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656 lines
34 KiB
OpenSCAD
656 lines
34 KiB
OpenSCAD
//////////////////////////////////////////////////////////////////////
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// LibFile: skin.scad
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// Functions to skin arbitrary 2D profiles/paths in 3-space.
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// To use, add the following line to the beginning of your file:
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// ```
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// include <BOSL2/std.scad>
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// include <BOSL2/skin.scad>
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// ```
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// Derived from list-comprehension-demos skin():
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// - https://github.com/openscad/list-comprehension-demos/blob/master/skin.scad
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//////////////////////////////////////////////////////////////////////
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include <vnf.scad>
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// Section: Skinning
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//
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// Function&Module: skin()
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// Usage: As module:
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// skin(profiles, [slices], [refine], [method], [sampling], [caps], [closed], [z]);
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// Usage: As function:
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// vnf = skin(profiles, [slices], [refine], [method], [sampling], [caps], [closed], [z]);
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// Description:
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// Given a list of two ore more path `profiles` in 3d space, produces faces to skin a surface between
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// the profiles. Optionally the first and last profiles can have endcaps, or the first and last profiles
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// can be connected together. Each profile should be roughly planar, but some variation is allowed.
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// Each profile must rotate in the same clockwise direction. If called as a function, returns a
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// [VNF structure](vnf.scad) like `[VERTICES, FACES]`. If called as a module, creates a polyhedron
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// of the skined profiles.
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//
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// The profiles can be specified either as a list of 3d curves or they can be specified as
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// 2d curves with heights given in the `z` parameter.
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//
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// For this operation to be well-defined, the profiles must all have the same vertex count and
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// we must assume that profiles are aligned so that vertex `i` links to vertex `i` on all polygons.
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// Many interesting cases do not comply with this restriction. Two basic methods can handle
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// these cases: either add points to edges (resample) so that the profiles are compatible,
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// or repeat vertices. Repeating vertices allows two edges to terminate at the same point, creating
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// triangular faces. You can adjust non-matchines profiles yourself
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// either by resampling them using `subdivide_path` or by duplicating vertices using
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// `repeat_entries`. It is OK to pass a profile that has the same vertex repeated, such as
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// a square with 5 points (two of which are identical), so that it can match up to a pentagon.
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// Such a combination would create a triangular face at the location of the duplicated vertex.
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// Alternatively, `skin` provides methods (described below) for matching up incompatible paths.
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//
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// In order for skinned surfaces to look good it is usually necessary to use a fine sampling of
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// points on all of the profiles, and a large number of extra interpolated slices between the
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// profiles that you specify. It is generally best if the triangules forming your polyhedron
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// are approximately equilateral. The `slices` parameter specifies the number of slices to insert
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// between each pair of profiles, either a scalar to insert the same number everywhere, or a vector
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// to insert a different number between each pair. To resample the profiles you can use set
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// `refine=N` which will place `N` points on each edge of your profile. This has the effect of
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// muliplying the number of points by N, so a profile with 8 points will have 8*N points afer
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// refinement. Note that when dealing with continuous curves it is always better to adjust the
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// sampling in your code to generate the desired sampling rather than using the `refine` argument.
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//
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// Two methods are available for resampling, `"length"` and `"segment"`. Specify them using
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// the `sampling` argument. The length resampling method resamples proportional to length.
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// The segment method divides each segment of a profile into the same number of points.
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// A uniform division may be impossible, in which case the code computes an approximation.
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// See `subdivide_path` for more details.
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//
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// You can choose from four methods for specifying alignment for incomensurate profiles.
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// The available methods are `"distance"`, `"tangent"`, `"direct"` and `"reindex"`.
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// It is useful to distinguish between continuous curves like a circle and discrete profiles
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// like a hexagon or star, because the algorithms' suitability depend on this distinction.
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//
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// The "direct" and "reindex" methods work by resampling the profiles if necessary. As noted above,
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// for continuous input curves, it is better to generate your curves directly at the desired sample size,
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// but for mapping between a discrete profile like a hexagon and a circle, the hexagon must be resampled
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// to match the circle. You can do this in two different ways using the `sampling` parameter. The default
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// of `sampling="length"` approximates a uniform length sampling of the profile. The other option
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// is `sampling="segment"` which attempts to place the same number of new points on each segment.
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// If the segments are of varying length, this will produce a different result. Note that "direct" is
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// the default method. If you simply supply a list of compatible profiles it will link them up
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// exactly as you have provided them. You may find that profiles you want to connect define the
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// right shapes but the point lists don't start from points that you want aligned in your skinned
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// polyhedron. You can correct this yourself using `reindex_polygon`, or you can use the "reindex"
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// method which will look for the index choice that will minimize the length of all of the edges
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// in the polyhedron---in will produce the least twisted possible result. This algorithm has quadratic
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// run time so it can be slow with very large profiles.
