# set terminal canvas solid butt size 600,400 fsize 10 lw 1 fontscale 1 name "spline_6" jsdir "." # set output 'spline.6.js' set dummy t,y set grid nopolar set grid xtics nomxtics ytics nomytics noztics nomztics \ nox2tics nomx2tics noy2tics nomy2tics nocbtics nomcbtics set grid layerdefault linetype -1 linecolor rgb "gray" linewidth 0.200, linetype -1 linecolor rgb "gray" linewidth 0.200 set key inside right top vertical Right noreverse enhanced autotitles box linetype -1 linewidth 1.000 set arrow 1 from 0.33, 0.2, 0 to 0.23, 0.366667, 0 head back nofilled linetype -1 linewidth 1.000 set arrow 2 from 0.66, 0.8, 0 to 0.526667, 0.866667, 0 head back nofilled linetype -1 linewidth 1.000 set arrow 3 from 0.33, 0.2, 0 to 0.03, 0.7, 0 head back nofilled linetype -1 linewidth 1.000 set arrow 4 from 0.66, 0.8, 0 to 0.26, 1, 0 head back nofilled linetype -1 linewidth 1.000 set parametric set title "The cubic Hermite basis functions in use" set trange [ 0.00000 : 1.00000 ] noreverse nowriteback set xrange [ 0.00000 : 1.00000 ] noreverse nowriteback set yrange [ -0.200000 : 1.40000 ] noreverse nowriteback m0(x) = 1 m1(x) = x m2(x) = x**2 m3(x) = x**3 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) bez0(x) = (1 - x)**3 bez1(x) = 3 * (1 - x)**2 * x bez2(x) = 3 * (1 - x) * x**2 bez3(x) = x**3 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 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 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 GPFUN_m0 = "m0(x) = 1" GPFUN_m1 = "m1(x) = x" GPFUN_m2 = "m2(x) = x**2" GPFUN_m3 = "m3(x) = x**3" GPFUN_h00 = "h00(x) = x**2 * ( 2 * x - 3) + 1" GPFUN_h01 = "h01(x) = -x**2 * (2 * x - 3)" GPFUN_h10 = "h10(x) = x * (x - 1)**2" GPFUN_h11 = "h11(x) = x**2 * (x - 1)" GPFUN_bez0 = "bez0(x) = (1 - x)**3" GPFUN_bez1 = "bez1(x) = 3 * (1 - x)**2 * x" GPFUN_bez2 = "bez2(x) = 3 * (1 - x) * x**2" GPFUN_bez3 = "bez3(x) = x**3" GPFUN_bsp0 = "bsp0(x) = ( 1 - 3 * x + 3 * x**2 - x**3 ) / 6" GPFUN_bsp1 = "bsp1(x) = ( 4 - 6 * x**2 + 3 * x**3 ) / 6" GPFUN_bsp2 = "bsp2(x) = ( 1 + 3 * x + 3 * x**2 - 3 * x**3 ) / 6" GPFUN_bsp3 = "bsp3(x) = x**3 / 6" 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 GPFUN_cub_bezier_x = "cub_bezier_x(t) = bez0(t) * x0 + bez1(t) * x1 + bez2(t) * x2 + bez3(t) * x3" GPFUN_cub_bezier_y = "cub_bezier_y(t) = bez0(t) * y0 + bez1(t) * y1 + bez2(t) * y2 + bez3(t) * y3" GPFUN_cub_bsplin_x = "cub_bsplin_x(t) = bsp0(t) * x0 + bsp1(t) * x1 + bsp2(t) * x2 + bsp3(t) * x3" GPFUN_cub_bsplin_y = "cub_bsplin_y(t) = bsp0(t) * y0 + bsp1(t) * y1 + bsp2(t) * y2 + bsp3(t) * y3" GPFUN_cub_hermit_x1 = "cub_hermit_x1(t) = h00(t) * x1 + h01(t) * x2 + h10(t) * xv0 + h11(t) * xv1" GPFUN_cub_hermit_y1 = "cub_hermit_y1(t) = h00(t) * y1 + h01(t) * y2 + h10(t) * yv0 + h11(t) * yv1" GPFUN_cub_hermit_x2 = "cub_hermit_x2(t) = h00(t) * x1 + h01(t) * x2 + h10(t) * xv0*3 + h11(t) * xv1*3" GPFUN_cub_hermit_y2 = "cub_hermit_y2(t) = h00(t) * y1 + h01(t) * y2 + h10(t) * yv0*3 + h11(t) * yv1*3" plot cub_hermit_x1(t), cub_hermit_y1(t) with lines lt 2, cub_hermit_x2(t), cub_hermit_y2(t) with lines lt 3