307 lines
7.7 KiB
Go
307 lines
7.7 KiB
Go
// Copyright 2010 The draw2d Authors. All rights reserved.
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// created: 21/11/2010 by Laurent Le Goff
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package draw2d
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import (
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"math"
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"code.google.com/p/freetype-go/freetype/raster"
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)
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type MatrixTransform [6]float64
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const (
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epsilon = 1e-6
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)
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func (tr MatrixTransform) Determinant() float64 {
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return tr[0]*tr[3] - tr[1]*tr[2]
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}
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func (tr MatrixTransform) Transform(points ...*float64) {
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for i, j := 0, 1; j < len(points); i, j = i+2, j+2 {
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x := *points[i]
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y := *points[j]
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*points[i] = x*tr[0] + y*tr[2] + tr[4]
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*points[j] = x*tr[1] + y*tr[3] + tr[5]
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}
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}
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func (tr MatrixTransform) TransformArray(points []float64) {
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for i, j := 0, 1; j < len(points); i, j = i+2, j+2 {
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x := points[i]
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y := points[j]
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points[i] = x*tr[0] + y*tr[2] + tr[4]
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points[j] = x*tr[1] + y*tr[3] + tr[5]
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}
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}
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func (tr MatrixTransform) TransformRectangle(x0, y0, x2, y2 *float64) {
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x1 := *x2
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y1 := *y0
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x3 := *x0
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y3 := *y2
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tr.Transform(x0, y0, &x1, &y1, x2, y2, &x3, &y3)
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*x0, x1 = minMax(*x0, x1)
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*x2, x3 = minMax(*x2, x3)
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*y0, y1 = minMax(*y0, y1)
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*y2, y3 = minMax(*y2, y3)
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*x0 = min(*x0, *x2)
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*y0 = min(*y0, *y2)
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*x2 = max(x1, x3)
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*y2 = max(y1, y3)
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}
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func (tr MatrixTransform) TransformRasterPoint(points ...*raster.Point) {
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for _, point := range points {
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x := float64(point.X) / 256
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y := float64(point.Y) / 256
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point.X = raster.Fix32((x*tr[0] + y*tr[2] + tr[4]) * 256)
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point.Y = raster.Fix32((x*tr[1] + y*tr[3] + tr[5]) * 256)
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}
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}
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func (tr MatrixTransform) InverseTransform(points ...*float64) {
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d := tr.Determinant() // matrix determinant
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for i, j := 0, 1; j < len(points); i, j = i+2, j+2 {
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x := *points[i]
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y := *points[j]
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*points[i] = ((x-tr[4])*tr[3] - (y-tr[5])*tr[2]) / d
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*points[j] = ((y-tr[5])*tr[0] - (x-tr[4])*tr[1]) / d
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}
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}
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// ******************** Vector transformations ********************
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func (tr MatrixTransform) VectorTransform(points ...*float64) {
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for i, j := 0, 1; j < len(points); i, j = i+2, j+2 {
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x := *points[i]
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y := *points[j]
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*points[i] = x*tr[0] + y*tr[2]
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*points[j] = x*tr[1] + y*tr[3]
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}
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}
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// ******************** Transformations creation ********************
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/** Creates an identity transformation. */
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func NewIdentityMatrix() MatrixTransform {
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return [6]float64{1, 0, 0, 1, 0, 0}
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}
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/**
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* Creates a transformation with a translation, that,
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* transform point1 into point2.
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*/
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func NewTranslationMatrix(tx, ty float64) MatrixTransform {
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return [6]float64{1, 0, 0, 1, tx, ty}
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}
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/**
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* Creates a transformation with a sx, sy scale factor
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*/
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func NewScaleMatrix(sx, sy float64) MatrixTransform {
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return [6]float64{sx, 0, 0, sy, 0, 0}
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}
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/**
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* Creates a rotation transformation.
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*/
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func NewRotationMatrix(angle float64) MatrixTransform {
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c := math.Cos(angle)
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s := math.Sin(angle)
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return [6]float64{c, s, -s, c, 0, 0}
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}
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/**
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* Creates a transformation, combining a scale and a translation, that transform rectangle1 into rectangle2.
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*/
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func NewMatrixTransform(rectangle1, rectangle2 [4]float64) MatrixTransform {
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xScale := (rectangle2[2] - rectangle2[0]) / (rectangle1[2] - rectangle1[0])
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yScale := (rectangle2[3] - rectangle2[1]) / (rectangle1[3] - rectangle1[1])
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xOffset := rectangle2[0] - (rectangle1[0] * xScale)
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yOffset := rectangle2[1] - (rectangle1[1] * yScale)
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return [6]float64{xScale, 0, 0, yScale, xOffset, yOffset}
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}
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// ******************** Transformations operations ********************
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/**
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* Returns a transformation that is the inverse of the given transformation.
