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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 ""