Annotation of OpenXM_contrib/gnuplot/demo/spline.dem, Revision 1.1.1.1
1.1 maekawa 1: #
2: # $Id: spline.dem,v 1.3 1997/04/05 19:44:48 drd Exp $
3: #
4: # Some curve plotting using common cubic polynomial basis function for cagd.
5: #
6: # Gershon Elber, Aug. 1992
7: #
8: set xrang [0:1]
9: set grid
10:
11: set yrange[-0.2:1.4]
12: m0(x) = 1
13: m1(x) = x
14: m2(x) = x**2
15: m3(x) = x**3
16: set title "The cubic Monomial basis functions"
17: plot m0(x), m1(x), m2(x), m3(x)
18: pause -1 "Press return to continue"
19:
20: h00(x) = x**2 * ( 2 * x - 3) + 1
21: h01(x) = -x**2 * (2 * x - 3)
22: h10(x) = x * (x - 1)**2
23: h11(x) = x**2 * (x - 1)
24:
25: set title "The cubic Hermite basis functions"
26: plot h00(x), h01(x), h10(x), h11(x)
27: pause -1 "Press return to continue"
28:
29: bez0(x) = (1 - x)**3
30: bez1(x) = 3 * (1 - x)**2 * x
31: bez2(x) = 3 * (1 - x) * x**2
32: bez3(x) = x**3
33: set title "The cubic Bezier basis functions"
34: plot bez0(x), bez1(x), bez2(x), bez3(x)
35: pause -1 "Press return to continue"
36:
37: bsp0(x) = ( 1 - 3 * x + 3 * x**2 - x**3 ) / 6;
38: bsp1(x) = ( 4 - 6 * x**2 + 3 * x**3 ) / 6;
39: bsp2(x) = ( 1 + 3 * x + 3 * x**2 - 3 * x**3 ) / 6
40: bsp3(x) = x**3 / 6
41: set title "The cubic uniform Bspline basis functions"
42: plot bsp0(x), bsp1(x), bsp2(x), bsp3(x)
43: pause -1 "Press return to continue"
44:
45: y0 = 1
46: y1 = 0.2
47: y2 = 0.8
48: y3 = 0
49:
50: x0 = 0
51: x1 = 0.33
52: x2 = 0.66
53: x3 = 1
54:
55: xv0 = -0.3
56: yv0 = 0.5
57: xv1 = -0.4
58: yv1 = 0.2
59:
60: set arrow from x0,y0 to x1,y1 nohead
61: set arrow from x1,y1 to x2,y2 nohead
62: set arrow from x2,y2 to x3,y3 nohead
63:
64: cub_bezier_x(t) = bez0(t) * x0 + bez1(t) * x1 + bez2(t) * x2 + bez3(t) * x3
65: cub_bezier_y(t) = bez0(t) * y0 + bez1(t) * y1 + bez2(t) * y2 + bez3(t) * y3
66: cub_bsplin_x(t) = bsp0(t) * x0 + bsp1(t) * x1 + bsp2(t) * x2 + bsp3(t) * x3
67: cub_bsplin_y(t) = bsp0(t) * y0 + bsp1(t) * y1 + bsp2(t) * y2 + bsp3(t) * y3
68:
69: set parametric
70: set trange [0:1]
71: set title "The cubic Bezier/Bspline basis functions in use"
72: plot cub_bezier_x(t), cub_bezier_y(t) with lines 2,\
73: cub_bsplin_x(t), cub_bsplin_y(t) with lines 3
74: pause -1 "Press return to continue"
75:
76: set noarrow
77: #
78: # Note the arrows here, scaled by 1/3 so they will fit into plotting area
79: #
80: set arrow from x1,y1 to x1+xv0/3,y1+yv0/3
81: set arrow from x2,y2 to x2+xv1/3,y2+yv1/3
82: set arrow from x1,y1 to x1+xv0,y1+yv0
83: set arrow from x2,y2 to x2+xv1,y2+yv1
84:
85: cub_hermit_x1(t) = h00(t) * x1 + h01(t) * x2 + h10(t) * xv0 + h11(t) * xv1
86: cub_hermit_y1(t) = h00(t) * y1 + h01(t) * y2 + h10(t) * yv0 + h11(t) * yv1
87: cub_hermit_x2(t) = h00(t) * x1 + h01(t) * x2 + h10(t) * xv0*3 + h11(t) * xv1*3
88: cub_hermit_y2(t) = h00(t) * y1 + h01(t) * y2 + h10(t) * yv0*3 + h11(t) * yv1*3
89: set title "The cubic Hermite basis functions in use"
90: plot cub_hermit_x1(t), cub_hermit_y1(t) with lines 2,\
91: cub_hermit_x2(t), cub_hermit_y2(t) with lines 3
92: pause -1 "Press return to continue"
93:
94: set noparametric
95: set noarrow
96: set auto
97: set nogrid
98: set title ""
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