31. Computer Aided Design t = [0,1,2,3,4,5]
B-Spline ノットは1ずつ単純増加
t - ti
ti+1 - ti bi,0
t - ti
bi,1
ti+2 - ti ti+2 - t bi+1,0
ti+2 - ti+1
bi,2
t - ti+1
ti+2 - ti+1 bi+1,0
ti+3 - t
bi+1,1
ti+3 - ti+1 ti+3 - t
bi+2,0
ti+3 - ti+2
32. Computer Aided Design
B-Spline
t - ti bi,0
t - ti
bi,1
2
ti+2 - t bi+1,0
bi,2
t - ti+1 bi+1,0
ti+3 - t
bi+1,1
2
ti+3 - t bi+2,0
33. Computer Aided Design
B-Spline
i=0のとき
t b0,0
t
bi,1
2
2-t b1,0
b0,2
t - 1 b1,0
3-t
bi+1,1
2
3 - t b2,0
34. Computer Aided Design
B-Spline
i=0 0 t<1のとき t2
t b0,0
t 2
bi,1
2
2-t b1,0
b0,2
t - 1 b1,0
3-t
bi+1,1
2
3 - t b2,0
35. Computer Aided Design
B-Spline
i=0 1 t<2のとき
t b0,0
t
bi,1
2
2-t b1,0
2
3
b0,2 -t + 3t - 2
t - 1 b1,0
3-t
bi+1,1
2
3 - t b2,0
36. Computer Aided Design
B-Spline
i=0 2 t<3のとき
t b0,0
t
bi,1
2
2-t b1,0
b0,2
t - 1 b1,0
3-t
bi+1,1 t 2 - 6t + 9
2
3 - t b2,0 2
46. t - ti
ti+1 - ti bi,0
Computer Aided Design t - ti
bi,1
ti+2 - ti ti+2 - t bi+1,0
Cubic B-Spline ti+2 - ti+1
t - ti
bi,2
ti+3 - t
t - ti+1
ti+2 - ti+1
bi+1,0
ti+3 - t
bi+1,1
ti+3 - ti+1 ti+3 - t
ti+3 - ti+2
bi+2,0
bi,3
t - ti
ti+2 - ti bi+1,0
t - ti+1
bi+1,1
ti+3 - ti+1 ti+3 - t bi+2,0
ti+3 - ti+2
ti+4 - t bi+1,2
ti+4 - ti+1
t - ti+2
ti+3 - ti+2
bi+2,0
ti+4 - t
bi+2,1
ti+4 - ti+2 ti+4 - t
ti+4 - ti+3
bi+3,0