derecursify casteljau
This commit is contained in:
Laurent Le Goff
parent
c49d784e7f
commit
9606b186e0
2 changed files with 190 additions and 43 deletions
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@ -7,56 +7,102 @@ import (
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)
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var (
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m_distance_tolerance float64 = 0.25
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flattening_threshold float64 = 0.25
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)
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type CubicCurveFloat64 struct {
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x1, y1, x2, y2, x3, y3, x4, y4 float64
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segments []float64
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}
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func NewCubicCurveFloat64(x1, y1, x2, y2, x3, y3, x4, y4 float64) (*CubicCurveFloat64){
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return &CubicCurveFloat64{x1, y1, x2, y2, x3, y3, x4, y4, make([]float64, 0, 2)}
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func NewCubicCurveFloat64(x1, y1, x2, y2, x3, y3, x4, y4 float64) *CubicCurveFloat64 {
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return &CubicCurveFloat64{x1, y1, x2, y2, x3, y3, x4, y4}
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}
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func (c *CubicCurveFloat64) addPoint(x, y float64) {
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c.segments = append(c.segments, x, y)
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//mu ranges from 0 to 1, start to end of curve
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func (c *CubicCurveFloat64) ArbitraryPoint(mu float64) (x, y float64) {
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mum1 := 1 - mu
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mum13 := mum1 * mum1 * mum1
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mu3 := mu * mu * mu
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x = mum13*c.x1 + 3*mu*mum1*mum1*c.x2 + 3*mu*mu*mum1*c.x3 + mu3*c.x4
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y = mum13*c.y1 + 3*mu*mum1*mum1*c.y2 + 3*mu*mu*mum1*c.y3 + mu3*c.y4
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return
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}
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func (c *CubicCurveFloat64) Subdivide() (c1, c2 *CubicCurveFloat64) {
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func (c *CubicCurveFloat64) SubdivideAt(c1, c2 *CubicCurveFloat64, t float64) {
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inv_t := (1 - t)
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c1.x1, c1.y1 = c.x1, c.y1
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c2.x4, c2.y4 = c.x4, c.y4
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c1.x2 = inv_t * c.x1 + t * c.x2
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c1.y2 = inv_t * c.y1 + t * c.y2
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x23 := inv_t * c.x2 + t * c.x3
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y23 := inv_t * c.y2 + t * c.y3
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c2.x3 = inv_t * c.x3 + t * c.x4
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c2.y3 = inv_t * c.y3 + t * c.y4
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c1.x3 = inv_t * c1.x2 + t * x23
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c1.y3 = inv_t * c1.y2 + t * y23
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c2.x2 = inv_t * x23 + t * c2.x3
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c2.y2 = inv_t * y23 + t * c2.y3
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c1.x4 = inv_t * c1.x3 + t * c2.x2
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c1.y4 = inv_t * c1.y3 + t * c2.y2
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c2.x1, c2.y1 = c1.x4, c1.y4
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}
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func (c *CubicCurveFloat64) Subdivide(c1, c2 *CubicCurveFloat64) {
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// Calculate all the mid-points of the line segments
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//----------------------
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x12 := (c.x1 + c.x2) / 2
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y12 := (c.y1 + c.y2) / 2
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c1.x1, c1.y1 = c.x1, c.y1
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c2.x4, c2.y4 = c.x4, c.y4
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c1.x2 = (c.x1 + c.x2) / 2
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c1.y2 = (c.y1 + c.y2) / 2
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x23 := (c.x2 + c.x3) / 2
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y23 := (c.y2 + c.y3) / 2
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x34 := (c.x3 + c.x4) / 2
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y34 := (c.y3 + c.y4) / 2
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x123 := (x12 + x23) / 2
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y123 := (y12 + y23) / 2
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x234 := (x23 + x34) / 2
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y234 := (y23 + y34) / 2
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x1234 := (x123 + x234) / 2
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y1234 := (y123 + y234) / 2
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c1 = &CubicCurveFloat64{c.x1, c.y1, x12, y12, x123, y123, x1234, y1234, c.segments}
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c2 = &CubicCurveFloat64{x1234, y1234, x234, y234, x34, y34, c.x4, c.y4, c.segments}
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return
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c2.x3 = (c.x3 + c.x4) / 2
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c2.y3 = (c.y3 + c.y4) / 2
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c1.x3 = (c1.x2 + x23) / 2
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c1.y3 = (c1.y2 + y23) / 2
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c2.x2 = (x23 + c2.x3) / 2
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c2.y2 = (y23 + c2.y3) / 2
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c1.x4 = (c1.x3 + c2.x2) / 2
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c1.y4 = (c1.y3 + c2.y2) / 2
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c2.x1, c2.y1 = c1.x4, c1.y4
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}
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func (c *CubicCurveFloat64) EstimateDistance() float64 {
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dx1 := c.x2 - c.x1
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dy1 := c.y2 - c.y1
