Begin to work on matrix transformation (does not yet really work)
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legoff.laurent
parent
2fed1b9393
commit
aec12d2759
2 changed files with 254 additions and 2 deletions
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@ -39,6 +39,7 @@ type GraphicContext struct {
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}
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type contextStack struct {
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tr MatrixTransform
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path *Path
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lineWidth float
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dash []float
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@ -48,7 +49,6 @@ type contextStack struct {
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fillRule FillRule
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cap Cap
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join Join
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previous *contextStack
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}
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@ -62,16 +62,50 @@ func NewGraphicContext(pi *image.RGBA) *GraphicContext {
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gc.rasterizer = raster.NewRasterizer(width, height)
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gc.current = new(contextStack)
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gc.current.tr = NewIdentityMatrix()
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gc.current.path = new(Path)
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gc.current.lineWidth = 1.0
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gc.current.strokeColor = image.Black
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gc.current.fillColor = image.White
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gc.current.cap = RoundCap
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gc.current.fillRule = FillRuleEvenOdd
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gc.current.join = RoundJoin
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gc.current.path = new(Path)
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return gc
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}
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func (gc *GraphicContext) SetMatrixTransform(tr MatrixTransform) {
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gc.current.tr = tr
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}
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func (gc *GraphicContext) ComposeMatrixTransform(tr MatrixTransform) {
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gc.current.tr.Compose(tr)
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}
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func (gc *GraphicContext) Rotate(angle float) {
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ox, oy := gc.current.path.LastPoint()
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tr := NewTranslationMatrix(ox, oy)
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tr2 := NewRotationMatrix(angle)
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tr1 := tr.GetInverseTransformation()
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gc.current.tr.Compose(tr).Compose(tr2).Compose(tr1)
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}
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func (gc *GraphicContext) Translate(tx, ty float) {
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ox, oy := gc.current.path.LastPoint()
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tr := NewTranslationMatrix(ox, oy)
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tr2 := NewTranslationMatrix(tx, ty)
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tr1 := tr.GetInverseTransformation()
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gc.current.tr.Compose(tr).Compose(tr2).Compose(tr1)
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}
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func (gc *GraphicContext) Scale(sx, sy float) {
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ox, oy := gc.current.path.LastPoint()
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tr := NewTranslationMatrix(ox, oy)
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tr2 := NewScaleMatrix(sx, sy)
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tr1 := tr.GetInverseTransformation()
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gc.current.tr.Compose(tr).Compose(tr2).Compose(tr1)
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}
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func (gc *GraphicContext) Clear() {
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width, height := gc.PaintedImage.Bounds().Dx(), gc.PaintedImage.Bounds().Dy()
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gc.ClearRect(0, 0, width, height)
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@ -139,50 +173,64 @@ func (gc *GraphicContext) BeginPath() {
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}
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func (gc *GraphicContext) MoveTo(x, y float) {
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gc.current.tr.Transform(&x, &y)
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gc.current.path.MoveTo(x, y)
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}
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func (gc *GraphicContext) RMoveTo(dx, dy float) {
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gc.current.tr.VectorTransform(&dx, &dy)
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gc.current.path.RMoveTo(dx, dy)
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}
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func (gc *GraphicContext) LineTo(x, y float) {
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gc.current.tr.Transform(&x, &y)
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gc.current.path.LineTo(x, y)
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}
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func (gc *GraphicContext) RLineTo(dx, dy float) {
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gc.current.tr.VectorTransform(&dx, &dy)
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gc.current.path.RLineTo(dx, dy)
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}
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func (gc *GraphicContext) Rect(x1, y1, x2, y2 float) {
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gc.current.tr.Transform(&x1, &y1, &x2, &y2)
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gc.current.path.Rect(x1, y1, x2, y2)
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}
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func (gc *GraphicContext) RRect(dx1, dy1, dx2, dy2 float) {
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gc.current.tr.VectorTransform(&dx1, &dy1, &dx2, &dy2)
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gc.current.path.RRect(dx1, dy1, dx2, dy2)
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}
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func (gc *GraphicContext) QuadCurveTo(cx, cy, x, y float) {
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gc.current.tr.Transform(&cx, &cy, &x, &y)
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gc.current.path.QuadCurveTo(cx, cy, x, y)
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}
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func (gc *GraphicContext) RQuadCurveTo(dcx, dcy, dx, dy float) {
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gc.current.tr.VectorTransform(&dcx, &dcy, &dx, &dy)
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gc.current.path.RQuadCurveTo(dcx, dcy, dx, dy)
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}
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func (gc *GraphicContext) CubicCurveTo(cx1, cy1, cx2, cy2, x, y float) {
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gc.current.tr.Transform(&cx1, &cy1, &cx2, &cy2, &x, &y)
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gc.current.path.CubicCurveTo(cx1, cy1, cx2, cy2, x, y)
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}
