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doc tweaks for skin(), faster 2d hull()

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Adrian Mariano 2021-03-04 18:34:17 -05:00
parent 5ce8ba4728
commit 863c410404
2 changed files with 71 additions and 68 deletions
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85
hull.scad
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@ -74,6 +74,15 @@ module hull_points(points, fast=false) {
} }
function _backtracking(i,points,h,t,m) =
m<t || _is_cw(points[i], points[h[m-1]], points[h[m-2]]) ? m :
_backtracking(i,points,h,t,m-1) ;
// clockwise check (2d)
function _is_cw(a,b,c) = cross(a-c,b-c)<=0;
// Function: hull2d_path() // Function: hull2d_path()
// Usage: // Usage:
// hull2d_path(points) // hull2d_path(points)
@ -85,34 +94,42 @@ module hull_points(points, fast=false) {
// path = hull2d_path(pts); // path = hull2d_path(pts);
// move_copies(pts) color("red") sphere(1); // move_copies(pts) color("red") sphere(1);
// polygon(points=pts, paths=[path]); // polygon(points=pts, paths=[path]);
// Code based on this method:
// https://www.hackerearth.com/practice/math/geometry/line-sweep-technique/tutorial/
//
function hull2d_path(points) = function hull2d_path(points) =
assert(is_path(points,2),"Invalid input to hull2d_path") assert(is_path(points,2),"Invalid input to hull2d_path")
len(points) < 2 ? [] len(points) < 2 ? []
: len(points) == 2 ? [0,1] : len(points) == 2 ? [0,1]
: let(tri=noncollinear_triple(points, error=false)) : let(tri=noncollinear_triple(points, error=false))
tri == [] ? _hull_collinear(points) tri == [] ? _hull_collinear(points)
: let( :
remaining = [ for (i = [0:1:len(points)-1]) if (i != tri[0] && i!=tri[1] && i!=tri[2]) i ], assert(is_path(points,2))
ccw = triangle_area(points[tri[0]], points[tri[1]], points[tri[2]]) > 0, assert(len(points)>=3, "Point list must contain at least 3 points.")
polygon = ccw ? [tri[0],tri[1],tri[2]] : [tri[0],tri[2],tri[1]] let( n = len(points),
) _hull2d_iterative(points, polygon, remaining); ip = sortidx(points) )
// lower hull points
let( lh =
[ for( i = 2,
// Adds the remaining points one by one to the convex hull k = 2,
function _hull2d_iterative(points, polygon, remaining, _i=0) = h = [ip[0],ip[1]]; // current list of hull point indices
(_i >= len(remaining))? polygon : let ( i <= n;
// pick a point k = i<n ? _backtracking(ip[i],points,h,2,k)+1 : k,
i = remaining[_i], h = i<n ? [for(j=[0:1:k-2]) h[j], ip[i]] : [],
// find the segments that are in conflict with the point (point not inside) i = i+1
conflicts = _find_conflicting_segments(points, polygon, points[i]) ) if( i==n ) h ][0] )
// no conflicts, skip point and move on // concat lower hull points with upper hull ones
) (len(conflicts) == 0)? _hull2d_iterative(points, polygon, remaining, _i+1) : let( [ for( i = n-2,
// find the first conflicting segment and the first not conflicting k = len(lh),
// conflict will be sorted, if not wrapping around, do it the easy way t = k+1,
polygon = _remove_conflicts_and_insert_point(polygon, conflicts, i) h = lh; // current list of hull point indices
) _hull2d_iterative(points, polygon, remaining, _i+1); i >= -1;
k = i>=0 ? _backtracking(ip[i],points,h,t,k)+1 : k,
h = [for(j=[0:1:k-2]) h[j], if(i>0) ip[i]],
i = i-1
) if( i==-1 ) h ][0] ;
function _hull_collinear(points) = function _hull_collinear(points) =
let( let(
@ -124,30 +141,6 @@ function _hull_collinear(points) =
) [min_i, max_i]; ) [min_i, max_i];
function _find_conflicting_segments(points, polygon, point) = [
for (i = [0:1:len(polygon)-1]) let(
j = (i+1) % len(polygon),
p1 = points[polygon[i]],
p2 = points[polygon[j]],
area = triangle_area(p1, p2, point)
) if (area < 0) i
];
// remove the conflicting segments from the polygon
function _remove_conflicts_and_insert_point(polygon, conflicts, point) =
(conflicts[0] == 0)? let(
nonconflicting = [ for(i = [0:1:len(polygon)-1]) if (!in_list(i, conflicts)) i ],
new_indices = concat(nonconflicting, (nonconflicting[len(nonconflicting)-1]+1) % len(polygon)),
polygon = concat([ for (i = new_indices) polygon[i] ], point)
) polygon : let(
before_conflicts = [ for(i = [0:1:min(conflicts)]) polygon[i] ],
after_conflicts = (max(conflicts) >= (len(polygon)-1))? [] : [ for(i = [max(conflicts)+1:1:len(polygon)-1]) polygon[i] ],
polygon = concat(before_conflicts, point, after_conflicts)
) polygon;
// Function: hull3d_faces() // Function: hull3d_faces()
