Snake curve by B-spline

snake.jl

using BasicBSpline
using ExportNURBS
using Colors

p = 3
f(u) = [u[1],sin(u[1])]

N = 80
w = 5
W = 7
for i in 1:N
    t = (w+W)-i/N * 2*(w+W)
    a,b = -w-t, w-t
    nnn = 4
    global k = Knots(range(a,b,length=nnn-p+1))+p*Knots(a,b)
    global P = FastBSplineSpace(p, k)
    global a = fittingcontrolpoints(f, [P])
    global M = BSplineManifold([P],a)
    save_png("docs/src/img/sine_curve_a"*lpad(i,3,"0")*".png", M, unitlength=50, up=3, down=-3, left=-W, right=W, thickness=2, backgroundcolor=RGB(1,0.8,0.8), linecolor=RGB(1,0,0))
end
for i in 1:N
    t = (w+W)-i/N * 2*(w+W)
    a,b = -w-t, w-t
    nnn = 5
    global k = Knots(range(a,b,length=nnn-p+1))+p*Knots(a,b)
    global P = FastBSplineSpace(p, k)
    global a = fittingcontrolpoints(f, [P])
    global M = BSplineManifold([P],a)
    save_png("sine_curve_b"*lpad(i,3,"0")*".png", M, unitlength=50, up=3, down=-3, left=-W, right=W, thickness=2, backgroundcolor=RGB(0.9,0.9,0.8), linecolor=RGB(0.5,0.5,0))
end
for i in 1:N
    t = (w+W)-i/N * 2*(w+W)
    a,b = -w-t, w-t
    nnn = 6
    global k = Knots(range(a,b,length=nnn-p+1))+p*Knots(a,b)
    global P = FastBSplineSpace(p, k)
    global a = fittingcontrolpoints(f, [P])
    global M = BSplineManifold([P],a)
    save_png("sine_curve_c"*lpad(i,3,"0")*".png", M, unitlength=50, up=3, down=-3, left=-W, right=W, thickness=2, backgroundcolor=RGB(0.8,1,0.8), linecolor=RGB(0,1,0))
end
for i in 1:N
    t = (w+W)-i/N * 2*(w+W)
    a,b = -w-t, w-t
    nnn = 7
    global k = Knots(range(a,b,length=nnn-p+1))+p*Knots(a,b)
    global P = FastBSplineSpace(p, k)
    global a = fittingcontrolpoints(f, [P])
    global M = BSplineManifold([P],a)
    save_png("sine_curve_d"*lpad(i,3,"0")*".png", M, unitlength=50, up=3, down=-3, left=-W, right=W, thickness=2, backgroundcolor=RGB(0.8,0.9,0.9), linecolor=RGB(0,0.5,0.5))
end
for i in 1:N
    t = (w+W)-i/N * 2*(w+W)
    a,b = -w-t, w-t
    nnn = 8
    global k = Knots(range(a,b,length=nnn-p+1))+p*Knots(a,b)
    global P = FastBSplineSpace(p, k)
    global a = fittingcontrolpoints(f, [P])
    global M = BSplineManifold([P],a)
    save_png("sine_curve_e"*lpad(i,3,"0")*".png", M, unitlength=50, up=3, down=-3, left=-W, right=W, thickness=2, backgroundcolor=RGB(0.8,0.8,1), linecolor=RGB(0,0,1))
end
for i in 1:N
    t = (w+W)-i/N * 2*(w+W)
    a,b = -w-t, w-t
    nnn = 30
    global k = Knots(range(a,b,length=nnn-p+1))+p*Knots(a,b)
    global P = FastBSplineSpace(p, k)
    global a = fittingcontrolpoints(f, [P])
    global M = BSplineManifold([P],a)
    save_png("sine_curve_z"*lpad(i,3,"0")*".png", M, unitlength=50, up=3, down=-3, left=-W, right=W, thickness=2, backgroundcolor=RGB(0.9,0.9,0.9), linecolor=RGB(0.2,0.2,0.2))
end

snake_no_points.jl

using BasicBSpline
using ExportNURBS
using Colors

p = 3
f(u) = [u[1],sin(u[1])]

