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matrix.go
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matrix.go
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package vkm
import (
"unsafe"
"github.com/chewxy/math32"
)
// Mat is a column-major 4x4 matrix of float32s. Because it is fundamentally an array of arrays,
// elements can be directly addressed via double brackets: m[col][row]
type Mat [4]Vec
func (m *Mat) AsBytes() []byte {
return (*[64]byte)(unsafe.Pointer(m))[:]
}
// MultV computes a matrix multiplication on the provided vector
func (m Mat) MultV(v Vec) Vec {
return Vec{
m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0]*v[3],
m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1]*v[3],
m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2]*v[3],
m[0][3]*v[0] + m[1][3]*v[1] + m[2][3]*v[2] + m[3][3]*v[3],
}
}
// MultP computes a matrix multiplication on the provided point
func (m Mat) MultP(v Pt) Pt {
return Pt(m.MultV(Vec(v)))
}
// MultM performs a matrix multiplication.
func (m Mat) MultM(n Mat) Mat {
return Mat{
{
m[0][0]*n[0][0] + m[1][0]*n[0][1] + m[2][0]*n[0][2] + m[3][0]*n[0][3],
m[0][1]*n[0][0] + m[1][1]*n[0][1] + m[2][1]*n[0][2] + m[3][1]*n[0][3],
m[0][2]*n[0][0] + m[1][2]*n[0][1] + m[2][2]*n[0][2] + m[3][2]*n[0][3],
m[0][3]*n[0][0] + m[1][3]*n[0][1] + m[2][3]*n[0][2] + m[3][3]*n[0][3],
},
{
m[0][0]*n[1][0] + m[1][0]*n[1][1] + m[2][0]*n[1][2] + m[3][0]*n[1][3],
m[0][1]*n[1][0] + m[1][1]*n[1][1] + m[2][1]*n[1][2] + m[3][1]*n[1][3],
m[0][2]*n[1][0] + m[1][2]*n[1][1] + m[2][2]*n[1][2] + m[3][2]*n[1][3],
m[0][3]*n[1][0] + m[1][3]*n[1][1] + m[2][3]*n[1][2] + m[3][3]*n[1][3],
},
{
m[0][0]*n[2][0] + m[1][0]*n[2][1] + m[2][0]*n[2][2] + m[3][0]*n[2][3],
m[0][1]*n[2][0] + m[1][1]*n[2][1] + m[2][1]*n[2][2] + m[3][1]*n[2][3],
m[0][2]*n[2][0] + m[1][2]*n[2][1] + m[2][2]*n[2][2] + m[3][2]*n[2][3],
m[0][3]*n[2][0] + m[1][3]*n[2][1] + m[2][3]*n[2][2] + m[3][3]*n[2][3],
},
{
m[0][0]*n[3][0] + m[1][0]*n[3][1] + m[2][0]*n[3][2] + m[3][0]*n[3][3],
m[0][1]*n[3][0] + m[1][1]*n[3][1] + m[2][1]*n[3][2] + m[3][1]*n[3][3],
m[0][2]*n[3][0] + m[1][2]*n[3][1] + m[2][2]*n[3][2] + m[3][2]*n[3][3],
m[0][3]*n[3][0] + m[1][3]*n[3][1] + m[2][3]*n[3][2] + m[3][3]*n[3][3],
},
}
}
// Identity returns a 4x4 identity matrix
func Identity() Mat {
return Mat{
{1, 0, 0, 0},
{0, 1, 0, 0},
{0, 0, 1, 0},
{0, 0, 0, 1},
}
}
// Equals returns true if m and n are exactly equal. Note that this
// function does not allow for "approximately equal" conditions, like many
// floating point comparison functions.
func (m Mat) Equals(n Mat) bool {
for i := range m {
for j := range m[i] {
if m[i][j] != n[i][j] {
return false
}
}
}
return true
}
// ApproximatelyEquals returns true if m and n are equal component-for-component to within `precision`. Use this
// function if comparing two calculated matrices to determine if they are equal to within a reasonable precision.
func (m Mat) ApproximatelyEquals(n Mat, precision float32) bool {
for i := range m {
for j := range m[i] {
if math32.Abs(m[i][j]-n[i][j]) > precision {
return false
}
}
}
return true
}
// Transpose returns the transpose matrix of m.
func (m Mat) Transpose() Mat {
return Mat{
{m[0][0], m[1][0], m[2][0], m[3][0]},
{m[0][1], m[1][1], m[2][1], m[3][1]},
{m[0][2], m[1][2], m[2][2], m[3][2]},
{m[0][3], m[1][3], m[2][3], m[3][3]},
}
}
func (m Mat) Determinant() float32 {
return m[0][0]*
(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][3]*m[2][2]*m[3][1]-m[1][2]*m[2][1]*m[3][3]-m[1][1]*m[2][3]*m[3][2]) -
m[1][0]*
(m[0][1]*m[2][2]*m[3][3]+m[0][2]*m[2][3]*m[3][1]+m[0][3]*m[2][1]*m[3][2]-
m[0][3]*m[2][2]*m[3][1]-m[0][2]*m[2][1]*m[3][3]-m[0][1]*m[2][3]*m[3][2]) +
m[2][0]*
(m[0][1]*m[1][2]*m[3][3]+m[0][2]*m[1][3]*m[3][1]+m[0][3]*m[1][1]*m[3][2]-
m[0][3]*m[1][2]*m[3][1]-m[0][2]*m[1][1]*m[3][3]-m[0][1]*m[1][3]*m[3][2]) -
m[3][0]*
(m[0][1]*m[1][2]*m[2][3]+m[0][2]*m[1][3]*m[2][1]+m[0][3]*m[1][1]*m[2][2]-
m[0][3]*m[1][2]*m[2][1]-m[0][2]*m[1][1]*m[2][3]-m[0][1]*m[1][3]*m[2][2])
}
// Inverse returns the inverse matrix of m, i.e. the matrix such that m.MultM(m.Inverse()) yields the identity matrix.
