deg/2)
return Mat4{[4]float64{f / aspect, 0, 0, 0},
[4]float64{0, f, 0, 0},
[4]float64{0, 0, (zNear + zFar) / (zNear - zFar), (2 * zNear * zFar) / (zNear - zFar)},
[4]float64{0, 0, -1, 0}}
}
// Scale returns a scale matrix
func Scale(x, y, z float64) Mat4 {
return Mat4{[4]float64{x, 0, 0, 0},
[4]float64{0, y, 0, 0},
[4]float64{0, 0, z, 0},
[4]float64{0, 0, 0, 1}}
}
//calculate the inverse Mat4 of original Mat4
func (m Mat4) Inverse() Mat4 {
var u = m[0][0]*m[1][1]*m[2][2]*m[3][3] +
m[0][0]*m[1][2]*m[2][3]*m[3][1] +
m[0][0]*m[1][3]*m[2][1]*m[3][2] +
m[0][1]*m[1][0]*m[2][3]*m[3][2] +
m[0][1]*m[1][2]*m[2][0]*m[3][3] +
m[0][1]*m[1][3]*m[2][2]*m[3][0] +
m[0][2]*m[1][0]*m[2][1]*m[3][3] +
m[0][2]*m[1][1]*m[2][3]*m[3][0] +
m[0][2]*m[1][3]*m[2][0]*m[3][1] +
m[0][3]*m[1][0]*m[2][2]*m[3][1] +
m[0][3]*m[1][1]*m[2][0]*m[3][2] +
m[0][3]*m[1][2]*m[2][1]*m[3][0] -
m[0][0]*m[1][1]*m[2][3]*m[3][2] -
m[0][0]*m[1][2]*m[2][1]*m[3][3] -
m[0][0]*m[1][3]*m[2][2]*m[3][1] -
m[0][1]*m[1][0]*m[2][2]*m[3][3] -
m[0][1]*m[1][2]*m[2][3]*m[3][0] -
m[0][1]*m[1][3]*m[2][0]*m[3][2] -
m[0][2]*m[1][0]*m[2][3]*m[3][1] -
m[0][2]*m[1][1]*m[2][0]*m[3][3] -
m[0][2]*m[1][3]*m[2][1]*m[3][0] -
m[0][3]*m[1][0]*m[2][1]*m[3][2] -
m[0][3]*m[1][1]*m[2][2]*m[3][0] -
m[0][3]*m[1][2]*m[2][0]*m[3][1]
var n = 1 / u
return Mat4{
[4]float64{
(m[1][1]*m[2][2]*m[3][3] + m[1][2]*m[2][3]*m[3][1] + m[1][3]*m[2][1]*m[3][2] - m[1][1]*m[2][3]*m[3][2] - m[1][2]*m[2][1]*m[3][3] - m[1][3]*m[2][2]*m[3][1]) * n,
(m[0][1]*m[2][3]*m[3][2] + m[0][2]*m[2][1]*m[3][3] + m[1][3]*m[2][2]*m[3][1] - m[0][1]*m[2][2]*m[3][3] - m[0][2]*m[2][3]*m[3][1] - m[1][3]*m[2][1]*m[3][2]) * n,
(m[0][1]*m[1][2]*m[3][3] + m[0][2]*m[1][3]*m[3][1] + m[1][3]*m[1][1]*m[3][2] - m[0][1]*m[1][3]*m[3][2] - m[0][2]*m[1][1]*m[3][3] - m[1][3]*m[1][2]*m[3][1]) * n,
(m[0][1]*m[1][3]*m[2][2] + m[0][2]*m[1][1]*m[2][3] + m[1][3]*m[1][2]*m[2][1] - m[0][1]*m[1][2]*m[2][3] - m[0][2]*m[1][3]*m[2][1] - m[1][3]*m[1][1]*m[2][2]) * n,
},
[4]float64{
(m[1][0]*m[2][3]*m[3][2] + m[1][2]*m[2][0]*m[3][3] + m[1][3]*m[2][2]*m[3][0] - m[1][0]*m[2][2]*m[3][3] - m[1][2]*m[2][3]*m[3][0] - m[1][3]*m[2][0]*m[3][2]) * n,