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//
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// The "distance" and "tangent" methods are work by duplicating vertices to create
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// triangular faces. The "distance" method finds the global minimum distance method for connecting two
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// profiles. This algorithm generally produces a good result when both profiles are discrete ones with
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// a small number of vertices. It is computationally intensive (O(N^3)) and may be
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// slow on large inputs. The resulting surfaces generally have curves faces, so be
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// sure to select a sufficiently large value for `slices` and `refine`.
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// The `"tangent"` method generally produces good results when
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// connecting a discrete polygon to a convex, finely sampled curve. It works by finding
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// a plane that passed through each edge of the polygon that is tangent to
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// the curve. It may fail if the curved profile is non-convex, or doesn't have enough points to distinguish
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// all of the tangent points from each other. It connects all of the points of the curve to the corners of the discrete
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// polygon using triangular faces. Using `refine` with this method will have little effect on the model, so
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// you should do it only for agreement with other profiles, and these models are linear, so extra slices also
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// have no effect. For best efficiency set `refine=1` and `slices=0`. When you use refinement with either
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// of these methods, it is always the "segment" based resampling described above. This is necessary because
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// sampling by length will ignore the repeated vertices and break the alignment.
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//
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// It is possible to specify `method` and `refine` as arrays, but it is important to observe
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// matching rules when you do this. If a pair of profiles is connected using "tangent" or "distance"
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// then the `refine` values for those two profiles must be equal. If a profile is connected by
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// a vertex duplicating method on one side and a resampling method on the other side, then
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// `refine` must be set so that the resulting number of vertices matches the number that is
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// used for the resampled profiles. The best way to avoid confusion is to ensure that the
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// profiles connected by "direct" or "realign" all have the same number of points and at the
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// transition, the refined number of points matches.
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//
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// Arguments:
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// profiles = list of 2d or 3d profiles to be skinned. (If 2d must also give `z`.)
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// slices = scalar or vector number of slices to insert between each pair of profiles. Set to zero to use only the profiles you provided. Recommend starting with a value around 10.
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// refine = resample profiles to this number of points per edge. Can be a list to give a refinement for each profile. Recommend using a value above 10 when using the "distance" method. Default: 1.
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// sampling = sampling method to use with "direct" and "reindex" methods. Can be "length" or "segment". Ignored if any profile pair uses either the "distance" or "tangent" methods. Default: "length".
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// closed = set to true to connect first and last profile (to make a torus). Default: false
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// caps = true to create endcap faces when closed is false. Can be a length 2 boolean array. Default is true if closed is false.
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// method = method for connecting profiles, one of "distance", "tangent", "direct" or "reindex". Default: "direct".
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// z = array of height values for each profile if the profiles are 2d
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// Example(FlatSpin):
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// skin([octagon(4), regular_ngon(n=70,r=2)], z=[0,3], slices=10);
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// Example(FlatSpin): The circle() and pentagon() modules place the zero index at different locations, giving a twist
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// skin([pentagon(4), circle($fn=80,r=2)], z=[0,3], slices=10);
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// Example(FlatSpin): You can untwist it with the "reindex" method
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// skin([pentagon(4), circle($fn=80,r=2)], z=[0,3], slices=10, method="reindex");
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// Example(FlatSpin): Offsetting the starting edge connects to circles in an interesting way:
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// circ = circle($fn=80, r=3);
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// skin([circ, rot(110,p=circ)], z=[0,5], slices=20);
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// Example(FlatSpin):
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// skin([ yrot(37,p=path3d(circle($fn=128, r=4))), path3d(square(3),3)], method="reindex",slices=10);
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// Example(FlatSpin): Ellipses connected with twist
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// ellipse = xscale(2.5,p=circle($fn=80));
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// skin([ellipse, rot(45,p=ellipse)], z=[0,1.5], slices=10);
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// Example(FlatSpin): Ellipses connected without a twist. (Note ellipses stay in the same position: just the connecting edges are different.)
