Uniform non-rational cubic B-spline

Uniform non-rational cubic B-spline

    A special form of B-spline curve is Coons cubic. It is defined by its 4 operative dots V0 V1, V2 and V3 and by relation 

       1     | -1  3 -3  1 | | V0 |
B(t)= --- T. |  3 -6  3  0 | | V1 |.

       6     | -3  0  3  0 | | V2 |
             |  1  4  1  0 | | V3 |

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Coons cubic


     This cubic does not cross outer dots of its operative polygon. The curve starts and ends in dots 

        V0 + 4V1 +V2

B(0) = -----------------
              6
        V1 + 4V2 +V3
B(1) = -----------------
              6
Uniform non-rational cubic B-spline     Uniform non-rational cubic B-spline is termed also Coons cubic B-tangle. We obtain it by joining the following Coons kubics with particular operative angles: Bi    : Vi-3,Vi-2,Vi-1 a Vi
Bi+1 : Vi-2,Vi-1,Vi aVi+1,
Bi+2 : Vi-1,Vi,Vi+1 a Vi+2, where Coons cubic B-spline is given with n>=4 points and consist from n-3 segment's.

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Coons cubic B-spline with 8 points and 5 segment's

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Closed Coons cubic B-spline with 8 points and 5 segments, where first three and last three points are identical