#!/usr/local/bin/gnuplot -persist
# set terminal canvas  rounded size 600,400 enhanced fsize 10 lw 1.6 fontscale 1 name "spline_5" jsdir "."
# set output 'spline.5.js'
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 0.00000, 1.00000, 0.00000 to 0.330000, 0.200000, 0.00000 nohead back nofilled linewidth 1.000 dashtype solid
set arrow 2 from 0.330000, 0.200000, 0.00000 to 0.660000, 0.800000, 0.00000 nohead back nofilled linewidth 1.000 dashtype solid
set arrow 3 from 0.660000, 0.800000, 0.00000 to 1.00000, 0.00000, 0.00000 nohead back nofilled linewidth 1.000 dashtype solid
set parametric
set style data lines
set title "The cubic Bezier/Bspline 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
set colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front  noinvert bdefault
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
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_bezier_x(t), cub_bezier_y(t) with lines lt 2,     cub_bsplin_x(t), cub_bsplin_y(t) with lines lt 3