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Update nurbs.scad
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‎nurbs.scad‎

Lines changed: 60 additions & 21 deletions
Original file line numberDiff line numberDiff line change
@@ -637,24 +637,24 @@ module debug_nurbs(control,degree,splinesteps=16,width=1, size, mult,weights,typ
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// extra_pts = Number of extra control points to add to provide additional freedom to control undesirable oscillations. Default: 0
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// smooth = Smoothness criterion used with extra control points. Set to 1 (minimize control-polygon length), 2 (minimize control-polygon bending) or 3 (minimize curve bending energy). Default: 3
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//
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// Example(2D): Clamped curve (default)
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// Example(2D): 2D Clamped curve (default)
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// data = [[0,0], [10,30], [25,15], [40,35], [60,10], [80,25]];
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// path = nurbs_curve(nurbs_interp(data, 3));
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// stroke(path);
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// color("red") move_copies(data) circle(r=1, $fn=16);
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// debug_nurbs_interp(data, 3);
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//
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// Example(2D): Closed curve - Do NOT repeat the first point at the end.
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// Example(2D,VPT=[40,12,0],VPD = 200): Closed curve - Do NOT repeat the first point at the end.
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// data = [[0,0], [30,50], [60,40], [80,10], [50,-20], [20,-10]];
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// path = nurbs_curve(nurbs_interp(data, 3, closed = true));
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// stroke(path, closed = true);
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// color("red") move_copies(data) circle(r=1, $fn=16);
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// debug_nurbs_interp(data, 3, closed = true);
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//
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// Example(2D): Closed polygon - All data points lie exactly on the polygon boundary.
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// Example(2D, VPT=[40,12,0],VPD = 200): Closed polygon - All data points lie exactly on the polygon boundary.
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// data = [[0,0], [30,50], [60,40], [80,10], [50,-20], [20,-10]];
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// path = nurbs_curve(nurbs_interp(data, 3, closed=true), splinesteps=16);
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// polygon(path);
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// color("red") move_copies(data) circle(r=1, $fn=16);
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//
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// Example(3D,VPT=[0,0,10],VPR=[60,0,330],VPD=120): 3D closed curve
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// data3d = [[20,0,0],[0,20,20],[-20,0,0],[0,-20,10]];
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// debug_nurbs_interp(data3d, 3, splinesteps=32, closed=true);
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//
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// Example(2D): Get just the path
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// data = [[0,0], [10,30], [25,15], [40,35], [60,10], [80,25]];
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// path = nurbs_curve(nurbs_interp(data, 3), splinesteps=16);
@@ -668,17 +668,17 @@ module debug_nurbs(control,degree,splinesteps=16,width=1, size, mult,weights,typ
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// stroke(curve, width=0.5);
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// color("red") move_copies(data) circle(r=1, $fn=16);
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//
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// Example(2D,Med): Endpoint tangent control - Specify start and/or end tangent vectors. Each vector is automatically scaled by the total chord length; a unit vector produces natural arc-length speed. Magnitude > 1 increases pull, < 1 weakens it.
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// Example(2D,Med,VPT=[40,20,0],VPD=160): Endpoint tangent control - Specify start and/or end tangent vectors. Each vector is automatically scaled by the total chord length; a unit vector produces natural arc-length speed. Magnitude > 1 increases pull, < 1 weakens it.
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// data = [[0,0], [20,30], [50,25], [80,0]];
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// // No tangent control (natural):
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// color("gray") stroke(nurbs_curve(nurbs_interp(data, 3)), width=0.3);
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// color("lime") stroke(nurbs_curve(nurbs_interp(data, 3)), width=0.3);
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// // Start going straight up, end going straight down:
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// color("blue") stroke(
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// nurbs_curve(nurbs_interp(data, 3, start_deriv=[0,1], end_deriv=[0,-1])), width=0.3);
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// // Start going right, end going right:
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// color("red") stroke(
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// nurbs_curve(nurbs_interp(data, 3, start_deriv=[1,0], end_deriv=[1,0])), width=0.3);
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// color("black") move_copies(data) circle(r=0.5, $fn=16);
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// color("black") move_copies(data) circle(r=0.75, $fn=16);
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//
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// Example(2D,Huge,NoAxes,VPT=[55,50,0],VPR=[0,0,0],VPD=600): Controlling the start and end of an otherwise unconstrained NURBS curve using derivitives.
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// data = [[0,0], [20,30], [30,90], [36,111],[50,25], [80,0]];
@@ -702,7 +702,7 @@ module debug_nurbs(control,degree,splinesteps=16,width=1, size, mult,weights,typ
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// Example(2D,Huge,NoAxes,VPT=[45,50,0],VPR=[0,0,0],VPD=600): Controlling the shape with derivatives and corners
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// data = [[0,0], [20,30], [30,90], [36,111],[50,25], [80,0]];
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// xdistribute(110){
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// union(){
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// back(20) union(){
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// debug_nurbs_interp(data,3, splinesteps=32, data_size=1,
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// deriv=[2*RIGHT,[0,1],undef,undef,undef,RIGHT],
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// );
@@ -714,18 +714,18 @@ module debug_nurbs(control,degree,splinesteps=16,width=1, size, mult,weights,typ
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// );
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// fwd(15)text("derivs at pts 1, 4",size=6);
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// }
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// union(){
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// fwd(20) union(){
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// debug_nurbs_interp(data,3, splinesteps=32, data_size=1,
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// deriv=[undef,[0,1],undef,undef,NAN,undef],
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// );
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// fwd(15)text("corner and pt 1 deriv",size=6);
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// }
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// }
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//
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// Example(2D,Huge,NoAxes,VPT=[70,50,0],VPR=[0,0,0],VPD=725):
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// Example(2D,Huge,NoAxes,VPT=[70,50,0],VPR=[0,0,0],VPD=725): Specifying the curvature at select points. In the middle example shows continuous curvature joins to arcs at each end.
