#
# Look at the effect of B-spline approximation on a prefix of the
# input data as more points are added.
#
read bspline:
x := 0,1,2,3,4,5,6,7:
y := 0,2,4,1,0,-1,1,0:

p3 := BsplineApprox(3,[y],[x],t):
plot3 := plot({p3}, 0..7, colour=GREEN):

plot4 := plot([pairs([x],[y])],style=point, colour=WHITE):

with(plots):
display({plot3,plot4},title=`Uniform B-Spline Approximation to Points`);

x := 0,1,2,3,3.5,5,6,7:
p3 := BsplineApprox(3,[y],[x],t):
plot3a := plot({p3}, 0..7, colour=YELLOW):
plot4a := plot([pairs([x],[y])],style=point, colour=WHITE):
x := 0,1,2,3,3.25,5,6,7:
p3 := BsplineApprox(3,[y],[x],t):
plot3b := plot({p3}, 0..7, colour=CYAN):
plot4b := plot([pairs([x],[y])],style=point, colour=WHITE):
x := 0,1,2,3,3,5,6,7:
p3 := BsplineApprox(3,[y],[x],t):
plot3c := plot({p3}, 0..7, colour=RED):
plot4c := plot([pairs([x],[y])],style=point, colour=WHITE):
display({plot4,plot4a,plot4b,plot4c,plot3,plot3a,plot3b,plot3c},title=`Adjusting the spacing of an interior knot`);

x := 0,1,2,3,3,3,6,7:
p3 := BsplineApprox(3,[y],[x],t):
plot3d := plot({p3}, 0..7, colour=YELLOW):
plot4d := plot([pairs([x],[y])],style=point, colour=WHITE):
display({plot4,plot4d,plot3,plot3d},title=`A triple knot at 3`);

x := 0,1,2,3,3,3,3,7:
p3 := BsplineApprox(3,[y],[x],t):
plot3e := plot({p3}, 0..7, colour=YELLOW):
plot4e := plot([pairs([x],[y])],style=point, colour=WHITE):
display({plot4,plot4e,plot3,plot3e},title=`A quadruple knot at 3`);