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Construct Bezier curves from a B-spline curve

Shows a geometric construction of four cubic Bezier spans from a seven control point cubic B-spline (uniform knots, no weights) curve.

Download the MultiSurf file used to create the image.

Download an evaluation copy of MultiSurf.

The contents of the MultiSurf file:

MultiSurf 1.15 
// Show how a seven point cubic b-spline is broken into 4 cubic
// Bezier spans
Units: none
Symmetry: 
Extents:  -2.683 -5.134 -0.000 3.663 5.776 0.000
View:  90.00 0.00 1 
Places: 3
Layers: FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF
DivMult: 1
BeginModel;
AbsPoint pA  14  1 / -0.732 3.939 -0.000 ;
AbsPoint pB  14  1 / 2.589 4.516 0.000 ;
AbsPoint pC  14  1 / 3.452 0.660 0.000 ;
AbsPoint pD  14  1 / -2.485 3.107 -0.000 ;
AbsPoint pE  14  1 / 2.426 -2.075 0.000 ;
AbsPoint pF  14  1 / -0.686 -2.971 0.000 ;
AbsPoint pG  14  1 / 1.635 -5.134 0.000 ;
BCurve c0  11  1 32x4 / * 3
  { pA pB pC pD pE pF pG } ;
Line l0   6  1 1x1 / * pB pC ;
Line l1   6  1 1x1 / * pC pD ;
Line l2   6  1 1x1 / * pD pE ;
Line l3   6  1 1x1 / * pE pF ;
AbsBead e0  10  1 R:1 / l0 0.50000 ;
AbsBead e1  10  1 R:1 / l3 0.50000 ;
AbsBead e2  10  1 R:1 / l1 0.33333 ;
AbsBead e3  10  1 R:1 / l1 0.66667 ;
AbsBead e4  10  1 R:1 / l2 0.33333 ;
AbsBead e5  10  1 R:1 / l2 0.66667 ;
Line l4   6  1 1x1 / * e0 e2 ;
Line l5   6  1 1x1 / * e3 e4 ;
Line l6   6  1 1x1 / * e5 e1 ;
AbsBead e6  10  1 R:1 / l4 0.50000 ;
AbsBead e7  10  1 R:1 / l5 0.50000 ;
AbsBead e8  10  1 R:1 / l6 0.50000 ;
BCurve c1  14  1 8x4 / * 3
  { pA pB e0 e6 } ;
BCurve c2  14  1 8x4 R:1 / * 3
  { e7 e4 e5 e8 } ;
BCurve c3  13  1 8x4 R:1 / * 3
  { e6 e2 e3 e7 } ;
BCurve c4  13  1 8x4 R:1 / * 3
  { e8 e1 pF pG } ;
EndModel;

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