Method Transform

path.go:1267–1341

Transform transforms the path by the given transformation matrix. It modifies the path in-place.

(m Matrix)

// Transform transforms the path by the given transformation matrix. It modifies the path in-place.
func (p *Path) Transform(m Matrix) *Path {
	_, _, _, xscale, yscale, _ := m.Decompose()
	for i := 0; i < len(p.d); {
		cmd := p.d[i]
		switch cmd {
		case MoveToCmd, LineToCmd, CloseCmd:
			end := m.Dot(Point{p.d[i+1], p.d[i+2]})
			p.d[i+1] = end.X
			p.d[i+2] = end.Y
		case QuadToCmd:
			cp := m.Dot(Point{p.d[i+1], p.d[i+2]})
			end := m.Dot(Point{p.d[i+3], p.d[i+4]})
			p.d[i+1] = cp.X
			p.d[i+2] = cp.Y
			p.d[i+3] = end.X
			p.d[i+4] = end.Y
		case CubeToCmd:
			cp1 := m.Dot(Point{p.d[i+1], p.d[i+2]})
			cp2 := m.Dot(Point{p.d[i+3], p.d[i+4]})
			end := m.Dot(Point{p.d[i+5], p.d[i+6]})
			p.d[i+1] = cp1.X
			p.d[i+2] = cp1.Y
			p.d[i+3] = cp2.X
			p.d[i+4] = cp2.Y
			p.d[i+5] = end.X
			p.d[i+6] = end.Y
		case ArcToCmd:
			rx := p.d[i+1]
			ry := p.d[i+2]
			phi := p.d[i+3]
			large, sweep := toArcFlags(p.d[i+4])
			end := Point{p.d[i+5], p.d[i+6]}

			// For ellipses written as the conic section equation in matrix form, we have:
			// [x, y] E [x; y] = 0, with E = [1/rx^2, 0; 0, 1/ry^2]
			// For our transformed ellipse we have [x', y'] = T [x, y], with T the affine
			// transformation matrix so that
			// (T^-1 [x'; y'])^T E (T^-1 [x'; y'] = 0  =>  [x', y'] T^(-T) E T^(-1) [x'; y'] = 0
			// We define Q = T^(-1,T) E T^(-1) the new ellipse equation which is typically rotated
			// from the x-axis. That's why we find the eigenvalues and eigenvectors (the new
			// direction and length of the major and minor axes).
			T := m.Rotate(phi * 180.0 / math.Pi)
			invT := T.Inv()
			Q := Identity.Scale(1.0/rx/rx, 1.0/ry/ry)
			Q = invT.T().Mul(Q).Mul(invT)

			lambda1, lambda2, v1, v2 := Q.Eigen()
			rx = 1 / math.Sqrt(lambda1)
			ry = 1 / math.Sqrt(lambda2)
			phi = v1.Angle()
			if rx < ry {
				rx, ry = ry, rx
				phi = v2.Angle()
			}
			phi = angleNorm(phi)
			if math.Pi <= phi { // phi is canonical within 0 <= phi < 180
				phi -= math.Pi
			}