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221 lines
6.8 KiB
Go
221 lines
6.8 KiB
Go
package drawing
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import (
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"math"
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)
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// Matrix represents an affine transformation
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type Matrix [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 Matrix) 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 Matrix) 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 Matrix) 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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// TransformRectangle applies the transformation matrix to the rectangle represented by the min and the max point of the rectangle
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func (tr Matrix) 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 Matrix) 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 Matrix) 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 Matrix) 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() Matrix {
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return Matrix{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) Matrix {
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return Matrix{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) Matrix {
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return Matrix{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) Matrix {
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c := math.Cos(angle)
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s := math.Sin(angle)
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return Matrix{c, s, -s, c, 0, 0}
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}
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// NewMatrixFromRects 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) Matrix {
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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 Matrix{xScale, 0, 0, yScale, xOffset, yOffset}
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}
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// Inverse computes the inverse matrix
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func (tr *Matrix) Inverse() {
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d := tr.Determinant() // matrix determinant
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tr0, tr1, tr2, tr3, tr4, tr5 := tr[0], tr[1], tr[2], tr[3], tr[4], tr[5]
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tr[0] = tr3 / d
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tr[1] = -tr1 / d
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tr[2] = -tr2 / d
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tr[3] = tr0 / d
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tr[4] = (tr2*tr5 - tr3*tr4) / d
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tr[5] = (tr1*tr4 - tr0*tr5) / d
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}
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// Copy copies the matrix.
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func (tr Matrix) Copy() Matrix {
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var result Matrix
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copy(result[:], tr[:])
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return result
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}
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// Compose multiplies trToConcat x tr
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func (tr *Matrix) Compose(trToCompose Matrix) {
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tr0, tr1, tr2, tr3, tr4, tr5 := tr[0], tr[1], tr[2], tr[3], tr[4], tr[5]
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tr[0] = trToCompose[0]*tr0 + trToCompose[1]*tr2
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tr[1] = trToCompose[1]*tr3 + trToCompose[0]*tr1
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tr[2] = trToCompose[2]*tr0 + trToCompose[3]*tr2
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tr[3] = trToCompose[3]*tr3 + trToCompose[2]*tr1
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tr[4] = trToCompose[4]*tr0 + trToCompose[5]*tr2 + tr4
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tr[5] = trToCompose[5]*tr3 + trToCompose[4]*tr1 + tr5
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}
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// Scale adds a scale to the matrix
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func (tr *Matrix) Scale(sx, sy float64) {
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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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}
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// Translate adds a translation to the matrix
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func (tr *Matrix) Translate(tx, ty float64) {
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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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}
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// Rotate adds a rotation to the matrix.
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func (tr *Matrix) Rotate(radians float64) {
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c := math.Cos(radians)
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s := math.Sin(radians)
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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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}
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// GetTranslation gets the matrix traslation.
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func (tr Matrix) GetTranslation() (x, y float64) {
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return tr[4], tr[5]
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}
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// GetScaling gets the matrix scaling.
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func (tr Matrix) GetScaling() (x, y float64) {
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return tr[0], tr[3]
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}
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// GetScale computes a scale for the matrix
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func (tr Matrix) 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 (tr Matrix) Equals(tr2 Matrix) bool {
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for i := 0; i < 6; i = i + 1 {
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if !fequals(tr[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 Matrix) 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 Matrix) 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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