# set terminal pngcairo  transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 
# set output 'spline.5.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   linecolor rgb "gray"  linewidth 0.200 dashtype solid,  linecolor rgb "gray"  linewidth 0.200 dashtype solid
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 urange [ * : * ] noreverse nowriteback
set vrange [ * : * ] 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
NO_ANIMATION = 1
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