# set terminal pngcairo transparent enhanced font "arial,10" fontscale 1.0 size 500, 350 # set output 'spline.4.png' 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 title "The cubic uniform Bspline basis functions" 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 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" plot bsp0(x), bsp1(x), bsp2(x), bsp3(x)