From b1408da3422353e1a4bafb627af7bad51aa22aee Mon Sep 17 00:00:00 2001
From: Revar Desmera <revarbat@gmail.com>
Date: Wed, 24 Apr 2019 03:31:42 -0700
Subject: [PATCH] Renamed convex_hull stuff.
---
convex_hull.scad => hull.scad | 144 +++++++++++++++++++++++-----------
1 file changed, 99 insertions(+), 45 deletions(-)
rename convex_hull.scad => hull.scad (64%)
diff --git a/convex_hull.scad b/hull.scad
similarity index 64%
rename from convex_hull.scad
rename to hull.scad
index a62813ef..926f74b1 100644
--- a/convex_hull.scad
+++ b/hull.scad
@@ -1,68 +1,92 @@
//////////////////////////////////////////////////////////////////////
-// LibFile: convex_hull.scad
+// LibFile: hull.scad
// Functions to create 2D and 3D convex hulls.
// To use, add the following line to the beginning of your file:
// ```
// include <BOSL2/std.scad>
-// include <BOSL2/convex_hull.scad>
+// include <BOSL2/hull.scad>
// ```
-// Derived from Linde's Hull:
+// Derived from Oskar Linde's Hull:
// - https://github.com/openscad/scad-utils
//////////////////////////////////////////////////////////////////////
-// Section: Convex Hulls
+// Section: 2D Convex Hulls
-// Function: convex_hull()
+
+// Module: hull2d_points()
// Usage:
-// convex_hull(points)
+// hull2d_points(points);
// Description:
-// When given a list of 3D points, returns a list of faces for
-// the minimal convex hull polyhedron of those points. Each face
-// is a list of indexes into `points`.
-// When given a list of 2D points, or 3D points that are all
-// coplanar, returns a list of indices into `points` for the path
-// that forms the minimal convex hull polygon of those points.
-// Arguments:
-// points = The list of points to find the minimal convex hull of.
-function convex_hull(points) =
- !(len(points) > 0) ? [] :
- len(points[0]) == 2 ? convex_hull2d(points) :
- len(points[0]) == 3 ? convex_hull3d(points) : [];
+// Takes a list of 2D points and creates a 2D convex polygon that encloses all those points.
+// Example(2D):
+// pts = [[-10,-10], [0,10], [10,10], [12,-10]];
+// hull2d_points(pts);
+module hull2d_points(points) {
+ polygon(points=points, paths=[hull2d_path(points)]);
+}
-
-// Function: convex_hull2d()
+// Module: hull2d_points_fast()
// Usage:
-// convex_hull2d(points)
+// hull2d_points_fast(points);
+// Description:
+// Takes a list of 2D points and creates a 2D convex polygon that encloses all
+// those points, using a faster method that may emit warning messages.
+// Example(2D):
+// pts = [[-10,-10], [0,10], [10,10], [12,-10]];
+// hull2d_points_fast(pts);
+module hull2d_points_fast(points) {
+ hull() polygon(points);
+}
+
+
+// Function: hull2d_path()
+// Usage:
+// hull2d_path(points)
// Description:
// Takes a list of arbitrary 2D points, and finds the minimal convex
// hull polygon to enclose them. Returns a path as a list of indices
// into `points`.
-function convex_hull2d(points) =
+// Example(2D):
+// pts = [[-10,-10], [0,10], [10,10], [12,-10]];
+// path = hull2d_path(pts);
+// place_copies(pts) color("red") sphere(1);
+// polygon(points=pts, paths=[path]);
+function hull2d_path(points) =
(len(points) < 3)? [] : let(
a=0, b=1,
c = _find_first_noncollinear([a,b], points, 2)
- ) (c == len(points))? _convex_hull_collinear(points) : let(
+ ) (c == len(points))? _hull2d_collinear(points) : let(
remaining = [ for (i = [2:len(points)-1]) if (i != c) i ],
ccw = triangle_area2d(points[a], points[b], points[c]) > 0,
polygon = ccw? [a,b,c] : [a,c,b]
- ) _convex_hull_iterative_2d(points, polygon, remaining);
+ ) _hull2d_iterative(points, polygon, remaining);
// Adds the remaining points one by one to the convex hull
-function _convex_hull_iterative_2d(points, polygon, remaining, _i=0) =
+function _hull2d_iterative(points, polygon, remaining, _i=0) =
(_i >= len(remaining))? polygon : let (
// pick a point
i = remaining[_i],
// find the segments that are in conflict with the point (point not inside)
conflicts = _find_conflicting_segments(points, polygon, points[i])
// no conflicts, skip point and move on
- ) (len(conflicts) == 0)? _convex_hull_iterative_2d(points, polygon, remaining, _i+1) : let(
+ ) (len(conflicts) == 0)? _hull2d_iterative(points, polygon, remaining, _i+1) : let(
// find the first conflicting segment and the first not conflicting
// conflict will be sorted, if not wrapping around, do it the easy way
polygon = _remove_conflicts_and_insert_point(polygon, conflicts, i)
- ) _convex_hull_iterative_2d(points, polygon, remaining, _i+1);
+ ) _hull2d_iterative(points, polygon, remaining, _i+1);
+
+
+function _hull2d_collinear(points) =
+ let(
+ a = points[0],
+ n = points[1] - a,
+ points1d = [ for(p = points) (p-a)*n ],
+ min_i = min_index(points1d),
+ max_i = max_index(points1d)
+ ) [min_i, max_i];
function _find_first_noncollinear(line, points, i) =
@@ -94,16 +118,57 @@ function _remove_conflicts_and_insert_point(polygon, conflicts, point) =
-// Function: convex_hull3d()
+// Section: 3D Convex Hulls
+
+
+// Module: hull3d_points()
// Usage:
-// convex_hull3d(points)
+// hull3d_points(points);
+// Description:
+// Takes a list of 3D points and creates a 3D convex polyhedron that encloses all those points.
