# set terminal pngcairo  transparent enhanced font "arial,10" fontscale 1.0 size 500, 350 
# set output 'spline.3.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 Bezier 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
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"
plot bez0(x), bez1(x), bez2(x), bez3(x)