readlib(bspline):
with(plots):

#
# plot various B-spline basis functions
#

plot(convert(bspline(0,u), procedure), 0..1, title=`Uniform Constant B-Spline`);
plot(convert(bspline(1,u), procedure), 0..2, title=`Uniform Linear B-Spline`);
plot(convert(bspline(2,u), procedure), 0..3, title=`Uniform Quadratic B-Spline`);
plot(convert(bspline(3,u), procedure), 0..4, title=`Uniform Cubic B-Spline`);
plot(convert(bspline(4,u), procedure), 0..5, title=`Uniform Quartic B-Spline`);

k := [0, 1, 2, 3, 4]:
p1 := plot(convert(bspline(3,u,k), procedure), 0..4, colour=YELLOW):

k := [0, 1, 2.5, 3, 4]:
p2 := plot(convert(bspline(3,u,k), procedure), 0..4, colour=GREEN):

k := [0, 1, 2.5, 2.75, 4]:
p3 := plot(convert(bspline(3,u,k), procedure), 0..4, colour=CYAN):

k := [0, 1, 2.5, 2.6, 4]:
p4 := plot(convert(bspline(3,u,k), procedure), 0..4, colour=MAGENTA,
	title=`Cubic B-Spline on varying interior knot spacing`):

display({p1,p2,p3,p4});

k := [0, 1, 2, 3]:
p1 := convert(bspline(2,u,k), procedure):
k := [1, 2, 2, 3]:
p2 := convert(bspline(2,u,k), procedure):
k := [2, 3, 4, 4]:
p3 := convert(bspline(2,u,k), procedure):
plot({p1,p2,p3}, 0..4,
	title=`Quadratic B-Splines on knot vectors [0 1 2 3], [1 2 2 3] and [2 3 4 4]`);

k := [0, 1, 2, 3.5, 4]:
p1 := plot(convert(bspline(3,u,k), procedure), 0..4, colour=YELLOW):

k := [0, 1, 2, 3.9, 4]:
p2 := plot(convert(bspline(3,u,k), procedure), 0..4, colour=GREEN):

k := [0, 1, 2, 4, 4]:
p3 := plot(convert(bspline(3,u,k), procedure), 0..4, colour=CYAN):

k := [0, 1, 4, 4, 4]:
p4 := plot(convert(bspline(3,u,k), procedure), 0..4, colour=MAGENTA,
	title=`Cubic B-Spline with knots going from [0 1 2 3 4] to [0 1 4 4 4]`):

display({p1,p2,p3,p4});

k := [-1, 0, 1]:
p1 := plot(convert(bspline(1,u,k), procedure), -3..3, colour=YELLOW):
p1;
k := [-2,-1, 0, 1,2]:
p3 := plot(convert(bspline(3,u,k), procedure), -3..3, colour=GREEN):
p3;
k := [-3,-2,-1, 0, 1,2,3]:
p5 := plot(convert(bspline(5,u,k), procedure), -3..3, colour=CYAN):
k := [-4,-3,-2,-1, 0, 1,2,3,4]:
p7 := plot(convert(bspline(7,u,k), procedure), -3..3, colour=MAGENTA):
p7;

k := [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5]:
p9 := plot(convert(bspline(9,u,k), procedure), -3..3, colour=YELLOW):
s := 0.93:
pg := plot(1/(sqrt(2*Pi)*s)*exp(-(t^2/(2*s^2))), t=-3..3, colour=CYAN):
display({pg, p9},
title=`Degree 9 Uniform B-splines and Gaussian with sigma=0.93`);