This package provides fittingcontrolpoints and related functions.
These functions have been moved from BasicBSpline.jl v0.9.0.
Try on Desmos graphing calculator!
using BasicBSplineFitting
p1 = 2
p2 = 2
k1 = KnotVector(-10:10)+p1*KnotVector([-10,10])
k2 = KnotVector(-10:10)+p2*KnotVector([-10,10])
P1 = BSplineSpace{p1}(k1)
P2 = BSplineSpace{p2}(k2)
f(u1, u2) = SVector(2u1 + sin(u1) + cos(u2) + u2 / 2, 3u2 + sin(u2) + sin(u1) / 2 + u1^2 / 6) / 5
a = fittingcontrolpoints(f, (P1, P2))
M = BSplineManifold(a, (P1, P2))
save_png("fitting.png", M, unitlength=50, xlims=(-10,10), ylims=(-10,10))
If the knot vector span is too coarse, the approximation will be coarse.
p1 = 2
p2 = 2
k1 = KnotVector(-10:5:10)+p1*KnotVector([-10,10])
k2 = KnotVector(-10:5:10)+p2*KnotVector([-10,10])
P1 = BSplineSpace{p1}(k1)
P2 = BSplineSpace{p2}(k2)
f(u1, u2) = SVector(2u1 + sin(u1) + cos(u2) + u2 / 2, 3u2 + sin(u2) + sin(u1) / 2 + u1^2 / 6) / 5
a = fittingcontrolpoints(f, (P1, P2))
M = BSplineManifold(a, (P1, P2))
save_png("fitting_coarse.png", M, unitlength=50, xlims=(-10,10), ylims=(-10,10))
p = 3
k = KnotVector(range(-2π,2π,length=8))+p*KnotVector(-2π,2π)
P = BSplineSpace{p}(k)
f(u) = SVector(u,sin(u))
a = fittingcontrolpoints(f, P)
M = BSplineManifold(a, P)
save_svg("sine-curve.svg", M, unitlength=50, xlims=(-2,2), ylims=(-8,8))
save_svg("sine-curve_no-points.svg", M, unitlength=50, xlims=(-2,2), ylims=(-8,8), points=false)
This is useful when you edit graphs (or curves) with your favorite vector graphics editor.
See Plotting smooth graphs with Julia for more tutorials.