## $Id: spline.dem,v 1.5 2003/10/28 05:35:54 sfeam Exp $## Some curve plotting using common cubic polynomial basis function for cagd.##				Gershon Elber, Aug. 1992#set xrang [0:1]set gridset key boxset yrange[-0.2:1.4]m0(x) = 1m1(x) = xm2(x) = x**2m3(x) = x**3set title "The cubic Monomial basis functions"plot m0(x), m1(x), m2(x), m3(x)pause -1 "Press return to continue"h00(x) = x**2 * ( 2 * x - 3) + 1h01(x) = -x**2 * (2 * x - 3)h10(x) = x * (x - 1)**2h11(x) = x**2 * (x - 1)set title "The cubic Hermite basis functions"plot h00(x), h01(x), h10(x), h11(x)pause -1 "Press return to continue"bez0(x) = (1 - x)**3bez1(x) = 3 * (1 - x)**2 * xbez2(x) = 3 * (1 - x) * x**2bez3(x) = x**3set title "The cubic Bezier basis functions"plot bez0(x), bez1(x), bez2(x), bez3(x)pause -1 "Press return to continue"bsp0(x) = ( 1 - 3 * x + 3 * x**2 - x**3 ) / 6;bsp1(x) = ( 4 - 6 * x**2 + 3 * x**3 ) / 6;bsp2(x) = ( 1 + 3 * x + 3 * x**2 - 3 * x**3 ) / 6bsp3(x) = x**3 / 6set title "The cubic uniform Bspline basis functions"plot bsp0(x), bsp1(x), bsp2(x), bsp3(x)pause -1 "Press return to continue"y0 = 1y1 = 0.2y2 = 0.8y3 = 0x0 = 0x1 = 0.33x2 = 0.66x3 = 1xv0 = -0.3yv0 = 0.5xv1 = -0.4yv1 = 0.2set arrow from x0,y0 to x1,y1 noheadset arrow from x1,y1 to x2,y2 noheadset arrow from x2,y2 to x3,y3 noheadcub_bezier_x(t) = bez0(t) * x0 + bez1(t) * x1 + bez2(t) * x2 + bez3(t) * x3cub_bezier_y(t) = bez0(t) * y0 + bez1(t) * y1 + bez2(t) * y2 + bez3(t) * y3cub_bsplin_x(t) = bsp0(t) * x0 + bsp1(t) * x1 + bsp2(t) * x2 + bsp3(t) * x3cub_bsplin_y(t) = bsp0(t) * y0 + bsp1(t) * y1 + bsp2(t) * y2 + bsp3(t) * y3set parametricset trange [0:1]set title "The cubic Bezier/Bspline basis functions in use"plot cub_bezier_x(t), cub_bezier_y(t) with lines 2,\     cub_bsplin_x(t), cub_bsplin_y(t) with lines 3pause -1 "Press return to continue"unset arrow## Note the arrows here, scaled by 1/3 so they will fit into plotting area#set arrow from x1,y1 to x1+xv0/3,y1+yv0/3set arrow from x2,y2 to x2+xv1/3,y2+yv1/3set arrow from x1,y1 to x1+xv0,y1+yv0set arrow from x2,y2 to x2+xv1,y2+yv1cub_hermit_x1(t) = h00(t) * x1 + h01(t) * x2 + h10(t) * xv0 + h11(t) * xv1cub_hermit_y1(t) = h00(t) * y1 + h01(t) * y2 + h10(t) * yv0 + h11(t) * yv1cub_hermit_x2(t) = h00(t) * x1 + h01(t) * x2 + h10(t) * xv0*3 + h11(t) * xv1*3cub_hermit_y2(t) = h00(t) * y1 + h01(t) * y2 + h10(t) * yv0*3 + h11(t) * yv1*3set title "The cubic Hermite basis functions in use"plot cub_hermit_x1(t), cub_hermit_y1(t) with lines 2,\     cub_hermit_x2(t), cub_hermit_y2(t) with lines 3pause -1 "Press return to continue"reset