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// ellipse = xscale(2.5,p=circle($fn=80));
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// skin([ellipse, rot(45,p=ellipse)], z=[0,1.5], slices=10, method="reindex");
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// Example(FlatSpin):
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// $fn=24;
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// skin([
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// yrot(35, p=yscale(2,p=path3d(circle(d=75)))),
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// [[40,0,100], [35,-15,100], [20,-30,100],[0,-40,100],[-40,0,100],[0,40,100],[20,30,100], [35,15,100]]
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// ],slices=10);
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// Example(FlatSpin):
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// $fn=48;
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// skin([
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// for (b=[0,90]) [
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// for (a=[360:-360/$fn:0.01])
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// point3d(polar_to_xy((100+50*cos((a+b)*2))/2,a),b/90*100)
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// ]
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// ], slices=20);
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// Example(FlatSpin): Vaccum connector example from list-comprehension-demos
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// include <BOSL2/rounding.scad>
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// $fn=32;
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// base = round_corners(square([2,4],center=true), measure="radius", size=0.5);
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// skin([
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// path3d(base,0),
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// path3d(base,2),
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// path3d(circle(r=0.5),3),
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// path3d(circle(r=0.5),4),
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// for(i=[0:2]) each [path3d(circle(r=0.6), i+4),
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// path3d(circle(r=0.5), i+5)]
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// ],slices=0);
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// Example(FlatSpin): Vaccum nozzle example from list-comprehension-demos, using "length" sampling (the default)
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// xrot(90)down(1.5)
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// difference() {
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// skin(
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// [square([2,.2],center=true),
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// circle($fn=64,r=0.5)], z=[0,3],
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// slices=40,sampling="length",method="reindex");
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// skin(
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// [square([1.9,.1],center=true),
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// circle($fn=64,r=0.45)], z=[-.01,3.01],
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// slices=40,sampling="length",method="reindex");
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// }
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// Example(FlatSpin): Same thing with "segment" sampling
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// xrot(90)down(1.5)
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// difference() {
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// skin(
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// [square([2,.2],center=true),
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// circle($fn=64,r=0.5)], z=[0,3],
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// slices=40,sampling="segment",method="reindex");
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// skin(
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// [square([1.9,.1],center=true),
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// circle($fn=64,r=0.45)], z=[-.01,3.01],
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// slices=40,sampling="segment",method="reindex");
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// }
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// Example(FlatSpin): Forma Candle Holder (from list-comprehension-demos)
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// r = 50;
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// height = 140;
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// layers = 10;
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// wallthickness = 5;
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// holeradius = r - wallthickness;
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// difference() {
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// skin([for (i=[0:layers-1]) zrot(-30*i,p=path3d(hexagon(ir=r),i*height/layers))],slices=0);
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// up(height/layers) cylinder(r=holeradius, h=height);
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// }
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// Example(FlatSpin): Connecting a pentagon and circle with the "tangent" method produces triangular faces.
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// skin([pentagon(4), circle($fn=80,r=2)], z=[0,3], slices=10, method="tangent");
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// Example(FlatSpin): Another "tangent" example with non-parallel profiles
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// skin([path3d(pentagon(4)),
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// yrot(35,p=path3d(right(4,p=circle($fn=80,r=2)),5))], slices=10, method="tangent");
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// Example(FlatSpin): Connecting square to pentagon using "direct" method.
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// skin([regular_ngon(n=4, r=4), regular_ngon(n=5,r=5)], z=[0,4], refine=10, slices=10);
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// Example(FlatSpin): Connecting square to pentagon using "direct" method.
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// skin([regular_ngon(n=4, r=4), right(4)regular_ngon(n=5,r=5)], z=[0,4], refine=10, slices=10);
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// Example(FlatSpin): To improve the look, you can actually rotate the polygons for a more symmetric pattern of lines. You have to resample yourself before calling `align_polygon` and you should choose a length that is a multiple of both polygon lengths.
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// sq = subdivide_path(regular_ngon(n=4, r=4),40);
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// pent = subdivide_path(regular_ngon(n=5,r=5),40);
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// skin([sq, align_polygon(sq,pent,[0:1:360/5])], z=[0,4], slices=10);
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// Example(FlatSpin): The "distance" method is a completely different approach.
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// skin([regular_ngon(n=4, r=4), regular_ngon(n=5,r=5)], z=[0,4], refine=10, slices=10, method="distance");
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// Example(FlatSpin): Connecting pentagon to heptagon inserts two triangular faces on each side
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// small = path3d(circle(r=3, $fn=5));
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// big = up(2,p=yrot( 0,p=path3d(circle(r=3, $fn=7), 6)));
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// skin([small,big],method="distance", slices=10, refine=10);
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// Example(FlatSpin): But just a slight rotation moves the two triangles to one end
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// small = path3d(circle(r=3, $fn=5));
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// big = up(2,p=yrot(14,p=path3d(circle(r=3, $fn=7), 6)));
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// skin([small,big],method="distance", slices=10, refine=10);
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// Example(FlatSpin): Another "distance" example:
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// off = [0,2];
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// shape = turtle(["right",45,"move", "left",45,"move", "left",45, "move", "jump", [.5+sqrt(2)/2,8]]);
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// rshape = rot(180,cp=centroid(shape)+off, p=shape);
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// skin([shape,rshape],z=[0,4], method="distance",slices=10,refine=15);
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// Example(FlatSpin): Slightly shifting the profile changes the optimal linkage
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// off = [0,1];
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// shape = turtle(["right",45,"move", "left",45,"move", "left",45, "move", "jump", [.5+sqrt(2)/2,8]]);
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// rshape = rot(180,cp=centroid(shape)+off, p=shape);
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// skin([shape,rshape],z=[0,4], method="distance",slices=10,refine=15);
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// Example(FlatSpin): This optimal solution doesn't look terrible:
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// prof1 = path3d([[50,-50], [-50,-50], [-50,50], [-25,25], [0,50], [25,25], [50,50]]);
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// prof2 = path3d(regular_ngon(n=7, r=50),100);
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// skin([prof1, prof2], method="distance", slices=10, refine=10);
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// Example(FlatSpin): But this one looks better. The "distance" method doesn't find it because it uses two more edges, so it clearly has a higher total edge distance. We force it by doubling the first two vertices of one of the profiles.