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// data = [[0,0], [20,30], [30,90], [36,111],[50,25], [80,0]];
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// xdistribute(110){
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// union(){
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// back(30) union(){
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// debug_nurbs_interp(data,3, splinesteps=32, data_size=1,
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// start_deriv=RIGHT,end_deriv=RIGHT, start_curvature=0,end_curvature=0
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// );
@@ -741,7 +741,7 @@ module debug_nurbs(control,degree,splinesteps=16,width=1, size, mult,weights,typ
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// }
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// fwd(15)text("ends curvature>0",size=6);
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// }
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// union(){
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// fwd(30) union(){
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// debug_nurbs_interp(data,3, splinesteps=32, data_size=1,
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// deriv=[undef,[0,1],undef,[1,0],undef,undef],
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// curvature=[undef,-1/10,undef,0,undef,undef]
@@ -750,6 +750,45 @@ module debug_nurbs(control,degree,splinesteps=16,width=1, size, mult,weights,typ
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// }
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// }
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//
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// Example(2D,Huge,NoAxes,VPT=[45,50,0],VPR=[0,0,0],VPD=700): Closed NURBS curves
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// data = [[0,0], [20,30], [30,90], [36,111],[50,25], [80,0]];
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// xdistribute(120){
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// union(){
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// debug_nurbs_interp(data,3, splinesteps=32, data_size=1, closed = true
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// );
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// fwd(22)text("unconstrained",size=6);
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// }
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// union(){
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// debug_nurbs_interp(data,3, splinesteps=32, data_size=1, closed = true,
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// deriv=[[0,1]/4, undef, undef, undef, undef, [0,-1]/3]
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// );
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// fwd(15)text("deriv at pts 0 and 5",size=6);
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// }
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// union(){
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// debug_nurbs_interp(data,3, splinesteps=32, data_size=1, closed = true,
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// deriv=[undef,undef,undef,[1,0],undef,undef]
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// );
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// fwd(15)text("deriv at point 4",size=6);
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// }
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// }
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//
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// Example(2D,Huge,NoAxes,VPT=[45,50,0],VPR=[0,0,0],VPD=500): Closed NURBS curves with corners
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// data = [[0,0], [20,30], [30,90], [36,111],[50,25], [80,0]];
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// xdistribute(120){
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// union(){
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// debug_nurbs_interp(data,3, splinesteps=32, data_size=1, closed = true,
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// deriv=[undef,[0,1],undef,undef,NAN,undef]
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// );
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// fwd(20)text("pt 1 deriv and pt 4 corner",size=6);
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// }
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// union(){
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// debug_nurbs_interp(data,3, splinesteps=32, data_size=1, closed = true,
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// deriv=[undef,NAN,undef,undef,NAN,undef]
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// );
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// fwd(20)text("corners at pts 1 and 4", size=6);
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// }
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// }
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//
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// Example(2D,NoAxes,Big): Unconstrained NURBS through the same data points vary depending on the paramaterization method chosen
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// data = [[0,0], [20,30], [35,120], [50,30], [70,0]];
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// method = ["length", "centripetal", "dynamic", "foley", "fang"];
@@ -815,13 +854,13 @@ module debug_nurbs(control,degree,splinesteps=16,width=1, size, mult,weights,typ
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// curvature = [undef,-0.06,undef,undef,undef,undef,undef,-0.06]));
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// right(75) stroke(path3, closed = true);
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//
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// Example(2D,Big): Parameterization methods for sharp turns. For data with sudden direction changes or uneven chord spacing, "centripetal" and "dynamic" reduce unwanted oscillations.
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// // "length" (blue), "centripetal" (red), "dynamic" (orange) compared.
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// Example(2D,Med,VPT=[30,15,0],VPD=147): Parameterization methods for sharp turns. For data with sudden direction changes or uneven chord spacing, "centripetal" and "dynamic" reduce unwanted oscillations.
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// // "length" (blue), "centripetal" (red), "dynamic" (green) compared.
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// sharp = [[0,0], [5,40],[6,40], [10,0], [50,0], [55,40],[56,42], [60,0]];
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// color("blue") stroke(nurbs_curve(nurbs_interp(sharp, 3, method = "centripetal"), splinesteps=32), width=0.25);
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// color("red") stroke(nurbs_curve(nurbs_interp(sharp, 3, method="foley"), splinesteps=32), width=0.25);
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// color("orange") stroke(nurbs_curve(nurbs_interp(sharp, 3, method="dynamic"), splinesteps=32), width=0.25);
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// color("green") move_copies(sharp) circle(r=.5, $fn=16);
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// color("lime") stroke(nurbs_curve(nurbs_interp(sharp, 3, method="dynamic"), splinesteps=32), width=0.25);
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// color("black") move_copies(sharp) circle(r=.6, $fn=16);
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function nurbs_interp(points, degree, method="centripetal", closed=false,

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