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dx2 := c.x3 - c.x2
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dy2 := c.y3 - c.y2
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dx3 := c.x4 - c.x3
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dy3 := c.y4 - c.y3
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return math.Sqrt(dx1*dx1+dy1*dy1) + math.Sqrt(dx2*dx2+dy2*dy2) + math.Sqrt(dx3*dx3+dy3*dy3)
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}
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// subdivide the curve in straight lines using Casteljau subdivision
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// and computing minimal distance tolerance
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func (c *CubicCurveFloat64) SegmentCasteljau() []float64{
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func (c *CubicCurveFloat64) SegmentCasteljauRec(segments []float64) []float64 {
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// reinit segments
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c.segments = make([]float64, 0, 2)
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c.addPoint(c.x1, c.y1)
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c.segmentCasteljauRec()
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c.addPoint(c.x4, c.y4)
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return c.segments
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segments = segments[0 : len(segments)+2]
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segments[len(segments)-2] = c.x1
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segments[len(segments)-1] = c.y1
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segments = c.segmentCasteljauRec(segments)
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segments = segments[0 : len(segments)+2]
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segments[len(segments)-2] = c.x4
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segments[len(segments)-1] = c.y4
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return segments
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}
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func (c *CubicCurveFloat64) segmentCasteljauRec() {
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c1, c2 := c.Subdivide()
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func (c *CubicCurveFloat64) segmentCasteljauRec(segments []float64) []float64 {
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var c1, c2 CubicCurveFloat64
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c.Subdivide(&c1, &c2)
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// Try to approximate the full cubic curve by a single straight line
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//------------------
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@ -66,15 +112,47 @@ func (c *CubicCurveFloat64) segmentCasteljauRec() {
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d2 := math.Fabs(((c.x2-c.x4)*dy - (c.y2-c.y4)*dx))
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d3 := math.Fabs(((c.x3-c.x4)*dy - (c.y3-c.y4)*dx))
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if (d2+d3)*(d2+d3) < m_distance_tolerance*(dx*dx+dy*dy) {
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c.addPoint(c2.x1, c2.y1)
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return
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} else {
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// Continue subdivision
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//----------------------
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c1.segmentCasteljauRec()
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c2.segments = c1.segments
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c2.segmentCasteljauRec()
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c.segments = c2.segments
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if (d2+d3)*(d2+d3) < flattening_threshold*(dx*dx+dy*dy) {
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segments = segments[0 : len(segments)+2]
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segments[len(segments)-2] = c2.x1
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segments[len(segments)-1] = c2.y1
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return segments
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}
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// Continue subdivision
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//----------------------
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segments = c1.segmentCasteljauRec(segments)
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segments = c2.segmentCasteljauRec(segments)
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return segments
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}
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func (curve *CubicCurveFloat64) SegmentCasteljau(segments []float64) ([]float64) {
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var curves [32]CubicCurveFloat64
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curves[0] = *curve
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i := 0
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// current curve
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var c *CubicCurveFloat64
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var dx, dy, d2, d3 float64
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for i >= 0 {
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c = &curves[i]
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dx = c.x4 - c.x1
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dy = c.y4 - c.y1
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d2 = math.Fabs(((c.x2-c.x4)*dy - (c.y2-c.y4)*dx))
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d3 = math.Fabs(((c.x3-c.x4)*dy - (c.y3-c.y4)*dx))
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if (d2+d3)*(d2+d3) < flattening_threshold*(dx*dx+dy*dy) || i == len(curves) - 1 {
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segments = segments[0 : len(segments)+2]
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segments[len(segments)-2] = c.x1
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segments[len(segments)-1] = c.y1
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i--;
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} else {
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// second half of bezier go lower onto the stack
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c.Subdivide(&curves[i+1], &curves[i])
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i++;
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}
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}
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segments = segments[0 : len(segments)+2]
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segments[len(segments)-2] = curve.x1
