219 lines
6.8 KiB
Go
219 lines
6.8 KiB
Go
package drawing
|
|
|
|
import (
|
|
"math"
|
|
)
|
|
|
|
// Matrix represents an affine transformation
|
|
type Matrix [6]float64
|
|
|
|
const (
|
|
epsilon = 1e-6
|
|
)
|
|
|
|
// Determinant compute the determinant of the matrix
|
|
func (tr Matrix) Determinant() float64 {
|
|
return tr[0]*tr[3] - tr[1]*tr[2]
|
|
}
|
|
|
|
// Transform applies the transformation matrix to points. It modify the points passed in parameter.
|
|
func (tr Matrix) Transform(points []float64) {
|
|
for i, j := 0, 1; j < len(points); i, j = i+2, j+2 {
|
|
x := points[i]
|
|
y := points[j]
|
|
points[i] = x*tr[0] + y*tr[2] + tr[4]
|
|
points[j] = x*tr[1] + y*tr[3] + tr[5]
|
|
}
|
|
}
|
|
|
|
// TransformPoint applies the transformation matrix to point. It returns the point the transformed point.
|
|
func (tr Matrix) TransformPoint(x, y float64) (xres, yres float64) {
|
|
xres = x*tr[0] + y*tr[2] + tr[4]
|
|
yres = x*tr[1] + y*tr[3] + tr[5]
|
|
return xres, yres
|
|
}
|
|
|
|
func minMax(x, y float64) (min, max float64) {
|
|
if x > y {
|
|
return y, x
|
|
}
|
|
return x, y
|
|
}
|
|
|
|
// Transform applies the transformation matrix to the rectangle represented by the min and the max point of the rectangle
|
|
func (tr Matrix) TransformRectangle(x0, y0, x2, y2 float64) (nx0, ny0, nx2, ny2 float64) {
|
|
points := []float64{x0, y0, x2, y0, x2, y2, x0, y2}
|
|
tr.Transform(points)
|
|
points[0], points[2] = minMax(points[0], points[2])
|
|
points[4], points[6] = minMax(points[4], points[6])
|
|
points[1], points[3] = minMax(points[1], points[3])
|
|
points[5], points[7] = minMax(points[5], points[7])
|
|
|
|
nx0 = math.Min(points[0], points[4])
|
|
ny0 = math.Min(points[1], points[5])
|
|
nx2 = math.Max(points[2], points[6])
|
|
ny2 = math.Max(points[3], points[7])
|
|
return nx0, ny0, nx2, ny2
|
|
}
|
|
|
|
// InverseTransform applies the transformation inverse matrix to the rectangle represented by the min and the max point of the rectangle
|
|
func (tr Matrix) InverseTransform(points []float64) {
|
|
d := tr.Determinant() // matrix determinant
|
|
for i, j := 0, 1; j < len(points); i, j = i+2, j+2 {
|
|
x := points[i]
|
|
y := points[j]
|
|
points[i] = ((x-tr[4])*tr[3] - (y-tr[5])*tr[2]) / d
|
|
points[j] = ((y-tr[5])*tr[0] - (x-tr[4])*tr[1]) / d
|
|
}
|
|
}
|
|
|
|
// InverseTransformPoint applies the transformation inverse matrix to point. It returns the point the transformed point.
|
|
func (tr Matrix) InverseTransformPoint(x, y float64) (xres, yres float64) {
|
|
d := tr.Determinant() // matrix determinant
|
|
xres = ((x-tr[4])*tr[3] - (y-tr[5])*tr[2]) / d
|
|
yres = ((y-tr[5])*tr[0] - (x-tr[4])*tr[1]) / d
|
|
return xres, yres
|
|
}
|
|
|
|
// VectorTransform applies the transformation matrix to points without using the translation parameter of the affine matrix.
|
|
// It modify the points passed in parameter.
|
|
func (tr Matrix) VectorTransform(points []float64) {
|
|
for i, j := 0, 1; j < len(points); i, j = i+2, j+2 {
|
|
x := points[i]
|
|
y := points[j]
|
|
points[i] = x*tr[0] + y*tr[2]
|
|
points[j] = x*tr[1] + y*tr[3]
|
|
}
|
|
}
|
|
|
|
// NewIdentityMatrix creates an identity transformation matrix.
|
|
func NewIdentityMatrix() Matrix {
|
|
return Matrix{1, 0, 0, 1, 0, 0}
|
|
}
|
|
|
|
// NewTranslationMatrix creates a transformation matrix with a translation tx and ty translation parameter
|
|
func NewTranslationMatrix(tx, ty float64) Matrix {
|
|
return Matrix{1, 0, 0, 1, tx, ty}
|
|
}
|
|
|
|
// NewScaleMatrix creates a transformation matrix with a sx, sy scale factor
|
|
func NewScaleMatrix(sx, sy float64) Matrix {
|
|
return Matrix{sx, 0, 0, sy, 0, 0}
|
|
}
|
|
|
|
// NewRotationMatrix creates a rotation transformation matrix. angle is in radian
|
|
func NewRotationMatrix(angle float64) Matrix {
|
|
c := math.Cos(angle)
|
|
s := math.Sin(angle)
|
|
return Matrix{c, s, -s, c, 0, 0}
|
|
}
|
|
|
|
// NewMatrixFromRects creates a transformation matrix, combining a scale and a translation, that transform rectangle1 into rectangle2.
