I have defined 4 controlpoints in a 2D coordinate system, x=1,...,40 and
y=1,...,40:
x y
P1 = [15 10]
P2 = [18 32]
P3 = [28 28]
P4 = [33 20]
I have then found the four first 4 order Basisfunction N_{i,4} on the knot
vector
U = [0,1,2,3,4,5,6]
for u=1 the corresponding spline is:
C(1) = P1*N_{14}(1) + P2*N_{24}(1) + P3*N_{34}(1) + P4*N_{44}(1)
Only N_{14} with the value 0.1666 weighs the above expression. For the
(x,y)-component the result is:
C(1)_x = 0.1666*15 = 2.5
C(1)_y = 0.1666*10 = 1.6
This meas that for u=1 the B-spline is defined in (2.5, 1.6) but that
points
is not within the convex hull of the controlpoints.
Are there any rules for the coordinate system where the controlpoints are
defined and where the corresponding spline is defined?
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