(m[0][0]*m[2][2]*m[3][3] + m[0][2]*m[2][3]*m[3][0] + m[1][3]*m[2][0]*m[3][2] - m[0][0]*m[2][3]*m[3][2] - m[0][2]*m[2][0]*m[3][3] - m[1][3]*m[2][2]*m[3][0]) * n,
(m[0][0]*m[1][3]*m[3][2] + m[0][2]*m[1][0]*m[3][3] + m[1][3]*m[1][2]*m[3][0] - m[0][0]*m[1][2]*m[3][3] - m[0][2]*m[1][3]*m[3][0] - m[1][3]*m[1][0]*m[3][2]) * n,
(m[0][0]*m[1][2]*m[2][3] + m[0][2]*m[1][3]*m[2][0] + m[1][3]*m[1][0]*m[2][2] - m[0][0]*m[1][3]*m[2][2] - m[0][2]*m[1][0]*m[2][3] - m[1][3]*m[1][2]*m[2][0]) * n,
},
[4]float64{
(m[1][0]*m[2][1]*m[3][3] + m[1][1]*m[2][3]*m[3][0] + m[1][3]*m[2][0]*m[3][1] - m[1][0]*m[2][3]*m[3][1] - m[1][1]*m[2][0]*m[3][3] - m[1][3]*m[2][1]*m[3][0]) * n,
(m[0][0]*m[2][3]*m[3][1] + m[0][1]*m[2][0]*m[3][3] + m[1][3]*m[2][1]*m[3][0] - m[0][0]*m[2][1]*m[3][3] - m[0][1]*m[2][3]*m[3][0] - m[1][3]*m[2][0]*m[3][1]) * n,
(m[0][0]*m[1][1]*m[3][3] + m[0][1]*m[1][3]*m[3][0] + m[1][3]*m[1][0]*m[3][1] - m[0][0]*m[1][3]*m[3][1] - m[0][1]*m[1][0]*m[3][3] - m[1][3]*m[1][1]*m[3][0]) * n,
(m[0][0]*m[1][3]*m[2][1] + m[0][1]*m[1][0]*m[2][3] + m[1][3]*m[1][1]*m[2][0] - m[0][0]*m[1][1]*m[2][3] - m[0][1]*m[1][3]*m[2][0] - m[1][3]*m[1][0]*m[2][1]) * n,
},
[4]float64{
(m[1][0]*m[2][2]*m[3][1] + m[1][1]*m[2][0]*m[3][2] + m[1][2]*m[2][1]*m[3][0] - m[1][0]*m[2][1]*m[3][2] - m[1][1]*m[2][2]*m[3][0] - m[1][2]*m[2][0]*m[3][1]) * n,
(m[0][0]*m[2][1]*m[3][2] + m[0][1]*m[2][2]*m[3][0] + m[0][2]*m[2][0]*m[3][1] - m[0][0]*m[2][2]*m[3][1] - m[0][1]*m[2][0]*m[3][2] - m[0][2]*m[2][1]*m[3][0]) * n,
(m[0][0]*m[1][2]*m[3][1] + m[0][1]*m[1][0]*m[3][2] + m[0][2]*m[1][1]*m[3][0] - m[0][0]*m[1][1]*m[3][2] - m[0][1]*m[1][2]*m[3][0] - m[0][2]*m[1][0]*m[3][1]) * n,
(m[0][0]*m[1][1]*m[2][2] + m[0][1]*m[1][2]*m[2][0] + m[0][2]*m[1][0]*m[2][1] - m[0][0]*m[1][2]*m[2][1] - m[0][1]*m[1][0]*m[2][2] - m[0][2]*m[1][1]*m[2][0]) * n,
},
}
}
//calculate the transpose Mat4 of original Mat4
func (m Mat4) Transpose() Mat4 {
return Mat4{
[4]float64{m[0][0], m[1][0], m[2][0], m[3][0]},
[4]float64{m[0][1], m[1][1], m[2][1], m[3][1]},
[4]float64{m[0][2], m[1][2], m[2][2], m[3][2]},
[4]float64{m[0][3], m[1][3], m[2][3], m[3][3]},
}
}