|
|
func NewMatrixFromRects(rectangle1, rectangle2 [4]float64) Matrix {
|
|
xScale := (rectangle2[2] - rectangle2[0]) / (rectangle1[2] - rectangle1[0])
|
|
yScale := (rectangle2[3] - rectangle2[1]) / (rectangle1[3] - rectangle1[1])
|
|
xOffset := rectangle2[0] - (rectangle1[0] * xScale)
|
|
yOffset := rectangle2[1] - (rectangle1[1] * yScale)
|
|
return Matrix{xScale, 0, 0, yScale, xOffset, yOffset}
|
|
}
|
|
|
|
// Inverse computes the inverse matrix
|
|
func (tr *Matrix) Inverse() {
|
|
d := tr.Determinant() // matrix determinant
|
|
tr0, tr1, tr2, tr3, tr4, tr5 := tr[0], tr[1], tr[2], tr[3], tr[4], tr[5]
|
|
tr[0] = tr3 / d
|
|
tr[1] = -tr1 / d
|
|
tr[2] = -tr2 / d
|
|
tr[3] = tr0 / d
|
|
tr[4] = (tr2*tr5 - tr3*tr4) / d
|
|
tr[5] = (tr1*tr4 - tr0*tr5) / d
|
|
}
|
|
|
|
func (tr Matrix) Copy() Matrix {
|
|
var result Matrix
|
|
copy(result[:], tr[:])
|
|
return result
|
|
}
|
|
|
|
// Compose multiplies trToConcat x tr
|
|
func (tr *Matrix) Compose(trToCompose Matrix) {
|
|
tr0, tr1, tr2, tr3, tr4, tr5 := tr[0], tr[1], tr[2], tr[3], tr[4], tr[5]
|
|
tr[0] = trToCompose[0]*tr0 + trToCompose[1]*tr2
|
|
tr[1] = trToCompose[1]*tr3 + trToCompose[0]*tr1
|
|
tr[2] = trToCompose[2]*tr0 + trToCompose[3]*tr2
|
|
tr[3] = trToCompose[3]*tr3 + trToCompose[2]*tr1
|
|
tr[4] = trToCompose[4]*tr0 + trToCompose[5]*tr2 + tr4
|
|
tr[5] = trToCompose[5]*tr3 + trToCompose[4]*tr1 + tr5
|
|
}
|
|
|
|
// Scale adds a scale to the matrix
|
|
func (tr *Matrix) Scale(sx, sy float64) {
|
|
tr[0] = sx * tr[0]
|
|
tr[1] = sx * tr[1]
|
|
tr[2] = sy * tr[2]
|
|
tr[3] = sy * tr[3]
|
|
}
|
|
|
|
// Translate adds a translation to the matrix
|
|
func (tr *Matrix) Translate(tx, ty float64) {
|
|
tr[4] = tx*tr[0] + ty*tr[2] + tr[4]
|
|
tr[5] = ty*tr[3] + tx*tr[1] + tr[5]
|
|
}
|
|
|
|
// Rotate adds a rotation to the matrix. angle is in radian
|
|
func (tr *Matrix) Rotate(angle float64) {
|
|
c := math.Cos(angle)
|
|
s := math.Sin(angle)
|
|
t0 := c*tr[0] + s*tr[2]
|
|
t1 := s*tr[3] + c*tr[1]
|
|
t2 := c*tr[2] - s*tr[0]
|
|
t3 := c*tr[3] - s*tr[1]
|
|
tr[0] = t0
|
|
tr[1] = t1
|
|
tr[2] = t2
|
|
tr[3] = t3
|
|
}
|
|
|
|
// GetTranslation
|
|
func (tr Matrix) GetTranslation() (x, y float64) {
|
|
return tr[4], tr[5]
|
|
}
|
|
|
|
// GetScaling
|
|
func (tr Matrix) GetScaling() (x, y float64) {
|
|
return tr[0], tr[3]
|
|
}
|
|
|
|
// GetScale computes a scale for the matrix
|
|
func (tr Matrix) GetScale() float64 {
|
|
x := 0.707106781*tr[0] + 0.707106781*tr[1]
|
|
y := 0.707106781*tr[2] + 0.707106781*tr[3]
|
|
return math.Sqrt(x*x + y*y)
|
|
}
|
|
|
|
// ******************** Testing ********************
|
|
|
|
// Equals tests if a two transformation are equal. A tolerance is applied when comparing matrix elements.
|
|
func (tr1 Matrix) Equals(tr2 Matrix) bool {
|
|
for i := 0; i < 6; i = i + 1 {
|
|
if !fequals(tr1[i], tr2[i]) {
|
|
return false
|
|
}
|
|
}
|
|
return true
|
|
}
|
|
|
|
// IsIdentity tests if a transformation is the identity transformation. A tolerance is applied when comparing matrix elements.
|
|
func (tr Matrix) IsIdentity() bool {
|
|
return fequals(tr[4], 0) && fequals(tr[5], 0) && tr.IsTranslation()
|
|
}
|
|
|
|
// IsTranslation tests if a transformation is is a pure translation. A tolerance is applied when comparing matrix elements.
|
|
func (tr Matrix) IsTranslation() bool {
|
|
return fequals(tr[0], 1) && fequals(tr[1], 0) && fequals(tr[2], 0) && fequals(tr[3], 1)
|
|
}
|
|
|
|
// fequals compares two floats. return true if the distance between the two floats is less than epsilon, false otherwise
|
|
func fequals(float1, float2 float64) bool {
|
|
return math.Abs(float1-float2) <= epsilon
|
|
}
|