// Usage: // Usage:
// hull3d_faces(points) // hull3d_faces(points)

54
skin.scad
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@ -47,31 +47,29 @@
// profiles that you specify. It is generally best if the triangles forming your polyhedron // profiles that you specify. It is generally best if the triangles forming your polyhedron
// are approximately equilateral. The `slices` parameter specifies the number of slices to insert // are approximately equilateral. The `slices` parameter specifies the number of slices to insert
// between each pair of profiles, either a scalar to insert the same number everywhere, or a vector // between each pair of profiles, either a scalar to insert the same number everywhere, or a vector
// to insert a different number between each pair. To resample the profiles you can use set // to insert a different number between each pair.
// `refine=N` which will place `N` points on each edge of your profile. This has the effect of // .
// multiplying the number of points by N, so a profile with 8 points will have 8*N points after // Resampling may occur, depending on the `method` parameter, to make profiles compatible.
// refinement. Note that when dealing with continuous curves it is always better to adjust the // To force (possibly additional) resampling of the profiles to increase the point density you can set `refine=N`, which
// will multiply the number of points on your profile by `N`. You can choose between two resampling
// schemes using the `sampling` option, which you can set to `"length"` or `"segment"`.
// The length resampling method resamples proportional to length.
// The segment method divides each segment of a profile into the same number of points.
// This means that if you refine a profile with the "segment" method you will get N points
// on each edge, but if you refine a profile with the "length" method you will get new points
// distributed around the profile based on length, so small segments will get fewer new points than longer ones.
// A uniform division may be impossible, in which case the code computes an approximation, which may result
// in arbitrary distribution of extra points. See `subdivide_path` for more details.
// Note that when dealing with continuous curves it is always better to adjust the
// sampling in your code to generate the desired sampling rather than using the `refine` argument. // sampling in your code to generate the desired sampling rather than using the `refine` argument.
// . // .
// Two methods are available for resampling, `"length"` and `"segment"`. Specify them using
// the `sampling` argument. The length resampling method resamples proportional to length.
// The segment method divides each segment of a profile into the same number of points.
// A uniform division may be impossible, in which case the code computes an approximation.
// See `subdivide_path` for more details.
//
// You can choose from four methods for specifying alignment for incommensurate profiles. // You can choose from four methods for specifying alignment for incommensurate profiles.
// The available methods are `"distance"`, `"tangent"`, `"direct"` and `"reindex"`. // The available methods are `"distance"`, `"tangent"`, `"direct"` and `"reindex"`.
// It is useful to distinguish between continuous curves like a circle and discrete profiles // It is useful to distinguish between continuous curves like a circle and discrete profiles
// like a hexagon or star, because the algorithms' suitability depend on this distinction. // like a hexagon or star, because the algorithms' suitability depend on this distinction.
// . // .
// The "direct" and "reindex" methods work by resampling the profiles if necessary. As noted above, // The default method for aligning profiles is `method="direct"`.
// for continuous input curves, it is better to generate your curves directly at the desired sample size, // If you simply supply a list of compatible profiles it will link them up
// but for mapping between a discrete profile like a hexagon and a circle, the hexagon must be resampled
// to match the circle. You can do this in two different ways using the `sampling` parameter. The default
// of `sampling="length"` approximates a uniform length sampling of the profile. The other option
// is `sampling="segment"` which attempts to place the same number of new points on each segment.
