## File: spline.dem

package info (click to toggle)
gnuplot 3.7.1p1-4
 `12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394` ``````# # \$Id: spline.dem,v 1.1.1.1.2.1 1999/10/11 13:24:09 lhecking Exp \$ # # Some curve plotting using common cubic polynomial basis function for cagd. # # Gershon Elber, Aug. 1992 # set xrang [0:1] set grid set key box set yrange[-0.2:1.4] m0(x) = 1 m1(x) = x m2(x) = x**2 m3(x) = x**3 set 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) + 1 h01(x) = -x**2 * (2 * x - 3) h10(x) = x * (x - 1)**2 h11(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)**3 bez1(x) = 3 * (1 - x)**2 * x bez2(x) = 3 * (1 - x) * x**2 bez3(x) = x**3 set 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 ) / 6 bsp3(x) = x**3 / 6 set title "The cubic uniform Bspline basis functions" plot bsp0(x), bsp1(x), bsp2(x), bsp3(x) pause -1 "Press return to continue" y0 = 1 y1 = 0.2 y2 = 0.8 y3 = 0 x0 = 0 x1 = 0.33 x2 = 0.66 x3 = 1 xv0 = -0.3 yv0 = 0.5 xv1 = -0.4 yv1 = 0.2 set arrow from x0,y0 to x1,y1 nohead set arrow from x1,y1 to x2,y2 nohead set arrow from x2,y2 to x3,y3 nohead cub_bezier_x(t) = bez0(t) * x0 + bez1(t) * x1 + bez2(t) * x2 + bez3(t) * x3 cub_bezier_y(t) = bez0(t) * y0 + bez1(t) * y1 + bez2(t) * y2 + bez3(t) * y3 cub_bsplin_x(t) = bsp0(t) * x0 + bsp1(t) * x1 + bsp2(t) * x2 + bsp3(t) * x3 cub_bsplin_y(t) = bsp0(t) * y0 + bsp1(t) * y1 + bsp2(t) * y2 + bsp3(t) * y3 set parametric set 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 3 pause -1 "Press return to continue" set noarrow # # 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+yv0/3 set arrow from x2,y2 to x2+xv1/3,y2+yv1/3 set arrow from x1,y1 to x1+xv0,y1+yv0 set arrow from x2,y2 to x2+xv1,y2+yv1 cub_hermit_x1(t) = h00(t) * x1 + h01(t) * x2 + h10(t) * xv0 + h11(t) * xv1 cub_hermit_y1(t) = h00(t) * y1 + h01(t) * y2 + h10(t) * yv0 + h11(t) * yv1 cub_hermit_x2(t) = h00(t) * x1 + h01(t) * x2 + h10(t) * xv0*3 + h11(t) * xv1*3 cub_hermit_y2(t) = h00(t) * y1 + h01(t) * y2 + h10(t) * yv0*3 + h11(t) * yv1*3 set 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 3 pause -1 "Press return to continue" reset ``````