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// prof1 = path3d([[50,-50], [-50,-50], [-50,50], [-25,25], [0,50], [25,25], [50,50]]);
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// prof2 = path3d(regular_ngon(n=7, r=50),100);
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// skin([repeat_entries(prof1,[2,2,1,1,1,1,1]),
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// prof2],
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// method="distance", slices=10, refine=10);
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// Example(FlatSpin): Torus using hexagons and pentagons, where `closed=true`
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// hex = back(7,p=path3d(hexagon(r=3)));
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// pent = back(7,p=path3d(pentagon(r=3)));
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// N=5;
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// skin(
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// [for(i=[0:2*N-1]) xrot(360*i/2/N, p=(i%2==0 ? hex : pent))],
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// refine=1,slices=0,method="distance",closed=true);
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// Example(FlatSpin): A smooth morph is achieved when you can calculate all the slices yourself. Since you provide all the slices, set `slices=0`.
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// skin([for(n=[.1:.02:.5])
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// yrot(n*60-.5*60,p=path3d(supershape(step=360/128,m1=5,n1=n, n2=1.7),5-10*n))],
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// slices=0);
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// Example(FlatSpin): Another smooth supershape morph:
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// skin([for(alpha=[-.2:.05:1.5])
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// path3d(supershape(step=360/256,m1=7, n1=lerp(2,3,alpha),
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// n2=lerp(8,4,alpha), n3=lerp(4,17,alpha)),alpha*5)],
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// slices=0);
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// Example(FlatSpin): Several polygons connected using "distance"
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// skin([regular_ngon(n=4, r=3),
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// regular_ngon(n=6, r=3),
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// regular_ngon(n=9, r=4),
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// rot(17,p=regular_ngon(n=6, r=3)),
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// rot(37,p=regular_ngon(n=4, r=3))],
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// z=[0,2,4,6,9], method="distance", slices=10, refine=10);
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// Example(FlatSpin): Size of the polygon changes every time
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// skin([
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// for (ang = [0:10:90])
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// rot([0,ang,0], cp=[200,0,0], p=path3d(circle(d=100,$fn=12-(ang/10))))
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// ],method="distance",slices=10,refine=10);
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module skin(profiles, slices, refine=1, method="direct", sampling, caps, closed=false, z, convexity=10)
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{
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vnf_polyhedron(skin(profiles, slices, refine, method, sampling, caps, closed, z), convexity=convexity);
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}
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function skin(profiles, slices, refine=1, method="direct", sampling, caps, closed=false, z) =
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assert(is_list(profiles) && len(profiles)>1, "Must provide at least two profiles")
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let( bad = [for(i=idx(profiles)) if (!(is_path(profiles[i]) && len(profiles[i])>2)) i])
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assert(len(bad)==0, str("Profiles ",bad," are not a paths or have length less than 3"))
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assert(is_integer(slices) && slices>=0,"slices must be specified as a nonnegative integer")
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let(
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legal_methods = ["direct","reindex","distance","tangent"],
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caps = is_def(caps) ? caps :
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closed ? false : true,
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capsOK = is_bool(caps) || (is_list(caps) && len(caps)==2 && is_bool(caps[0]) && is_bool(caps[1])),
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fullcaps = is_bool(caps) ? [caps,caps] : caps,
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refine = is_list(refine) ? refine :
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replist(refine, len(profiles)),
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refineOK = [for(i=idx(refine)) if (refine[i]<=0 || !is_integer(refine[i])) i],
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maxsize = list_longest(profiles),
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methodok = is_list(method) || in_list(method, legal_methods),
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methodlistok = is_list(method) ? [for(i=idx(method)) if (!in_list(method[i], legal_methods)) i] : [],
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method = is_string(method) ? replist(method, len(profiles)+ (closed?0:-1)) : method,
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// Define to be zero where a resampling method is used and 1 where a vertex duplicator is used
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RESAMPLING = 0,
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DUPLICATOR = 1,
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method_type = [for(m = method) m=="direct" || m=="reindex" ? 0 : 1],
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sampling = is_def(sampling) ? sampling :
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in_list(DUPLICATOR,method_type) ? "segment" : "length"
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)
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assert(len(refine)==len(profiles), "refine list is the wrong length")
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assert(refineOK==[],str("refine must be integer valued and postive"))
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assert(methodok,str("method must be one of ",legal_methods,". Got ",method))
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assert(methodlistok==[], str("method list contains invalid method at ",methodlistok))
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assert(len(method) == len(profiles) + (closed?0:-1),"Method list is the wrong length")
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assert(in_list(sampling,["length","segment"]), "sampling must be set to \"length\" or \"segment\"")
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assert(sampling=="segment" || (!in_list("distance",method) && !in_list("tangent",method)), "sampling is set to \"length\" which is only allowed iwith methods \"direct\" and \"reindex\"")
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assert(capsOK, "caps must be boolean or a list of two booleans")
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assert(!closed || !caps, "Cannot make closed shape with caps")
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let(
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profile_dim=array_dim(profiles,2),
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profiles_ok = (profile_dim==2 && is_list(z) && len(z)==len(profiles)) || profile_dim==3
|
|
)
|
|
assert(profiles_ok,"Profiles must all be 3d or must all be 2d, with matching length z parameter.")
