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