219 lines
6.9 KiB
Go
219 lines
6.9 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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)
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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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// Determinant compute the determinant of the matrix
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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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// Transform applies the transformation matrix to points. It modify the points passed in parameter.
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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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// TransformPoint applies the transformation matrix to point. It returns the point the transformed point.
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func (tr MatrixTransform) TransformPoint(x, y float64) (xres, yres float64) {
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xres = x*tr[0] + y*tr[2] + tr[4]
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yres = x*tr[1] + y*tr[3] + tr[5]
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return xres, yres
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}
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func minMax(x, y float64) (min, max float64) {
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if x > y {
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return y, x
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}
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return x, y
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}
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// Transform applies the transformation matrix to the rectangle represented by the min and the max point of the rectangle
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func (tr MatrixTransform) TransformRectangle(x0, y0, x2, y2 float64) (nx0, ny0, nx2, ny2 float64) {
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points := []float64{x0, y0, x2, y0, x2, y2, x0, y2}
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tr.Transform(points)
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points[0], points[2] = minMax(points[0], points[2])
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points[4], points[6] = minMax(points[4], points[6])
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points[1], points[3] = minMax(points[1], points[3])
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points[5], points[7] = minMax(points[5], points[7])
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nx0 = math.Min(points[0], points[4])
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ny0 = math.Min(points[1], points[5])
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nx2 = math.Max(points[2], points[6])
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ny2 = math.Max(points[3], points[7])
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return nx0, ny0, nx2, ny2
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}
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// InverseTransform applies the transformation inverse matrix to the rectangle represented by the min and the max point of the rectangle
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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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// InverseTransformPoint applies the transformation inverse matrix to point. It returns the point the transformed point.
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func (tr MatrixTransform) InverseTransformPoint(x, y float64) (xres, yres float64) {
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d := tr.Determinant() // matrix determinant
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xres = ((x-tr[4])*tr[3] - (y-tr[5])*tr[2]) / d
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yres = ((y-tr[5])*tr[0] - (x-tr[4])*tr[1]) / d
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return xres, yres
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}
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// VectorTransform applies the transformation matrix to points without using the translation parameter of the affine matrix.
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// It modify the points passed in parameter.
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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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// NewIdentityMatrix creates an identity transformation matrix.
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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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// NewTranslationMatrix creates a transformation matrix with a translation tx and ty translation parameter
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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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// NewScaleMatrix creates a transformation matrix with a sx, sy scale factor
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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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// NewRotationMatrix creates a rotation transformation matrix. angle is in radian
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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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// NewMatrixTransform creates a transformation matrix, combining a scale and a translation, that transform rectangle1 into rectangle2.
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func NewMatrixFromRects(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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// Inverse returns a matrix that is the inverse of the given matrix.
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func (tr MatrixTransform) Inverse() 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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// Multiply composes Matrix tr1 with tr2 returns the resulting matrix
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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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// Scale adds a scale to the matrix
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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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// Translate adds a translation to the matrix
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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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// Rotate adds a rotation to the matrix. angle is in radian
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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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// GetTranslation
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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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// GetScaling
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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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// GetScale computes the scale of the matrix
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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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// ******************** Testing ********************
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// Equals tests if a two transformation are equal. A tolerance is applied when comparing matrix elements.
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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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// IsIdentity tests if a transformation is the identity transformation. A tolerance is applied when comparing matrix elements.
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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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// IsTranslation tests if a transformation is is a pure translation. A tolerance is applied when comparing matrix elements.
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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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// fequals compares two floats. return true if the distance between the two floats is less than epsilon, false otherwise
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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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