128 lines
4.1 KiB
Go
128 lines
4.1 KiB
Go
package geom
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import (
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"errors"
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"image"
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)
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// IntMatrix3 implements a 3x3 integer matrix.
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type IntMatrix3 [3][3]int
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// Apply applies the matrix to a vector to obtain a transformed vector.
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func (a IntMatrix3) Apply(v Int3) Int3 {
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return Int3{
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X: v.X*a[0][0] + v.Y*a[0][1] + v.Z*a[0][2],
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Y: v.X*a[1][0] + v.Y*a[1][1] + v.Z*a[1][2],
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Z: v.X*a[2][0] + v.Y*a[2][1] + v.Z*a[2][2],
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}
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}
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// Concat returns the matrix equivalent to applying matrix a and then b.
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func (a IntMatrix3) Concat(b IntMatrix3) IntMatrix3 {
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return IntMatrix3{
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[3]int{
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a[0][0]*b[0][0] + a[0][1]*b[1][0] + a[0][2]*b[2][0],
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a[0][0]*b[0][1] + a[0][1]*b[1][1] + a[0][2]*b[2][1],
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a[0][0]*b[0][2] + a[0][1]*b[1][2] + a[0][2]*b[2][2],
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},
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[3]int{
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a[1][0]*b[0][0] + a[1][1]*b[1][0] + a[1][2]*b[2][0],
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a[1][0]*b[0][1] + a[1][1]*b[1][1] + a[1][2]*b[2][1],
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a[1][0]*b[0][2] + a[1][1]*b[1][2] + a[1][2]*b[2][2],
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},
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[3]int{
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a[2][0]*b[0][0] + a[2][1]*b[1][0] + a[2][2]*b[2][0],
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a[2][0]*b[0][1] + a[2][1]*b[1][1] + a[2][2]*b[2][1],
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a[2][0]*b[0][2] + a[2][1]*b[1][2] + a[2][2]*b[2][2],
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},
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}
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}
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// IntMatrix3x4 implements a 3 row, 4 column integer matrix, capable of
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// describing any integer affine transformation.
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type IntMatrix3x4 [3][4]int
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// Apply applies the matrix to a vector to obtain a transformed vector.
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func (a IntMatrix3x4) Apply(v Int3) Int3 {
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return Int3{
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X: v.X*a[0][0] + v.Y*a[0][1] + v.Z*a[0][2] + a[0][3],
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Y: v.X*a[1][0] + v.Y*a[1][1] + v.Z*a[1][2] + a[1][3],
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Z: v.X*a[2][0] + v.Y*a[2][1] + v.Z*a[2][2] + a[2][3],
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}
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}
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// ToRatMatrix3 returns the 3x3 submatrix as a rational matrix equivalent.
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func (a IntMatrix3x4) ToRatMatrix3() RatMatrix3 {
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return RatMatrix3{
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0: [3]Rat{{a[0][0], 1}, {a[0][1], 1}, {a[0][2], 1}},
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1: [3]Rat{{a[1][0], 1}, {a[1][1], 1}, {a[1][2], 1}},
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2: [3]Rat{{a[2][0], 1}, {a[2][1], 1}, {a[2][2], 1}},
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}
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}
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// Translation returns the translation component of the matrix (last column)
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// i.e. what you get if you Apply the matrix to the zero vector.
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func (a IntMatrix3x4) Translation() Int3 {
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return Int3{X: a[0][3], Y: a[1][3], Z: a[2][3]}
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}
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// IntMatrix2x3 implements a 2 row, 3 column matrix (as two row vectors).
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type IntMatrix2x3 struct{ X, Y Int3 }
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// Apply applies the matrix to a vector to obtain a transformed vector.
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func (a IntMatrix2x3) Apply(v Int3) image.Point {
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return image.Point{
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X: v.Dot(a.X),
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Y: v.Dot(a.Y),
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}
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}
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// RatMatrix3 implements a 3x3 matrix with rational number entries.
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type RatMatrix3 [3][3]Rat
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// IdentityRatMatrix3x4 is the identity matrix for RatMatrix3x4.
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var IdentityRatMatrix3 = RatMatrix3{
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0: [3]Rat{0: {1, 1}},
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1: [3]Rat{1: {1, 1}},
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2: [3]Rat{2: {1, 1}},
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}
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// IntApply applies the matrix to the integer vector v. Any remainder is lost.
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func (a RatMatrix3) IntApply(v Int3) Int3 {
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x, y, z := IntRat(v.X), IntRat(v.Y), IntRat(v.Z)
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return Int3{
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X: x.Mul(a[0][0]).Add(y.Mul(a[0][1])).Add(z.Mul(a[0][2])).Int(),
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Y: x.Mul(a[1][0]).Add(y.Mul(a[1][1])).Add(z.Mul(a[1][2])).Int(),
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Z: x.Mul(a[2][0]).Add(y.Mul(a[2][1])).Add(z.Mul(a[2][2])).Int(),
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}
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}
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// Inverse returns the inverse of the matrix.
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func (a RatMatrix3) Inverse() (RatMatrix3, error) {
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adj := RatMatrix3{
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0: [3]Rat{
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0: a[1][1].Mul(a[2][2]).Sub(a[1][2].Mul(a[2][1])),
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},
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1: [3]Rat{
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0: a[1][0].Mul(a[2][2]).Sub(a[1][2].Mul(a[2][0])).Neg(),
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},
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2: [3]Rat{
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0: a[1][0].Mul(a[2][1]).Sub(a[1][1].Mul(a[2][0])),
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},
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// other columns after determinant...
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}
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det := a[0][0].Mul(adj[0][0]).Add(a[0][1].Mul(adj[1][0])).Add(a[0][2].Mul(adj[2][0]))
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if det.N == 0 {
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return RatMatrix3{}, errors.New("matrix is singular")
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}
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adj[0][0] = adj[0][0].Div(det)
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adj[1][0] = adj[1][0].Div(det)
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adj[2][0] = adj[2][0].Div(det)
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adj[0][1] = a[0][1].Mul(a[2][2]).Sub(a[0][2].Mul(a[2][1])).Neg().Div(det)
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adj[0][2] = a[0][1].Mul(a[1][2]).Sub(a[0][2].Mul(a[1][1])).Div(det)
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adj[1][1] = a[0][0].Mul(a[2][2]).Sub(a[0][2].Mul(a[2][0])).Div(det)
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adj[1][2] = a[0][0].Mul(a[1][2]).Sub(a[0][2].Mul(a[1][0])).Neg().Div(det)
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adj[2][1] = a[0][0].Mul(a[2][1]).Sub(a[0][1].Mul(a[2][0])).Neg().Div(det)
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adj[2][2] = a[0][0].Mul(a[1][1]).Sub(a[0][1].Mul(a[1][0])).Div(det)
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return adj, nil
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}
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