N = 80
w = 5
W = 7
for i in 1:N
    t = (w+W)-i/N * 2*(w+W)
    a,b = -w-t, w-t
    nnn = 4
    global k = Knots(range(a,b,length=nnn-p+1))+p*Knots(a,b)
    global P = FastBSplineSpace(p, k)
    global a = fittingcontrolpoints(f, [P])
    global M = BSplineManifold([P],a)
    save_png("docs/src/img/sine_curve_a"*lpad(i,3,"0")*".png", M, unitlength=50, up=3, down=-3, left=-W, right=W, thickness=2, backgroundcolor=RGB(1,0.8,0.8), linecolor=RGB(1,0,0), points=false)
end
for i in 1:N
    t = (w+W)-i/N * 2*(w+W)
    a,b = -w-t, w-t
    nnn = 5
    global k = Knots(range(a,b,length=nnn-p+1))+p*Knots(a,b)
    global P = FastBSplineSpace(p, k)
    global a = fittingcontrolpoints(f, [P])
    global M = BSplineManifold([P],a)
    save_png("sine_curve_b"*lpad(i,3,"0")*".png", M, unitlength=50, up=3, down=-3, left=-W, right=W, thickness=2, backgroundcolor=RGB(0.9,0.9,0.8), linecolor=RGB(0.5,0.5,0), points=false)
end
for i in 1:N
    t = (w+W)-i/N * 2*(w+W)
    a,b = -w-t, w-t
    nnn = 6
    global k = Knots(range(a,b,length=nnn-p+1))+p*Knots(a,b)
    global P = FastBSplineSpace(p, k)
    global a = fittingcontrolpoints(f, [P])
    global M = BSplineManifold([P],a)
    save_png("sine_curve_c"*lpad(i,3,"0")*".png", M, unitlength=50, up=3, down=-3, left=-W, right=W, thickness=2, backgroundcolor=RGB(0.8,1,0.8), linecolor=RGB(0,1,0), points=false)
end
for i in 1:N
    t = (w+W)-i/N * 2*(w+W)
    a,b = -w-t, w-t
    nnn = 7
    global k = Knots(range(a,b,length=nnn-p+1))+p*Knots(a,b)
    global P = FastBSplineSpace(p, k)
    global a = fittingcontrolpoints(f, [P])
    global M = BSplineManifold([P],a)
    save_png("sine_curve_d"*lpad(i,3,"0")*".png", M, unitlength=50, up=3, down=-3, left=-W, right=W, thickness=2, backgroundcolor=RGB(0.8,0.9,0.9), linecolor=RGB(0,0.5,0.5), points=false)
end
for i in 1:N
    t = (w+W)-i/N * 2*(w+W)
    a,b = -w-t, w-t
    nnn = 8
    global k = Knots(range(a,b,length=nnn-p+1))+p*Knots(a,b)
    global P = FastBSplineSpace(p, k)
    global a = fittingcontrolpoints(f, [P])
    global M = BSplineManifold([P],a)
    save_png("sine_curve_e"*lpad(i,3,"0")*".png", M, unitlength=50, up=3, down=-3, left=-W, right=W, thickness=2, backgroundcolor=RGB(0.8,0.8,1), linecolor=RGB(0,0,1), points=false)
end
for i in 1:N
    t = (w+W)-i/N * 2*(w+W)
    a,b = -w-t, w-t
    nnn = 30
    global k = Knots(range(a,b,length=nnn-p+1))+p*Knots(a,b)
    global P = FastBSplineSpace(p, k)
    global a = fittingcontrolpoints(f, [P])
    global M = BSplineManifold([P],a)
    save_png("sine_curve_z"*lpad(i,3,"0")*".png", M, unitlength=50, up=3, down=-3, left=-W, right=W, thickness=2, backgroundcolor=RGB(0.9,0.9,0.9), linecolor=RGB(0.2,0.2,0.2), points=false)
end