# set terminal pngcairo transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 # set output 'spline.6.png' set dummy t, y set grid nopolar set grid xtics nomxtics ytics nomytics noztics nomztics nortics nomrtics \ nox2tics nomx2tics noy2tics nomy2tics nocbtics nomcbtics set grid layerdefault lt 0 linecolor 0 linewidth 0.500, lt 0 linecolor 0 linewidth 0.500 set key fixed right top vertical Right noreverse enhanced autotitle box lt black linewidth 1.000 dashtype solid set arrow 1 from 0.330000, 0.200000, 0.00000 to 0.230000, 0.366667, 0.00000 head back nofilled linewidth 1.000 dashtype solid set arrow 2 from 0.660000, 0.800000, 0.00000 to 0.526667, 0.866667, 0.00000 head back nofilled linewidth 1.000 dashtype solid set arrow 3 from 0.330000, 0.200000, 0.00000 to 0.0300000, 0.700000, 0.00000 head back nofilled linewidth 1.000 dashtype solid set arrow 4 from 0.660000, 0.800000, 0.00000 to 0.260000, 1.00000, 0.00000 head back nofilled linewidth 1.000 dashtype solid set style increment default set parametric set style data lines 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 x2range [ * : * ] noreverse writeback set yrange [ -0.200000 : 1.40000 ] noreverse nowriteback set y2range [ * : * ] noreverse writeback set zrange [ * : * ] noreverse writeback set cbrange [ * : * ] noreverse writeback set rrange [ * : * ] noreverse writeback 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 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 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