|
|
assert(is_undef(z) || profile_dim==2, "Do not specify z with 3d profiles")
|
|
assert(profile_dim==3 || len(z)==len(profiles),"Length of z does not match length of profiles.")
|
|
let(
|
|
// Adjoin Z coordinates to 2d profiles
|
|
profiles = profile_dim==3 ? profiles :
|
|
[for(i=idx(profiles)) path3d(profiles[i], z[i])],
|
|
// True length (not counting repeated vertices) of profiles after refinement
|
|
refined_len = [for(i=idx(profiles)) refine[i]*len(profiles[i])],
|
|
rety= echo(refine=refine),
|
|
fdabe= echo(refined_len = refined_len),
|
|
// Define this to be 1 if a profile is used on either side by a resampling method, zero otherwise.
|
|
profile_resampled = [for(i=idx(profiles))
|
|
1-(
|
|
i==0 ? method_type[0] * (closed? select(method_type,-1) : 1) :
|
|
i==len(profiles)-1 ? select(method_type,-1) * (closed ? select(method_type,-2) : 1) :
|
|
method_type[i] * method_type[i-1])],
|
|
|
|
|
|
efqqw=echo(method_type = method_type),
|
|
fdae= echo(profile_resampled=profile_resampled),
|
|
parts = search(1,[1,for(i=[0:1:len(profile_resampled)-2]) profile_resampled[i]!=profile_resampled[i+1] ? 1 : 0],0),
|
|
plen = [for(i=idx(parts)) (i== len(parts)-1? len(refined_len) : parts[i+1]) - parts[i]],
|
|
max_list = [for(i=idx(parts)) each replist(max(select(refined_len, parts[i], parts[i]+plen[i]-1)), plen[i])],
|
|
fdafee= echo(max_list=max_list),
|
|
transition_profiles = [for(i=[(closed?0:1):1:len(profiles)-(closed?1:2)]) if (select(method_type,i-1) != method_type[i]) i],
|
|
ttr=echo(transition_profiles=transition_profiles),
|
|
badind = [for(tranprof=transition_profiles) if (refined_len[tranprof] != max_list[tranprof]) tranprof]
|
|
)
|
|
assert(badind==[],str("Profile length mismatch at method transition at indices ",badind," in skin()"))
|
|
let(
|
|
|
|
// With "distance" and "tangent" methods, the path lengths are made equal by inserting
|
|
// repeated vertices, so no further adjustment is required. With "direct" and "reindex"
|
|
// lengths match due to resampling, and we have to upsample to the longest profile.
|
|
samples = in_list("direct", method) || in_list("reindex", method) ? max(refined_len) : 0,
|
|
full_list =
|
|
[for(i=[0:len(profiles)-(closed?1:2)])
|
|
let(
|
|
pair =
|
|
method[i]=="distance" ? minimum_distance_match(profiles[i],select(profiles,i+1)) :
|
|
method[i]=="tangent" ? tangent_align(profiles[i],select(profiles,i+1)) :
|
|
/*method[i]=="reindex" || method[i]=="direct" ?*/
|
|
let( p1 = subdivide_path(profiles[i],max_list[i], method=sampling),
|
|
p2 = subdivide_path(select(profiles,i+1),max_list[i], method=sampling)
|
|
) (method[i]=="direct" ? [p1,p2] : [p1, reindex_polygon(p1, p2)]),
|
|
nsamples = method_type[i]==RESAMPLING ? len(pair[0]) :
|
|
assert(refine[i]==select(refine,i+1),str("Refine value mismatch at indices ",[i,(i+1)%len(refine)],
|
|
". Method ",method[i]," requires equal values"))
|
|
refine[i] * len(pair[0])
|
|
)
|
|
each interp_and_slice(pair,slices, nsamples, submethod=sampling)]
|
|
)
|
|
_skin_core(full_list,caps=fullcaps);
|
|
|
|
|
|
|
|
function _skin_core(profiles, caps) =
|
|
let(
|
|
vertices = [for (prof=profiles) each prof],
|
|
plens = [for (prof=profiles) len(prof)],
|
|
sidefaces = [
|
|
for(pidx=idx(profiles,end=-2))
|
|
let(
|
|
prof1 = profiles[pidx%len(profiles)],
|
|
prof2 = profiles[(pidx+1)%len(profiles)],
|
|
voff = default(sum([for (i=[0:1:pidx-1]) plens[i]]),0),
|
|
faces = [
|
|
for(
|
|
first = true,
|
|
finishing = false,
|
|
finished = false,
|
|
plen1 = len(prof1),
|
|
plen2 = len(prof2),
