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mat3.go
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mat3.go
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// Copyright 2015 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 math
import (
"fmt"
)
// A 3x3 matrix:
// ╭ ╮
// │ M₀ M₁ M₂ │
// │ M₃ M₄ M₅ │
// │ M₆ M₇ M₈ │
// ╰ ╯
type Mat3 [9]float32
func CreateMat3(r0c0, r0c1, r0c2, r1c0, r1c1, r1c2, r2c0, r2c1, r2c2 float32) Mat3 {
return Mat3{
r0c0, r0c1, r0c2,
r1c0, r1c1, r1c2,
r2c0, r2c1, r2c2,
}
}
// Build a 3x3 matrix from 3 row vectors
// ╭ ╮
// │ R₀ │
// │ R₁ │
// │ R₂ │
// ╰ ╯
func CreateMat3FromRows(r0, r1, r2 Vec3) Mat3 {
return Mat3{
r0.X, r0.Y, r0.Z,
r1.X, r1.Y, r1.Z,
r2.X, r2.Y, r2.Z,
}
}
// A
// ╱ ╲
// ╱___╲
// B C
//
// [V₀, V₁, V₂] * M = [λ₀, λ₁, 1]
// λ₂ = 1 - (λ₀ + λ₁)
//
// [V₀, V₁, V₂] = A • λ₀ + B • λ₁ + C • λ₂
//
// A * M = (1, 0, 1)
// B * M = (0, 1, 1)
// C * M = (0, 0, 1)
func CreateMat3PositionToBarycentric(a, b, c Vec2) Mat3 {
m := CreateMat2FromRows(a.Sub(c), b.Sub(c)).Invert()
o := MulVM2(c, m)
return Mat3{
m[0], m[1], 0,
m[2], m[3], 0,
-o.X, -o.Y, 1,
}
}
func (m Mat3) String() string {
s := make([]string, 9)
l := 0
for i, v := range m {
s[i] = fmt.Sprintf("%.5f", v)
l = Max(l, len(s[i]))
}
for i, _ := range m {
for len(s[i]) < l {
s[i] = " " + s[i]
}
}
p := ""
for i := 0; i < l; i++ {
p += " "
}
return fmt.Sprintf(
"\n╭ %s %s %s ╮"+
"\n│ %s %s %s │"+
"\n│ %s %s %s │"+
"\n│ %s %s %s │"+
"\n╰ %s %s %s ╯",
p, p, p,
s[0], s[1], s[2],
s[3], s[4], s[5],
s[6], s[7], s[8],
p, p, p,
)
}
func (m Mat3) Rows() (r0, r1, r2 Vec3) {
return Vec3{m[0], m[1], m[2]}, Vec3{m[3], m[4], m[5]}, Vec3{m[6], m[7], m[8]}
}
func (m Mat3) Row(i int) Vec3 {
i *= 3
return Vec3{m[i+0], m[i+1], m[i+2]}
}
func (m Mat3) Invert() Mat3 {
// ╭ ╮
// 1 │ C₁ ⨯ C₂ │
// M⁻¹ = ─── │ C₂ ⨯ C₀ │
// det │ C₀ ⨯ C₁ │
// ╰ ╯
//
// Where: det = C₀ • (C₁ ⨯ C₂)
//
C0, C1, C2 := m.Transpose().Rows()
C0C1, C1C2, C2C0 := C0.Cross(C1), C1.Cross(C2), C2.Cross(C0)
det := C0.Dot(C1C2)
inv := CreateMat3FromRows(C1C2, C2C0, C0C1).DivS(det)
return inv
}
func (m Mat3) Transpose() Mat3 {
return CreateMat3(
m[0], m[3], m[6],
m[1], m[4], m[7],
m[2], m[5], m[8],
)
}
func (m Mat3) DivS(s float32) Mat3 {
return CreateMat3FromRows(
m.Row(0).DivS(s),
m.Row(1).DivS(s),
m.Row(2).DivS(s),
)
}