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func (gc *GraphicContext) RCubicCurveTo(dcx1, dcy1, dcx2, dcy2, dx, dy float) {
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gc.current.tr.VectorTransform(&dcx1, &dcy1, &dcx2, &dcy2, &dx, &dy)
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gc.current.path.RCubicCurveTo(dcx1, dcy1, dcx2, dcy2, dx, dy)
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}
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func (gc *GraphicContext) ArcTo(cx, cy, rx, ry, startAngle, angle float) {
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gc.current.tr.Transform(&cx, &cy)
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gc.current.tr.VectorTransform(&rx, &ry)
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gc.current.path.ArcTo(cx, cy, rx, ry, startAngle, angle)
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}
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func (gc *GraphicContext) RArcTo(dcx, dcy, rx, ry, startAngle, angle float) {
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gc.current.tr.VectorTransform(&dcx, &dcy)
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gc.current.tr.VectorTransform(&rx, &ry)
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gc.current.path.RArcTo(dcx, dcy, rx, ry, startAngle, angle)
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}
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204
draw2d/src/pkg/draw2d/transform.go
Normal file
204
draw2d/src/pkg/draw2d/transform.go
Normal file
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@ -0,0 +1,204 @@
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// 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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type MatrixTransform [6]float
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const (
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epsilon = 1e-6
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)
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func (tr MatrixTransform) TransformX(x, y float) float {
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return x*tr[0] + y*tr[2] + tr[4]
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}
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func (tr MatrixTransform) TransformY(x, y float) float {
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return x*tr[1] + y*tr[3] + tr[5]
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}
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func (tr MatrixTransform) Determinant() float {
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return tr[0]*tr[3] - tr[1]*tr[2]
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}
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func (tr MatrixTransform) InverseTransformX(x, y float) float {
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return ((x-tr[4])*tr[3] - (y-tr[5])*tr[2]) / tr.Determinant()
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}
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func (tr MatrixTransform) InverseTransformY(x, y float) float {
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return ((y-tr[5])*tr[0] - (x-tr[4])*tr[1]) / tr.Determinant()
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}
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func (tr MatrixTransform) Transform(points ...*float) {
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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] = tr.TransformX(x, y)
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*points[j] = tr.TransformY(x, y)
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}
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}
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func (tr MatrixTransform) InverseTransform(points ...*float) {
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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) VectorTransformX(x, y float) float {
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return x*tr[0] + y*tr[2]
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}
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func (tr MatrixTransform) VectorTransformY(x, y float) float {
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return x*tr[1] + y*tr[3]
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}
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func (tr MatrixTransform) VectorInverseTransformX(x, y float) float {
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d := tr.Determinant() // matrix determinant
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return (x*tr[3] - y*tr[2]) / d
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}
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func (tr MatrixTransform) VectorInverseTransformY(x, y float) float {
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d := tr.Determinant() // matrix determinant
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return (y*tr[0] - x*tr[1]) / d
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}
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func (tr MatrixTransform) VectorTransform(points ...*float) {
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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] = tr.VectorTransformX(x, y)
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*points[j] = tr.VectorTransformY(x, y)
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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]float{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 float) MatrixTransform {
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return [6]float{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 float) MatrixTransform {
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return [6]float{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 float) MatrixTransform {
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c := cos(angle)
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s := sin(angle)
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return [6]float{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 [4]float, rectangle2 [4]float) 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]float{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]float{
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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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/**
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* Returns a transformation that is the composition (tr2 o tr1) of the given
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* transformations tr2 and tr1.
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* For given point (x, y), the composed transformation is defined by the
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* equation:
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* (tr2 o tr1)(x, y) = tr2(tr1(x, y))
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*/
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func (tr1 MatrixTransform) GetComposedTransformation(tr2 MatrixTransform) MatrixTransform {
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return [6]float{
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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 (tr1 *MatrixTransform) Compose(tr2 MatrixTransform) (*MatrixTransform){
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tr1[0] = tr2[0]*tr1[0] + tr2[1]*tr1[2]
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tr1[1] = tr2[1]*tr1[3] + tr2[0]*tr1[1]
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tr1[2] = tr2[2]*tr1[0] + tr2[3]*tr1[2]
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tr1[3] = tr2[3]*tr1[3] + tr2[2]*tr1[1]
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tr1[4] = tr2[4]*tr1[0] + tr2[5]*tr1[2] + tr1[4]
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tr1[5] = tr2[5]*tr1[3] + tr2[4]*tr1[1] + tr1[5]
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return tr1
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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 float) bool {
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return fabs(float1-float2) <= epsilon
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}
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