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*/
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func (tr MatrixTransform) GetInverseTransformation() MatrixTransform {
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d := tr.Determinant() // matrix determinant
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return [6]float64{
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tr[3] / d,
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-tr[1] / d,
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-tr[2] / d,
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tr[0] / d,
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(tr[2]*tr[5] - tr[3]*tr[4]) / d,
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(tr[1]*tr[4] - tr[0]*tr[5]) / d}
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}
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func (tr1 MatrixTransform) Multiply(tr2 MatrixTransform) MatrixTransform {
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return [6]float64{
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tr1[0]*tr2[0] + tr1[1]*tr2[2],
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tr1[1]*tr2[3] + tr1[0]*tr2[1],
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tr1[2]*tr2[0] + tr1[3]*tr2[2],
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tr1[3]*tr2[3] + tr1[2]*tr2[1],
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tr1[4]*tr2[0] + tr1[5]*tr2[2] + tr2[4],
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tr1[5]*tr2[3] + tr1[4]*tr2[1] + tr2[5]}
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}
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func (tr *MatrixTransform) Scale(sx, sy float64) *MatrixTransform {
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tr[0] = sx * tr[0]
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tr[1] = sx * tr[1]
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tr[2] = sy * tr[2]
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tr[3] = sy * tr[3]
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return tr
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}
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func (tr *MatrixTransform) Translate(tx, ty float64) *MatrixTransform {
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tr[4] = tx*tr[0] + ty*tr[2] + tr[4]
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tr[5] = ty*tr[3] + tx*tr[1] + tr[5]
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return tr
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}
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func (tr *MatrixTransform) Rotate(angle float64) *MatrixTransform {
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c := math.Cos(angle)
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s := math.Sin(angle)
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t0 := c*tr[0] + s*tr[2]
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t1 := s*tr[3] + c*tr[1]
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t2 := c*tr[2] - s*tr[0]
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t3 := c*tr[3] - s*tr[1]
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tr[0] = t0
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tr[1] = t1
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tr[2] = t2
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tr[3] = t3
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return tr
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}
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func (tr MatrixTransform) GetTranslation() (x, y float64) {
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return tr[4], tr[5]
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}
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func (tr MatrixTransform) GetScaling() (x, y float64) {
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return tr[0], tr[3]
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}
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func (tr MatrixTransform) GetScale() float64 {
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x := 0.707106781*tr[0] + 0.707106781*tr[1]
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y := 0.707106781*tr[2] + 0.707106781*tr[3]
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return math.Sqrt(x*x + y*y)
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}
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func (tr MatrixTransform) GetMaxAbsScaling() (s float64) {
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sx := math.Abs(tr[0])
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sy := math.Abs(tr[3])
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if sx > sy {
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return sx
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}
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return sy
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}
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func (tr MatrixTransform) GetMinAbsScaling() (s float64) {
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sx := math.Abs(tr[0])
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sy := math.Abs(tr[3])
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if sx > sy {
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return sy
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}
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return sx
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}
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// ******************** Testing ********************
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/**
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* Tests if a two transformation are equal. A tolerance is applied when
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* comparing matrix elements.
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*/
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func (tr1 MatrixTransform) Equals(tr2 MatrixTransform) bool {
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for i := 0; i < 6; i = i + 1 {
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if !fequals(tr1[i], tr2[i]) {
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return false
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}
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}
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return true
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}
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/**
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* Tests if a transformation is the identity transformation. A tolerance
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* is applied when comparing matrix elements.
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*/
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func (tr MatrixTransform) IsIdentity() bool {
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return fequals(tr[4], 0) && fequals(tr[5], 0) && tr.IsTranslation()
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}
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/**
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* Tests if a transformation is is a pure translation. A tolerance
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* is applied when comparing matrix elements.
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*/
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func (tr MatrixTransform) IsTranslation() bool {
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return fequals(tr[0], 1) && fequals(tr[1], 0) && fequals(tr[2], 0) && fequals(tr[3], 1)
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}
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/**
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* Compares two floats.
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* return true if the distance between the two floats is less than epsilon, false otherwise
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*/
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func fequals(float1, float2 float64) bool {
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return math.Abs(float1-float2) <= epsilon
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}
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// this VertexConverter apply the Matrix transformation tr
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type VertexMatrixTransform struct {
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tr MatrixTransform
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Next VertexConverter
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}
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func NewVertexMatrixTransform(tr MatrixTransform, converter VertexConverter) *VertexMatrixTransform {
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return &VertexMatrixTransform{tr, converter}
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}
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// Vertex Matrix Transform
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func (vmt *VertexMatrixTransform) NextCommand(command VertexCommand) {
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vmt.Next.NextCommand(command)
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}
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func (vmt *VertexMatrixTransform) Vertex(x, y float64) {
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u := x*vmt.tr[0] + y*vmt.tr[2] + vmt.tr[4]
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v := x*vmt.tr[1] + y*vmt.tr[3] + vmt.tr[5]
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vmt.Next.Vertex(u, v)
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}
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// this adder apply a Matrix transformation to points
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type MatrixTransformAdder struct {
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tr MatrixTransform
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next raster.Adder
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}
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func NewMatrixTransformAdder(tr MatrixTransform, adder raster.Adder) *MatrixTransformAdder {
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return &MatrixTransformAdder{tr, adder}
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}
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// Start starts a new curve at the given point.
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func (mta MatrixTransformAdder) Start(a raster.Point) {
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mta.tr.TransformRasterPoint(&a)
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mta.next.Start(a)
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}
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// Add1 adds a linear segment to the current curve.
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func (mta MatrixTransformAdder) Add1(b raster.Point) {
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mta.tr.TransformRasterPoint(&b)
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mta.next.Add1(b)
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}
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// Add2 adds a quadratic segment to the current curve.
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func (mta MatrixTransformAdder) Add2(b, c raster.Point) {
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mta.tr.TransformRasterPoint(&b, &c)
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mta.next.Add2(b, c)
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}
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// Add3 adds a cubic segment to the current curve.
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func (mta MatrixTransformAdder) Add3(b, c, d raster.Point) {
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mta.tr.TransformRasterPoint(&b, &c, &d)
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mta.next.Add3(b, c, d)
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}
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