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segments[len(segments)-1] = curve.y1
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return segments
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}
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@ -8,12 +8,81 @@ import (
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var (
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cf64Test1 = NewCubicCurveFloat64(100, 100, 200, 100, 100, 200, 200, 200)
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cf64Test2 = NewCubicCurveFloat64(100, 100, 300, 200, 200, 200, 200, 100)
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)
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func TestCubicCurveCasteljauRecTest1(t *testing.T) {
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var s []float64
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d := cf64Test1.EstimateDistance()
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log.Printf("Distance estimation: %f\n", d)
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numSegments := int(d * 0.25)
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log.Printf("Max segments estimation: %d\n", numSegments)
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s = make([]float64, 0, numSegments)
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s = cf64Test1.SegmentCasteljauRec(s)
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log.Printf("points: %v\n", s)
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log.Printf("Num of points: %d\n", len(s))
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}
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func TestCubicCurveCasteljauTest1(t *testing.T) {
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var s []float64
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d := cf64Test1.EstimateDistance()
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log.Printf("Distance estimation: %f\n", d)
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numSegments := int(d * 0.25)
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log.Printf("Max segments estimation: %d\n", numSegments)
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s = make([]float64, 0, numSegments)
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s = cf64Test1.SegmentCasteljau(s)
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log.Printf("points: %v\n", s)
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log.Printf("Num of points: %d\n", len(s))
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}
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func BenchmarkCubicCurveCasteljauRecTest1(b *testing.B) {
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var s []float64
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d := cf64Test1.EstimateDistance()
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log.Printf("Distance estimation: %f\n", d)
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numSegments := int(d * 0.25)
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log.Printf("Max segments estimation: %d\n", numSegments)
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for i := 0; i < b.N; i++ {
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s = make([]float64, 0, numSegments)
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s = cf64Test1.SegmentCasteljauRec(s)
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}
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log.Printf("Num of points: %d\n", len(s))
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}
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func BenchmarkCubicCurveCasteljauRecTest2(b *testing.B) {
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var s []float64
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d := cf64Test1.EstimateDistance()
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log.Printf("Distance estimation: %f\n", d)
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numSegments := int(d * 0.25)
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log.Printf("Max segments estimation: %d\n", numSegments)
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for i := 0; i < b.N; i++ {
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s = make([]float64, 0, numSegments)
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s = cf64Test2.SegmentCasteljauRec(s)
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}
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log.Printf("Num of points: %d\n", len(s))
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}
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func BenchmarkCubicCurveCasteljauTest1(b *testing.B) {
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var s []float64
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d := cf64Test1.EstimateDistance()
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log.Printf("Distance estimation: %f\n", d)
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numSegments := int(d * 0.25)
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log.Printf("Max segments estimation: %d\n", numSegments)
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for i := 0; i < b.N; i++ {
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s = cf64Test1.SegmentCasteljau()
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}
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log.Printf("Num of points: %d\n", len(s));
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}
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s = make([]float64, 0, numSegments)
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s = cf64Test1.SegmentCasteljau(s)
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}
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log.Printf("Num of points: %d\n", len(s))
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}
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func BenchmarkCubicCurveCasteljauTest2(b *testing.B) {
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var s []float64
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d := cf64Test1.EstimateDistance()
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log.Printf("Distance estimation: %f\n", d)
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numSegments := int(d * 0.25)
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log.Printf("Max segments estimation: %d\n", numSegments)
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for i := 0; i < b.N; i++ {
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s = make([]float64, 0, numSegments)
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s = cf64Test2.SegmentCasteljau(s)
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}
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log.Printf("Num of points: %d\n", len(s))
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}
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