Curves

Curves can be refined, splitted, knots can be removed, and the degree can be manipulated.

Refining a Curve

Based on the principles of knot insertion, a single knot can be inserted multiple times into a curve (without changing the points the curve describes) by the insertKnot function.

NCurve2 = insertKnot(NCurve, 0.75, 2) # insert knot at 0.75 twice
C2 = NCurve2(evalpoints)

plotCurve3D(C2, controlPoints=NCurve2.controlPoints)

[ Info: The knot vector is being modified (normalized).

Several knots can be inserted by the refine function.

NCurve2 = refine(NCurve, [0.1, 0.2, 0.3, 0.8221]) # insert the array of knots
C2 = NCurve2(evalpoints)

plotCurve3D(C2, controlPoints=NCurve2.controlPoints)

Splitting a Curve

To split a curve into multiple separate curves the function split is provided which returns an array of curves.

cVec = split(NCurve, [0.2, 0.5]) # split at 0.2 and 0.5

# plot all three curves
data = PlotlyJS.GenericTrace[]
for (i, spC) in enumerate(cVec)
    push!(data, plotCurve3D(spC(evalpoints), returnTrace=true, controlPoints=spC.controlPoints)...)
end
PlotlyJS.plot(data)

To equally split a curve into $n$ curves as a second argument an integer can be provided:

cVec = split(NCurve, 4) # split into 4 curves

4-element Vector{NURBScurve{Float64}}:
 NURBScurve{Float64}(NURB{Float64}(3, [0.0, 0.0, 0.0, 0.0, 0.6666666666666666, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0]), StaticArraysCore.SVector{3, Float64}[[0.0, 0.0, 0.0], [0.1, 0.25, 0.0], [0.2125, 0.2875, 0.0], [0.259375, 0.37187500000000007, 0.0], [0.27239583333333334, 0.3963541666666668, 0.0]])
 NURBScurve{Float64}(NURB{Float64}(3, [0.0, 0.0, 0.0, 0.0, 0.33333333333333326, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.0, 1.0]), StaticArraysCore.SVector{3, Float64}[[0.27239583333333334, 0.3963541666666668, 0.0], [0.28541666666666665, 0.4208333333333334, 0.0], [0.31666666666666665, 0.4833333333333333, 0.0], [0.3666666666666667, 0.43333333333333335, 0.0], [0.41666666666666674, 0.4, 0.0]])
 NURBScurve{Float64}(NURB{Float64}(3, [0.0, 0.0, 0.0, 0.0, 0.6666666666666665, 1.0, 1.0, 1.0, 1.0], [1.0, 1.0, 1.0, 1.75, 1.9375]), StaticArraysCore.SVector{3, Float64}[[0.41666666666666674, 0.4, 0.0], [0.4666666666666667, 0.3666666666666667, 0.0], [0.5666666666666667, 0.31666666666666665, 0.0], [0.7238095238095238, 0.5595238095238094, 0.6428571428571427], [0.7494623655913979, 0.5930107526881719, 0.7258064516129032]])
 NURBScurve{Float64}(NURB{Float64}(3, [0.0, 0.0, 0.0, 0.0, 0.3333333333333335, 1.0, 1.0, 1.0, 1.0], [1.9375, 2.125, 2.5, 1.0, 1.0]), StaticArraysCore.SVector{3, Float64}[[0.7494623655913979, 0.5930107526881719, 0.7258064516129032], [0.7705882352941178, 0.6205882352941176, 0.7941176470588235], [0.8200000000000001, 0.6699999999999999, 0.9], [1.0, 0.4, 0.0], [1.1, 0.4, 0.0]])

Removing Knots from a Curve

Based on the principles of knot removal, an interior knot can potentially be removed multiple times from a curve (without changing the points the curve describes) by the removeKnot function.

p = 3

P1 = SVector(0.0, 0.0, 1.0)
P2 = SVector(0.0, 2.0, 0.0)
P3 = SVector(1.5, 3.0, 0.0)
P4 = SVector(3.0, 3.0, 0.0)
P5 = SVector(4.5, 3.0, 0.0)
P6 = SVector(6.0, 2.0, 0.0)
P7 = SVector(6.0, 0.0, 1.0)

cP = [P1, P2, P3, P4, P5, P6, P7]

kVec = Float64[0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2]

BCurve1 = BsplineCurve(Bspline(p, kVec), cP)
C1 = BCurve1(evalpoints)

BCurve2 = removeKnot(BCurve1, 0.5, 2) # remove knot at 0.5 twice
C2 = BCurve2(evalpoints)

# --- plot both curves
t1 = plotCurve3D(C1, controlPoints=BCurve1.controlPoints, returnTrace=true)
t2 = plotCurve3D(C2, controlPoints=BCurve2.controlPoints, returnTrace=true)

fig = make_subplots(
    rows=1, cols=2,
    specs=fill(Spec(kind="scene"), 1, 2)
)

add_trace!(fig, t1[1], row=1, col=1)
add_trace!(fig, t1[2], row=1, col=1)
add_trace!(fig, t2[1], row=1, col=2)
add_trace!(fig, t2[2], row=1, col=2)
fig

[ Info: The knot vector is being modified (normalized).

Degree Manipulation

To be done.