func (m Mat) Inverse() Mat {
d := m.Determinant()
return Mat{
{
(m[1][1]*m[2][2]*m[3][3] + m[1][2]*m[3][2]*m[1][3] + m[3][1]*m[1][2]*m[2][3] - m[3][1]*m[2][2]*m[1][3] - m[2][1]*m[1][2]*m[3][3] - m[1][1]*m[3][2]*m[2][3]) / d,
-(m[0][1]*m[2][2]*m[3][3] + m[2][1]*m[3][2]*m[0][3] + m[3][1]*m[0][2]*m[2][3] - m[3][1]*m[2][2]*m[0][3] - m[2][1]*m[0][2]*m[3][3] - m[0][1]*m[3][2]*m[2][3]) / d,
(m[0][1]*m[1][2]*m[3][3] + m[1][1]*m[3][2]*m[0][3] + m[3][1]*m[0][2]*m[1][3] - m[3][1]*m[1][2]*m[0][3] - m[1][1]*m[0][2]*m[3][3] - m[0][1]*m[3][2]*m[1][3]) / d,
-(m[0][1]*m[1][2]*m[2][3] + m[1][1]*m[2][2]*m[0][3] + m[2][1]*m[0][2]*m[1][3] - m[2][1]*m[1][2]*m[0][3] - m[1][1]*m[0][2]*m[2][3] - m[0][1]*m[2][2]*m[1][3]) / d,
},
{
-(m[1][0]*m[2][2]*m[3][3] + m[2][0]*m[3][2]*m[1][3] + m[3][0]*m[1][2]*m[2][3] - m[3][0]*m[2][2]*m[1][3] - m[2][0]*m[1][2]*m[3][3] - m[1][0]*m[3][2]*m[2][3]) / d,
(m[0][0]*m[2][2]*m[3][3] + m[2][0]*m[3][2]*m[0][3] + m[3][0]*m[0][2]*m[2][3] - m[3][0]*m[2][2]*m[0][3] - m[2][0]*m[0][2]*m[3][3] - m[0][0]*m[3][2]*m[2][3]) / d,
-(m[0][0]*m[1][2]*m[3][3] + m[1][0]*m[3][2]*m[0][3] + m[3][0]*m[0][2]*m[1][3] - m[3][0]*m[1][2]*m[0][3] - m[1][0]*m[0][2]*m[3][3] - m[0][0]*m[3][2]*m[1][3]) / d,
(m[0][0]*m[1][2]*m[2][3] + m[1][0]*m[2][2]*m[0][3] + m[2][0]*m[0][2]*m[1][3] - m[2][0]*m[1][2]*m[0][3] - m[1][0]*m[0][2]*m[2][3] - m[0][0]*m[2][2]*m[1][3]) / d,
},
{
(m[1][0]*m[2][1]*m[3][3] + m[2][0]*m[3][1]*m[1][3] + m[3][0]*m[1][1]*m[2][3] - m[3][0]*m[2][1]*m[1][3] - m[2][0]*m[1][1]*m[3][3] - m[1][0]*m[3][1]*m[2][3]) / d,
-(m[0][0]*m[2][1]*m[3][3] + m[2][0]*m[3][1]*m[0][3] + m[3][0]*m[0][1]*m[2][3] - m[3][0]*m[2][1]*m[0][3] - m[2][0]*m[0][1]*m[3][3] - m[0][0]*m[3][1]*m[2][3]) / d,
(m[0][0]*m[1][1]*m[3][3] + m[1][0]*m[3][1]*m[0][3] + m[3][0]*m[0][1]*m[1][3] - m[3][0]*m[1][1]*m[0][3] - m[1][0]*m[0][1]*m[3][3] - m[0][0]*m[3][1]*m[1][3]) / d,
-(m[0][0]*m[1][1]*m[2][3] + m[1][0]*m[2][1]*m[0][3] + m[2][0]*m[0][1]*m[1][3] - m[2][0]*m[1][1]*m[0][3] - m[1][0]*m[0][1]*m[2][3] - m[0][0]*m[2][1]*m[1][3]) / d,
},
{
-(m[1][0]*m[2][1]*m[3][2] + m[2][0]*m[3][1]*m[1][2] + m[3][0]*m[1][1]*m[2][2] - m[3][0]*m[2][1]*m[1][2] - m[2][0]*m[1][1]*m[3][2] - m[1][0]*m[3][1]*m[2][2]) / d,
(m[0][0]*m[2][1]*m[3][2] + m[2][0]*m[3][1]*m[0][2] + m[3][0]*m[0][1]*m[2][2] - m[3][0]*m[2][1]*m[0][2] - m[2][0]*m[0][1]*m[3][2] - m[0][0]*m[3][1]*m[2][2]) / d,
-(m[0][0]*m[1][1]*m[3][2] + m[1][0]*m[3][1]*m[0][2] + m[3][0]*m[0][1]*m[1][2] - m[3][0]*m[1][1]*m[0][2] - m[1][0]*m[0][1]*m[3][2] - m[0][0]*m[3][1]*m[1][2]) / d,
(m[0][0]*m[1][1]*m[2][2] + m[1][0]*m[2][1]*m[0][2] + m[2][0]*m[0][1]*m[1][2] - m[2][0]*m[1][1]*m[0][2] - m[1][0]*m[0][1]*m[2][2] - m[0][0]*m[2][1]*m[1][2]) / d,
},
}
}