+// Example(3D):
+// pts = [[-20,-20,0], [20,-20,0], [0,20,5], [0,0,20]];
+// hull3d_points(pts);
+module hull3d_points(points) {
+ indices = hull3d_faces(points);
+ if (is_vector(indices)) {
+ polyhedron(points=points, faces=[indices]);
+ } else {
+ polyhedron(points=points, faces=indices);
+ }
+}
+
+
+// Module: hull3d_points_fast()
+// Usage:
+// hull3d_points_fast(points);
+// Description:
+// Takes a list of 3D points and creates a 3D convex polyhedron that encloses all
+// those points, using a faster method that may emit warning messages.
+// Example(3D):
+// pts = [[-20,-20,0], [20,-20,0], [0,20,5], [0,0,20]];
+// hull3d_points_fast(pts);
+module hull3d_points_fast(points) {
+ faces = [for (i=[0:len(points)-3]) let(c=_find_first_noncollinear([i,i+1], points, 2)) [i, i+1, c]];
+ hull() polyhedron(points=points, faces=faces);
+}
+
+
+// Function: hull3d_faces()
+// Usage:
+// hull3d_faces(points)
// Description:
// Takes a list of arbitrary 3D points, and finds the minimal convex
// hull polyhedron to enclose them. Returns a list of faces, where
// each face is a list of indexes into the given `points` list.
// If all points passed to it are coplanar, then the return is the
// list of indices of points forming the minimal convex hull polygon.
-function convex_hull3d(points) =
+// Example(3D):
+// pts = [[-20,-20,0], [20,-20,0], [0,20,5], [0,0,20]];
+// faces = hull3d_faces(pts);
+// place_copies(pts) color("red") sphere(1);
+// %polyhedron(points=pts, faces=faces);
+function hull3d_faces(points) =
(len(points) < 3)? list_range(len(points)) : let (
// start with a single triangle
a=0, b=1, c=2,
@@ -111,7 +176,7 @@ function convex_hull3d(points) =
d = _find_first_noncoplanar(plane, points, 3)
) (d == len(points))? /* all coplanar*/ let (
pts2d = [ for (p = points) xyz_to_planar(p, points[a], points[b], points[c]) ],
- hull2d = convex_hull2d(pts2d)
+ hull2d = hull2d_path(pts2d)
) hull2d : let(
remaining = [for (i = [3:len(points)-1]) if (i != d) i],
// Build an initial tetrahedron.
@@ -128,11 +193,11 @@ function convex_hull3d(points) =
],
// calculate the plane equations
planes = [ for (t = triangles) plane3pt_indexed(points, t[0], t[1], t[2]) ]
- ) _convex_hull_iterative(points, triangles, planes, remaining);
+ ) _hull3d_iterative(points, triangles, planes, remaining);
// Adds the remaining points one by one to the convex hull
-function _convex_hull_iterative(points, triangles, planes, remaining, _i=0) =
+function _hull3d_iterative(points, triangles, planes, remaining, _i=0) =
_i >= len(remaining) ? triangles :
let (
// pick a point
@@ -151,7 +216,7 @@ function _convex_hull_iterative(points, triangles, planes, remaining, _i=0) =
new_triangles = [ for (h = horizon) concat(h,i) ],
// calculate the corresponding plane equations
new_planes = [ for (t = new_triangles) plane3pt_indexed(points, t[0], t[1], t[2]) ]
- ) _convex_hull_iterative(
+ ) _hull3d_iterative(
points,
// remove the conflicting triangles and add the new ones
concat(list_remove(triangles, conflicts), new_triangles),
@@ -161,17 +226,6 @@ function _convex_hull_iterative(points, triangles, planes, remaining, _i=0) =
);
-function _convex_hull_collinear(points) =
- let(
- a = points[0],
- n = points[1] - a,
- points1d = [ for(p = points) (p-a)*n ],
- min_i = min_index(points1d),
- max_i = max_index(points1d)
- ) [min_i, max_i];
-
-
-
function _remove_internal_edges(halfedges) = [
for (h = halfedges)
if (!in_list(reverse(h), halfedges))