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155 lines
3.9 KiB
Go
155 lines
3.9 KiB
Go
// SPDX-License-Identifier: Unlicense OR MIT
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package f32
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import (
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"math"
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)
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// Affine2D represents an affine 2D transformation. The zero value if Affine2D
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// represents the identity transform.
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type Affine2D struct {
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// in order to make the zero value of Affine2D represent the identity
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// transform we store it with the identity matrix subtracted, that is
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// if the actual transformaiton matrix is:
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// [sx, hx, ox]
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// [hy, sy, oy]
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// [ 0, 0, 1]
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// we store a = sx-1 and e = sy-1
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a, b, c float32
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d, e, f float32
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}
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// NewAffine2D creates a new Affine2D transform from the matrix elements
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// in row major order. The rows are: [sx, hx, ox], [hy, sy, oy], [0, 0, 1].
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func NewAffine2D(sx, hx, ox, hy, sy, oy float32) Affine2D {
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return Affine2D{
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a: sx, b: hx, c: ox,
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d: hy, e: sy, f: oy,
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}.encode()
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}
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// Offset the transformation.
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func (a Affine2D) Offset(offset Point) Affine2D {
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return Affine2D{
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a.a, a.b, a.c + offset.X,
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a.d, a.e, a.f + offset.Y,
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}
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}
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// Scale the transformation around the given origin.
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func (a Affine2D) Scale(origin, factor Point) Affine2D {
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if origin == (Point{}) {
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return a.scale(factor)
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}
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a = a.Offset(origin.Mul(-1))
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a = a.scale(factor)
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return a.Offset(origin)
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}
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// Rotate the transformation by the given angle (in radians) counter clockwise around the given origin.
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func (a Affine2D) Rotate(origin Point, radians float32) Affine2D {
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if origin == (Point{}) {
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return a.rotate(radians)
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}
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a = a.Offset(origin.Mul(-1))
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a = a.rotate(radians)
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return a.Offset(origin)
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}
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// Shear the transformation by the given angle (in radians) around the given origin.
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func (a Affine2D) Shear(origin Point, radiansX, radiansY float32) Affine2D {
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if origin == (Point{}) {
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return a.shear(radiansX, radiansY)
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}
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a = a.Offset(origin.Mul(-1))
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a = a.shear(radiansX, radiansY)
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return a.Offset(origin)
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}
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// Mul returns A*B.
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func (A Affine2D) Mul(B Affine2D) (r Affine2D) {
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A, B = A.decode(), B.decode()
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r.a = A.a*B.a + A.b*B.d
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r.b = A.a*B.b + A.b*B.e
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r.c = A.a*B.c + A.b*B.f + A.c
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r.d = A.d*B.a + A.e*B.d
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r.e = A.d*B.b + A.e*B.e
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r.f = A.d*B.c + A.e*B.f + A.f
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return r.encode()
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}
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// Invert the transformation. Note that if the matrix is close to singular
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// numerical errors may become large or infinity.
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func (a Affine2D) Invert() Affine2D {
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if a.a == 0 && a.b == 0 && a.d == 0 && a.e == 0 {
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return Affine2D{a: 0, b: 0, c: -a.c, d: 0, e: 0, f: -a.f}
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}
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a = a.decode()
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det := a.a*a.e - a.b*a.d
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a.a, a.e = a.e/det, a.a/det
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a.b, a.d = -a.b/det, -a.d/det
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temp := a.c
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a.c = -a.a*a.c - a.b*a.f
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a.f = -a.d*temp - a.e*a.f
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return a.encode()
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}
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// Transform p by returning a*p.
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func (a Affine2D) Transform(p Point) Point {
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a = a.decode()
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return Point{
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X: p.X*a.a + p.Y*a.b + a.c,
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Y: p.X*a.d + p.Y*a.e + a.f,
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}
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}
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// Elems returns the matrix elements of the transform in row-major order. The
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// rows are: [sx, hx, ox], [hy, sy, oy], [0, 0, 1].
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func (a Affine2D) Elems() (sx, hx, ox, hy, sy, oy float32) {
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a = a.decode()
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return a.a, a.b, a.c, a.d, a.e, a.f
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}
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func (a Affine2D) encode() Affine2D {
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// since we store with identity matrix subtracted
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a.a -= 1
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a.e -= 1
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return a
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}
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func (a Affine2D) decode() Affine2D {
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// since we store with identity matrix subtracted
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a.a += 1
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a.e += 1
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return a
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}
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func (a Affine2D) scale(factor Point) Affine2D {
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a = a.decode()
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return Affine2D{
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a.a * factor.X, a.b * factor.X, a.c * factor.X,
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a.d * factor.Y, a.e * factor.Y, a.f * factor.Y,
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}.encode()
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}
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func (a Affine2D) rotate(radians float32) Affine2D {
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sin, cos := math.Sincos(float64(radians))
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s, c := float32(sin), float32(cos)
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a = a.decode()
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return Affine2D{
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a.a*c - a.d*s, a.b*c - a.e*s, a.c*c - a.f*s,
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a.a*s + a.d*c, a.b*s + a.e*c, a.c*s + a.f*c,
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}.encode()
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}
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func (a Affine2D) shear(radiansX, radiansY float32) Affine2D {
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tx := float32(math.Tan(float64(radiansX)))
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ty := float32(math.Tan(float64(radiansY)))
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a = a.decode()
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return Affine2D{
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a.a + a.d*tx, a.b + a.e*tx, a.c + a.f*tx,
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a.a*ty + a.d, a.b*ty + a.e, a.f*ty + a.f,
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}.encode()
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}
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