// If the segments are of varying length, this will produce a different result. Note that "direct" is
// the default method. If you simply supply a list of compatible profiles it will link them up
// exactly as you have provided them. You may find that profiles you want to connect define the // exactly as you have provided them. You may find that profiles you want to connect define the
// right shapes but the point lists don't start from points that you want aligned in your skinned // right shapes but the point lists don't start from points that you want aligned in your skinned
// polyhedron. You can correct this yourself using `reindex_polygon`, or you can use the "reindex" // polyhedron. You can correct this yourself using `reindex_polygon`, or you can use the "reindex"
@ -79,12 +77,25 @@
// in the polyhedron---in will produce the least twisted possible result. This algorithm has quadratic // in the polyhedron---in will produce the least twisted possible result. This algorithm has quadratic
// run time so it can be slow with very large profiles. // run time so it can be slow with very large profiles.
// . // .
// When the profiles are incommensurate, the "direct" and "reindex" resampling them to match. As noted above,
// for continuous input curves, it is better to generate your curves directly at the desired sample size,
// but for mapping between a discrete profile like a hexagon and a circle, the hexagon must be resampled
// to match the circle. When you use "direct" or "reindex" the default `sampling` value is
// of `sampling="length"` to approximate a uniform length sampling of the profile. This will generally
// produce the natural result for connecting two continuously sampled profiles or a continuous
// profile and a polygonal one. However depending on your particular case,
// `sampling="segment"` may produce a more pleasing result. These two approaches differ only when
// the segments of your input profiles have unequal length.
// .
// The "distance" and "tangent" methods work by duplicating vertices to create // The "distance" and "tangent" methods work by duplicating vertices to create
// triangular faces. The "distance" method finds the global minimum distance method for connecting two // triangular faces. The "distance" method finds the global minimum distance method for connecting two
// profiles. This algorithm generally produces a good result when both profiles are discrete ones with // profiles. This algorithm generally produces a good result when both profiles are discrete ones with
// a small number of vertices. It is computationally intensive (O(N^3)) and may be // a small number of vertices. It is computationally intensive (O(N^3)) and may be
// slow on large inputs. The resulting surfaces generally have curved faces, so be // slow on large inputs. The resulting surfaces generally have curved faces, so be
// sure to select a sufficiently large value for `slices` and `refine`. // sure to select a sufficiently large value for `slices` and `refine`. Note that for
// this method, `sampling` must be set to `"segment"`, and hence this is the default setting.
// Using sampling by length would ignore the repeated vertices and ruin the alignment.
// .
// The `"tangent"` method generally produces good results when // The `"tangent"` method generally produces good results when
// connecting a discrete polygon to a convex, finely sampled curve. It works by finding // connecting a discrete polygon to a convex, finely sampled curve. It works by finding
// a plane that passed through each edge of the polygon that is tangent to // a plane that passed through each edge of the polygon that is tangent to
@ -92,9 +103,8 @@
// all of the tangent points from each other. It connects all of the points of the curve to the corners of the discrete // all of the tangent points from each other. It connects all of the points of the curve to the corners of the discrete
// polygon using triangular faces. Using `refine` with this method will have little effect on the model, so // polygon using triangular faces. Using `refine` with this method will have little effect on the model, so
// you should do it only for agreement with other profiles, and these models are linear, so extra slices also // you should do it only for agreement with other profiles, and these models are linear, so extra slices also
// have no effect. For best efficiency set `refine=1` and `slices=0`. When you use refinement with either // have no effect. For best efficiency set `refine=1` and `slices=0`. As with the "distance" method, refinement
// of these methods, it is always the "segment" based resampling described above. This is necessary because // must be done using the "segment" sampling scheme to preserve alignment across duplicated points.
// sampling by length will ignore the repeated vertices and break the alignment.
// . // .
// It is possible to specify `method` and `refine` as arrays, but it is important to observe // It is possible to specify `method` and `refine` as arrays, but it is important to observe
// matching rules when you do this. If a pair of profiles is connected using "tangent" or "distance" // matching rules when you do this. If a pair of profiles is connected using "tangent" or "distance"