|
|
i=0, j=0, side=0;
|
|
|
|
!finished;
|
|
|
|
side =
|
|
let(
|
|
p1a = prof1[(i+0)%plen1],
|
|
p1b = prof1[(i+1)%plen1],
|
|
p2a = prof2[(j+0)%plen2],
|
|
p2b = prof2[(j+1)%plen2],
|
|
dist1 = norm(p1a-p2b),
|
|
dist2 = norm(p1b-p2a)
|
|
) (i==j) ? (dist1>dist2? 1 : 0) : (i<j ? 1 : 0) ,
|
|
p1 = voff + (i%plen1),
|
|
p2 = voff + (j%plen2) + plen1,
|
|
p3 = voff + (side? ((i+1)%plen1) : (((j+1)%plen2) + plen1)),
|
|
face = [p1, p3, p2],
|
|
i = i + (side? 1 : 0),
|
|
j = j + (side? 0 : 1),
|
|
first = false,
|
|
finished = finishing,
|
|
finishing = i>=plen1 && j>=plen2
|
|
) if (!first) face
|
|
]
|
|
) each faces
|
|
],
|
|
firstcap = !caps[0] ? [] : let(
|
|
prof1 = profiles[0]
|
|
) [[for (i=idx(prof1)) plens[0]-1-i]],
|
|
secondcap = !caps[1] ? [] : let(
|
|
prof2 = select(profiles,-1),
|
|
eoff = sum(select(plens,0,-2))
|
|
) [[for (i=idx(prof2)) eoff+i]]
|
|
) [vertices, concat(sidefaces,firstcap,secondcap)];
|
|
|
|
|
|
|
|
|
|
// plist is list of polygons, N is list or value for number of slices to insert
|
|
// numpoints can be "max", "lcm" or a number
|
|
function interp_and_slice(plist, N, numpoints="max", align=false,submethod="length") =
|
|
let(
|
|
maxsize = list_longest(plist),
|
|
numpoints = numpoints == "max" ? maxsize :
|
|
numpoints == "lcm" ? lcmlist([for(p=plist) len(p)]) :
|
|
is_num(numpoints) ? round(numpoints) : undef
|
|
)
|
|
assert(is_def(numpoints), "Parameter numpoints must be \"max\", \"lcm\" or a positive number")
|
|
assert(numpoints>=maxsize, "Number of points requested is smaller than largest profile")
|
|
let(fixpoly = [for(poly=plist) subdivide_path(poly, numpoints,method=submethod)])
|
|
add_slices(fixpoly, N);
|
|
|
|
|
|
|
|
|
|
function add_slices(plist,N) =
|
|
assert(is_num(N) || is_list(N))
|
|
let(listok = !is_list(N) || len(N)==len(plist)-1)
|
|
assert(listok, "Input N to add_slices is a list with the wrong length")
|
|
let(
|
|
count = is_num(N) ? replist(N,len(plist)-1) : N,
|
|
slicelist = [for (i=[0:len(plist)-2])
|
|
each [for(j = [0:count[i]]) lerp(plist[i],plist[i+1],j/(count[i]+1))]
|
|
]
|
|
)
|
|
concat(slicelist, [plist[len(plist)-1]]);
|
|
|
|
|
|
|
|
// Function: unique_count()
|
|
// Usage:
|
|
// unique_count(arr);
|
|
// Description:
|
|
// Returns `[sorted,counts]` where `sorted` is a sorted list of the unique items in `arr` and `counts` is a list such
|
|
// that `count[i]` gives the number of times that `sorted[i]` appears in `arr`.
|
|
// Arguments:
|
|
// arr = The list to analyze.
|
|
function unique_count(arr) =
|
|
assert(is_list(arr)||is_string(list))
|
|
len(arr)==0 ? [[],[]] :
|
|
len(arr)==1 ? [arr,[1]] :
|
|
_unique_count(sort(arr), ulist=[], counts=[], ind=1, curtot=1);
|
|
|
|
function _unique_count(arr, ulist, counts, ind, curtot) =
|
|
ind == len(arr)+1 ? [ulist, counts] :
|
|
ind==len(arr) || arr[ind] != arr[ind-1] ? _unique_count(arr,concat(ulist,[arr[ind-1]]), concat(counts,[curtot]),ind+1,1) :
|
|
_unique_count(arr,ulist,counts,ind+1,curtot+1);
|
|
|
|
///////////////////////////////////////////////////////
|
|
//
|
|
|
|
// Given inputs of a two polygons, computes a mapping between their vertices that minimizes the sum the sum of
|
|
// the distances between every matched pair of vertices. The algorithm uses dynamic programming to calculate
|
|
// the optimal mapping under the assumption that poly1[0] <-> poly2[0]. We then rotate through all the
|
|
// possible indexings of the longer polygon. The theoretical run time is quadratic in the longer polygon and
|
|
// linear in the shorter one.
