2 # $Id: spline.dem,v 1.6 2004/09/28 06:06:10 sfeam Exp $
4 # Some curve plotting using common cubic polynomial basis function for cagd.
6 # Gershon Elber, Aug. 1992
17 set title "The cubic Monomial basis functions"
18 plot m0(x), m1(x), m2(x), m3(x)
19 pause -1 "Press return to continue"
21 h00(x) = x**2 * ( 2 * x - 3) + 1
22 h01(x) = -x**2 * (2 * x - 3)
23 h10(x) = x * (x - 1)**2
24 h11(x) = x**2 * (x - 1)
26 set title "The cubic Hermite basis functions"
27 plot h00(x), h01(x), h10(x), h11(x)
28 pause -1 "Press return to continue"
31 bez1(x) = 3 * (1 - x)**2 * x
32 bez2(x) = 3 * (1 - x) * x**2
34 set title "The cubic Bezier basis functions"
35 plot bez0(x), bez1(x), bez2(x), bez3(x)
36 pause -1 "Press return to continue"
38 bsp0(x) = ( 1 - 3 * x + 3 * x**2 - x**3 ) / 6;
39 bsp1(x) = ( 4 - 6 * x**2 + 3 * x**3 ) / 6;
40 bsp2(x) = ( 1 + 3 * x + 3 * x**2 - 3 * x**3 ) / 6
42 set title "The cubic uniform Bspline basis functions"
43 plot bsp0(x), bsp1(x), bsp2(x), bsp3(x)
44 pause -1 "Press return to continue"
61 set arrow from x0,y0 to x1,y1 nohead
62 set arrow from x1,y1 to x2,y2 nohead
63 set arrow from x2,y2 to x3,y3 nohead
65 cub_bezier_x(t) = bez0(t) * x0 + bez1(t) * x1 + bez2(t) * x2 + bez3(t) * x3
66 cub_bezier_y(t) = bez0(t) * y0 + bez1(t) * y1 + bez2(t) * y2 + bez3(t) * y3
67 cub_bsplin_x(t) = bsp0(t) * x0 + bsp1(t) * x1 + bsp2(t) * x2 + bsp3(t) * x3
68 cub_bsplin_y(t) = bsp0(t) * y0 + bsp1(t) * y1 + bsp2(t) * y2 + bsp3(t) * y3
72 set title "The cubic Bezier/Bspline basis functions in use"
73 plot cub_bezier_x(t), cub_bezier_y(t) with lines lt 2,\
74 cub_bsplin_x(t), cub_bsplin_y(t) with lines lt 3
75 pause -1 "Press return to continue"
79 # Note the arrows here, scaled by 1/3 so they will fit into plotting area
81 set arrow from x1,y1 to x1+xv0/3,y1+yv0/3
82 set arrow from x2,y2 to x2+xv1/3,y2+yv1/3
83 set arrow from x1,y1 to x1+xv0,y1+yv0
84 set arrow from x2,y2 to x2+xv1,y2+yv1
86 cub_hermit_x1(t) = h00(t) * x1 + h01(t) * x2 + h10(t) * xv0 + h11(t) * xv1
87 cub_hermit_y1(t) = h00(t) * y1 + h01(t) * y2 + h10(t) * yv0 + h11(t) * yv1
88 cub_hermit_x2(t) = h00(t) * x1 + h01(t) * x2 + h10(t) * xv0*3 + h11(t) * xv1*3
89 cub_hermit_y2(t) = h00(t) * y1 + h01(t) * y2 + h10(t) * yv0*3 + h11(t) * yv1*3
90 set title "The cubic Hermite basis functions in use"
91 plot cub_hermit_x1(t), cub_hermit_y1(t) with lines lt 2,\
92 cub_hermit_x2(t), cub_hermit_y2(t) with lines lt 3
93 pause -1 "Press return to continue"