#

# $Id: spline.dem,v 1.5 2003/10/28 05:35:54 sfeam Exp $

#

# Some curve plotting using common cubic polynomial basis function for cagd.

#

#				Gershon Elber, Aug. 1992

#

set xrang [0:1]

set grid

set key box

set yrange[-0.2:1.4]

m0(x) = 1

m1(x) = x

m2(x) = x**2

m3(x) = x**3

set title "The cubic Monomial basis functions"

plot m0(x), m1(x), m2(x), m3(x)

pause -1 "Press return to continue"

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)

set title "The cubic Hermite basis functions"

plot h00(x), h01(x), h10(x), h11(x)

pause -1 "Press return to continue"

bez0(x) = (1 - x)**3

bez1(x) = 3 * (1 - x)**2 * x

bez2(x) = 3 * (1 - x) * x**2

bez3(x) = x**3

set title "The cubic Bezier basis functions"

plot bez0(x), bez1(x), bez2(x), bez3(x)

pause -1 "Press return to continue"

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

set title "The cubic uniform Bspline basis functions"

plot bsp0(x), bsp1(x), bsp2(x), bsp3(x)

pause -1 "Press return to continue"

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

set arrow from x0,y0 to x1,y1 nohead

set arrow from x1,y1 to x2,y2 nohead

set arrow from x2,y2 to x3,y3 nohead

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

set parametric

set trange [0:1]

set title "The cubic Bezier/Bspline basis functions in use"

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

pause -1 "Press return to continue"

unset arrow

#

# Note the arrows here, scaled by 1/3 so they will fit into plotting area

#

set arrow from x1,y1 to x1+xv0/3,y1+yv0/3

set arrow from x2,y2 to x2+xv1/3,y2+yv1/3

set arrow from x1,y1 to x1+xv0,y1+yv0

set arrow from x2,y2 to x2+xv1,y2+yv1

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

set title "The cubic Hermite basis functions in use"

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

pause -1 "Press return to continue"

reset