|
|
//
|
|
// The top level function, minimum_distance_match(), cycles through all the of the indexings of the larger
|
|
// polygon, computes the optimal value for each indexing, and chooses the overall best result. It uses
|
|
// _dp_extract_map() to thread back through the dynamic programming array to determine the actual mapping, and
|
|
// then converts the result to an index repetition count list, which is passed to repeat_entries().
|
|
//
|
|
// The function _dp_distance_array builds up the rows of the dynamic programming matrix with reference
|
|
// to the previous rows, where `tdist` holds the total distance for a given mapping, and `map`
|
|
// holds the information about which path was optimal for each position.
|
|
//
|
|
// The function _dp_distance_row constructs each row of the dynamic programming matrix in the usual
|
|
// way where entries fill in based on the three entries above and to the left. Note that we duplicate
|
|
// entry zero so account for wrap-around at the ends, and we initialize the distance to zero to avoid
|
|
// double counting the length of the 0-0 pair.
|
|
//
|
|
// This function builds up the dynamic programming distance array where each entry in the
|
|
// array gives the optimal distance for aligning the corresponding subparts of the two inputs.
|
|
// When the array is fully populated, the bottom right corner gives the minimum distance
|
|
// for matching the full input lists. The `map` array contains a the three key values for the three
|
|
// directions, where _MAP_DIAG means you map the next vertex of `big` to the next vertex of `small`,
|
|
// _MAP_LEFT means you map the next vertex of `big` to the current vertex of `small`, and _MAP_UP
|
|
// means you map the next vertex of `small` to the current vertex of `big`.
|
|
//
|
|
// Return value is [min_distance, map], where map is the array that is used to extract the actual
|
|
// vertex map.
|
|
|
|
_MAP_DIAG = 0;
|
|
_MAP_LEFT = 1;
|
|
_MAP_UP = 2;
|
|
|
|
|
|
/*
|
|
function _dp_distance_array(small, big, abort_thresh=1/0, small_ind=0, tdist=[], map=[]) =
|
|
small_ind == len(small)+1 ? [tdist[len(tdist)-1][len(big)-1], map] :
|
|
let( newrow = _dp_distance_row(small, big, small_ind, tdist) )
|
|
min(newrow[0]) > abort_thresh ? [tdist[len(tdist)-1][len(big)-1],map] :
|
|
_dp_distance_array(small, big, abort_thresh, small_ind+1, concat(tdist, [newrow[0]]), concat(map, [newrow[1]]));
|
|
*/
|
|
|
|
|
|
function _dp_distance_array(small, big, abort_thresh=1/0) =
|
|
[for(
|
|
small_ind = 0,
|
|
tdist = [],
|
|
map = []
|
|
;
|
|
small_ind<=len(small)+1
|
|
;
|
|
newrow =small_ind==len(small)+1 ? [0,0,0] : // dummy end case
|
|
_dp_distance_row(small,big,small_ind,tdist),
|
|
tdist = concat(tdist, [newrow[0]]),
|
|
map = concat(map, [newrow[1]]),
|
|
small_ind = min(newrow[0])>abort_thresh ? len(small)+1 : small_ind+1
|
|
)
|
|
if (small_ind==len(small)+1) each [tdist[len(tdist)-1][len(big)], map]];
|
|
//[tdist,map]];
|
|
|
|
|
|
function _dp_distance_row(small, big, small_ind, tdist) =
|
|
// Top left corner is zero because it gets counted at the end in bottom right corner
|
|
small_ind == 0 ? [cumsum([0,for(i=[1:len(big)]) norm(big[i%len(big)]-small[0])]), replist(_MAP_LEFT,len(big)+1)] :
|
|
[for(big_ind=1,
|
|
newrow=[ norm(big[0] - small[small_ind%len(small)]) + tdist[small_ind-1][0] ],
|
|
newmap = [_MAP_UP]
|
|
;
|
|
big_ind<=len(big)+1
|
|
;
|
|
costs = big_ind == len(big)+1 ? [0] : // handle extra iteration
|
|
[tdist[small_ind-1][big_ind-1], // diag
|
|
newrow[big_ind-1], // left
|
|
tdist[small_ind-1][big_ind]], // up
|
|
newrow = concat(newrow, [min(costs)+norm(big[big_ind%len(big)]-small[small_ind%len(small)])]),
