321 lines
8 KiB
Go
321 lines
8 KiB
Go
// Copyright 2010 The draw2d Authors. All rights reserved.
|
|
// created: 21/11/2010 by Laurent Le Goff
|
|
|
|
package draw2d
|
|
|
|
import (
|
|
"math"
|
|
|
|
"code.google.com/p/freetype-go/freetype/raster"
|
|
"github.com/llgcode/draw2d/path"
|
|
)
|
|
|
|
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) {
|
|
sx := math.Abs(tr[0])
|
|
sy := math.Abs(tr[3])
|
|
if sx > sy {
|
|
return sx
|
|
}
|
|
return sy
|
|
}
|
|
|
|
func (tr MatrixTransform) GetMinAbsScaling() (s float64) {
|
|
sx := math.Abs(tr[0])
|
|
sy := math.Abs(tr[3])
|
|
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 {
|
|
return math.Abs(float1-float2) <= epsilon
|
|
}
|
|
|
|
// this VertexConverter apply the Matrix transformation tr
|
|
type VertexMatrixTransform struct {
|
|
tr MatrixTransform
|
|
Next path.LineBuilder
|
|
}
|
|
|
|
func NewVertexMatrixTransform(tr MatrixTransform, converter path.LineBuilder) *VertexMatrixTransform {
|
|
return &VertexMatrixTransform{tr, converter}
|
|
}
|
|
|
|
func (vmt *VertexMatrixTransform) MoveTo(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.MoveTo(u, v)
|
|
}
|
|
|
|
func (vmt *VertexMatrixTransform) LineTo(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.LineTo(u, v)
|
|
}
|
|
|
|
func (vmt *VertexMatrixTransform) LineJoin() {
|
|
vmt.Next.LineJoin()
|
|
}
|
|
|
|
func (vmt *VertexMatrixTransform) Close() {
|
|
vmt.Next.Close()
|
|
}
|
|
|
|
func (vmt *VertexMatrixTransform) End() {
|
|
vmt.Next.End()
|
|
}
|
|
|
|
// 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)
|
|
}
|