draw2d/transform.go

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