# set terminal pngcairo  transparent enhanced font "arial,10" fontscale 1.0 size 600, 400 
# set output 'spline.6.png'
set bar 1.000000 front
set style circle radius graph 0.02, first 0.00000, 0.00000 
set style ellipse size graph 0.05, 0.03, first 0.00000 angle 0 units xy
set dummy t, y
set grid nopolar
set grid xtics nomxtics ytics nomytics noztics nomztics \
 nox2tics nomx2tics noy2tics nomy2tics nocbtics nomcbtics
set grid layerdefault   lt black linewidth 0.200 dashtype solid,  lt black linewidth 0.200 dashtype solid
set key inside 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 lt black 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 lt black 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 lt black 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 lt black linewidth 1.000 dashtype solid
set style textbox transparent margins  1.0,  1.0 border
unset logscale
set parametric
set style data lines
unset paxis 1 tics
unset paxis 2 tics
unset paxis 3 tics
unset paxis 4 tics
unset paxis 5 tics
unset paxis 6 tics
unset paxis 7 tics
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
set paxis 1 range [ * : * ] noreverse nowriteback
set paxis 2 range [ * : * ] noreverse nowriteback
set paxis 3 range [ * : * ] noreverse nowriteback
set paxis 4 range [ * : * ] noreverse nowriteback
set paxis 5 range [ * : * ] noreverse nowriteback
set paxis 6 range [ * : * ] noreverse nowriteback
set paxis 7 range [ * : * ] noreverse nowriteback
set colorbox vertical origin screen 0.9, 0.2, 0 size screen 0.05, 0.6, 0 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
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