|
|
newmap = concat(newmap, [min_index(costs)]),
|
|
big_ind = big_ind+1
|
|
) if (big_ind==len(big)+1) each [newrow,newmap]];
|
|
|
|
|
|
function _dp_extract_map(map) =
|
|
[for(
|
|
i=len(map)-1,
|
|
j=len(map[0])-1,
|
|
smallmap=[],
|
|
bigmap = []
|
|
;
|
|
j >= 0
|
|
;
|
|
advance_i = map[i][j]==_MAP_UP || map[i][j]==_MAP_DIAG,
|
|
advance_j = map[i][j]==_MAP_LEFT || map[i][j]==_MAP_DIAG,
|
|
i = i - (advance_i ? 1 : 0),
|
|
j = j - (advance_j ? 1 : 0),
|
|
bigmap = concat( [j%(len(map[0])-1)] , bigmap),
|
|
smallmap = concat( [i%(len(map)-1)] , smallmap)
|
|
)
|
|
if (i==0 && j==0) each [smallmap,bigmap]];
|
|
|
|
|
|
function minimum_distance_match(poly1,poly2) =
|
|
let(
|
|
swap = len(poly1)>len(poly2),
|
|
big = swap ? poly1 : poly2,
|
|
small = swap ? poly2 : poly1,
|
|
map_poly = [ for(
|
|
i=0,
|
|
bestcost = 1/0,
|
|
bestmap = -1,
|
|
bestpoly = -1
|
|
;
|
|
i<=len(big)
|
|
;
|
|
shifted = polygon_shift(big,i),
|
|
result =_dp_distance_array(small, shifted, abort_thresh = bestcost),
|
|
bestmap = result[0]<bestcost ? result[1] : bestmap,
|
|
bestpoly = result[0]<bestcost ? shifted : bestpoly,
|
|
best_i = result[0]<bestcost ? i : best_i,
|
|
bestcost = min(result[0], bestcost),
|
|
i=i+1
|
|
)
|
|
if (i==len(big)) each [bestmap,bestpoly,best_i]],
|
|
map = _dp_extract_map(map_poly[0]),
|
|
smallmap = map[0],
|
|
bigmap = map[1],
|
|
// These shifts are needed to handle the case when points from both ends of one curve map to a single point on the other
|
|
bigshift = len(bigmap) - max(max_index(bigmap,all=true))-1,
|
|
smallshift = len(smallmap) - max(max_index(smallmap,all=true))-1,
|
|
newsmall = polygon_shift(repeat_entries(small,unique_count(smallmap)[1]),smallshift),
|
|
newbig = polygon_shift(repeat_entries(map_poly[1],unique_count(bigmap)[1]),bigshift)
|
|
)
|
|
swap ? [newbig, newsmall] : [newsmall,newbig];
|
|
|
|
|
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
|
//////////////////////////////////////////////////////////////////////////////////////////////////////////////
|
|
|
|
function tangent_align(poly1, poly2) =
|
|
let(
|
|
swap = len(poly1)>len(poly2),
|
|
big = swap ? poly1 : poly2,
|
|
small = swap ? poly2 : poly1,
|
|
curve_offset = centroid(small)-centroid(big),
|
|
cutpts = [for(i=[0:len(small)-1]) find_one_tangent(big, select(small,i,i+1),curve_offset=curve_offset)],
|
|
d=echo(cutpts = cutpts),
|
|
shift = select(cutpts,-1)+1,
|
|
newbig = polygon_shift(big, shift),
|
|
repeat_counts = [for(i=[0:len(small)-1]) posmod(cutpts[i]-select(cutpts,i-1),len(big))],
|
|
newsmall = repeat_entries(small,repeat_counts)
|
|
)
|
|
assert(len(newsmall)==len(newbig), "Tangent alignment failed, probably because of insufficient points or a concave curve")
|
|
swap ? [newbig, newsmall] : [newsmall, newbig];
|
|
|
|
|
|
function find_one_tangent(curve, edge, curve_offset=[0,0,0], closed=true) =
|
|
let(
|
|
angles =
|
|
[for(i=[0:len(curve)-(closed?1:2)])
|
|
let(
|
|
plane = plane3pt( edge[0], edge[1], curve[i]),
|
|
tangent = [curve[i], select(curve,i+1)]
|
|
)
|
|
plane_line_angle(plane,tangent)],
|
|
zero_cross = [for(i=[0:len(curve)-(closed?1:2)]) if (sign(angles[i]) != sign(select(angles,i+1))) i],
|
|
d = [for(i=zero_cross) distance_from_line(edge, curve[i]+curve_offset)]
|
|
)
|
|
zero_cross[min_index(d)];//zcross;
|
|
|
|
|
|
|
|
function plane_line_angle(plane, line) =
|
|
let(
|
|
vect = line[1]-line[0],
|
|
zplane = select(plane,0,2),
|
|
sin_angle = vect*zplane/norm(zplane)/norm(vect)
|
|
)
|
|
asin(constrain(sin_angle,-1,1));
|
|
|
|
// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap
|