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matrix tweaks

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This commit is contained in:
Josh Deprez 2021-09-09 11:35:59 +10:00
parent 4c7b447a01
commit 74f72d06a6
2 changed files with 30 additions and 20 deletions
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6
engine/depth.go
View file

@ -8,20 +8,14 @@ import (
const screenShaderSrc = `package main const screenShaderSrc = `package main
var ScreenSize vec2
func Fragment(position vec4, texCoord vec2, color vec4) vec4 { func Fragment(position vec4, texCoord vec2, color vec4) vec4 {
return imageSrc0UnsafeAt(texCoord) return imageSrc0UnsafeAt(texCoord)
} }
` `
const depthShaderSrc = `package main const depthShaderSrc = `package main
var ScreenSize vec2
func Fragment(position vec4, texCoord vec2, color vec4) vec4 { func Fragment(position vec4, texCoord vec2, color vec4) vec4 {
return imageSrc0UnsafeAt(texCoord) return imageSrc0UnsafeAt(texCoord)
} }
` `

44
geom/matrix.go
View file

@ -97,32 +97,48 @@ func (a RatMatrix3) IntApply(v Int3) Int3 {
} }
} }
// Inverse returns the inverse of the matrix. // Mul multiplies the whole matrix by a scalar.
func (a RatMatrix3) Inverse() (RatMatrix3, error) { func (a RatMatrix3) Mul(r Rat) RatMatrix3 {
adj := RatMatrix3{ // "A little repetition..."
a[0][0] = a[0][0].Mul(r)
a[0][1] = a[0][1].Mul(r)
a[0][2] = a[0][2].Mul(r)
a[1][0] = a[1][0].Mul(r)
a[1][1] = a[1][1].Mul(r)
a[1][2] = a[1][2].Mul(r)
a[2][0] = a[2][0].Mul(r)
a[2][1] = a[2][1].Mul(r)
a[2][2] = a[2][2].Mul(r)
return a
}
// Adjugate returns the adjugate of the matrix.
func (a RatMatrix3) Adjugate() RatMatrix3 {
return RatMatrix3{
0: [3]Rat{ 0: [3]Rat{
0: a[1][1].Mul(a[2][2]).Sub(a[1][2].Mul(a[2][1])), 0: a[1][1].Mul(a[2][2]).Sub(a[1][2].Mul(a[2][1])),
1: a[0][1].Mul(a[2][2]).Sub(a[0][2].Mul(a[2][1])).Neg(),
2: a[0][1].Mul(a[1][2]).Sub(a[0][2].Mul(a[1][1])),
}, },
1: [3]Rat{ 1: [3]Rat{
0: a[1][0].Mul(a[2][2]).Sub(a[1][2].Mul(a[2][0])).Neg(), 0: a[1][0].Mul(a[2][2]).Sub(a[1][2].Mul(a[2][0])).Neg(),
1: a[0][0].Mul(a[2][2]).Sub(a[0][2].Mul(a[2][0])),
2: a[0][0].Mul(a[1][2]).Sub(a[0][2].Mul(a[1][0])).Neg(),
}, },
2: [3]Rat{ 2: [3]Rat{
0: a[1][0].Mul(a[2][1]).Sub(a[1][1].Mul(a[2][0])), 0: a[1][0].Mul(a[2][1]).Sub(a[1][1].Mul(a[2][0])),
1: a[0][0].Mul(a[2][1]).Sub(a[0][1].Mul(a[2][0])).Neg(),
2: a[0][0].Mul(a[1][1]).Sub(a[0][1].Mul(a[1][0])),
}, },
// other columns after determinant...
} }
}
// Inverse returns the inverse of the matrix.
func (a RatMatrix3) Inverse() (RatMatrix3, error) {
adj := a.Adjugate()
det := a[0][0].Mul(adj[0][0]).Add(a[0][1].Mul(adj[1][0])).Add(a[0][2].Mul(adj[2][0])) det := a[0][0].Mul(adj[0][0]).Add(a[0][1].Mul(adj[1][0])).Add(a[0][2].Mul(adj[2][0]))
if det.N == 0 { if det.N == 0 {
return RatMatrix3{}, errors.New("matrix is singular") return RatMatrix3{}, errors.New("matrix is singular")
} }
adj[0][0] = adj[0][0].Div(det) return adj.Mul(det.Invert()), nil
adj[1][0] = adj[1][0].Div(det)
adj[2][0] = adj[2][0].Div(det)
adj[0][1] = a[0][1].Mul(a[2][2]).Sub(a[0][2].Mul(a[2][1])).Neg().Div(det)
adj[0][2] = a[0][1].Mul(a[1][2]).Sub(a[0][2].Mul(a[1][1])).Div(det)
adj[1][1] = a[0][0].Mul(a[2][2]).Sub(a[0][2].Mul(a[2][0])).Div(det)
adj[1][2] = a[0][0].Mul(a[1][2]).Sub(a[0][2].Mul(a[1][0])).Neg().Div(det)
adj[2][1] = a[0][0].Mul(a[2][1]).Sub(a[0][1].Mul(a[2][0])).Neg().Div(det)
adj[2][2] = a[0][0].Mul(a[1][1]).Sub(a[0][1].Mul(a[1][0])).Div(det)
return adj, nil
} }