Added triangulation support code.

math.scad

@@ -71,6 +71,30 @@ function cdr(list) = len(list)>1?[for (i=[1:len(list)-1]) list[i]]:[];
 function reverse(list) = [ for (i = [len(list)-1 : -1 : 0]) list[i] ];
 
 
+// Returns a slice of the given array, wrapping around past the beginning, if end < start
+function wrap_range(list, start, end) =
+	(end<start)?
+		concat(
+			[for (i=[start:len(list)-1]) list[i]],
+			[for (i=[0:end]) list[i]]
+		)
+	:
+		[for (i=[start:end]) list[i]]
+;
+
+
+// Takes an array of arrays and flattens it by one level.
+// flatten([[1,2,3], [4,5,[6,7,8]]]) returns [1,2,3,4,5,[6,7,8]]
+function flatten(l) = [ for (a = l) for (b = a) b ];
+
+
+// Returns the sum of all entries in the given array.
+// If passed an array of vectors, returns a vector of sums of each part.
+// sum([1,2,3]) returns 6.
+// sum([[1,2,3], [3,4,5], [5,6,7]]) returns [9, 12, 15]
+function sum(v, i=0) = i<len(v)-1 ? v[i] + sum(v, i+1) : v[i];
+
+
 // Returns the sum of the square of each element of a vector.
 function sum_of_squares(v,n=0) = (n>=len(v))? 0 : ((v[n]*v[n]) + sum_of_squares(v,n+1));
 

paths.scad

@@ -33,6 +33,7 @@ OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
 include <math.scad>
 include <quaternions.scad>
+include <triangulation.scad>
 
 
 // Creates a 2D polygon circle, modulated by one or more superimposed
@@ -154,7 +155,8 @@ module extrude_2dpath_along_spiral(polyline, h, r, twist=360) {
 		[[for (b = [pline_count-1:-1:0]) b+(steps)*pline_count]]
 	);
 
-	polyhedron(points=poly_points, faces=poly_faces, convexity=10);
+	tri_faces = triangulate_faces(poly_points, poly_faces);
+	polyhedron(points=poly_points, faces=tri_faces, convexity=10);
 }
 
 
@@ -215,7 +217,8 @@ module extrude_2dpath_along_3dpath(polyline, path, convexity=10) {
 		[[for (b = [pline_count-1:-1:0]) b+(path_count-1)*pline_count]]
 	);
 
-	polyhedron(points=poly_points, faces=poly_faces, convexity=convexity);
+	tri_faces = triangulate_faces(poly_points, poly_faces);
+	polyhedron(points=poly_points, faces=tri_faces, convexity=convexity);
 }
 
 

transforms.scad

@@ -448,7 +448,7 @@ module xspread(spacing=1,n=2) for (i=[0:n-1]) right((i-(n-1)/2.0)*spacing) child
 //   yspread(25,3) sphere(1)
 //   yspread(25, n=3) sphere(1)
 //   yspread(spacing=20, n=4) sphere(1)
-module yspread(spacing=1,n=2) for (i=[0:n-1]) back((i-(n-1)/2.0)*spacing) children();
+module yspread(spacing=1,n=2) for (i=[0:n-1]) back((i-(n-1)/2)*spacing) children();
 
 
 // Spreads out n copies of the given children along the Z axis.

triangulation.scad

@@ -0,0 +1,134 @@
+use <math.scad>
+
+
+function winding_dir(points, face) =
+	let(count=len(face))
+	sum(
+		[
+			for(i=[0:count-1]) cross(
+				points[face[(i+1)%count]]-points[face[0]],
+				points[face[(i+2)%count]]-points[face[(i+1)%count]]
+			)
+		],
+		0
+	)
+;
+
+
+function find_convex_vertex(dir, points, face, i=0) =
+	let(count=len(face),
+		p0=points[face[i]],
+		p1=points[face[(i+1)%count]],
+		p2=points[face[(i+2)%count]]
+	)
+	(len(face)>i)?
+		(cross(p1-p0, p2-p1)*dir>0)? (i+1)%count : find_convex_vertex(dir, points, face, i+1)
+	: //This should never happen since there is at least 1 convex vertex.
+		undef
+;
+
+
+function point_in_ear(points, face, tests, i=0) =
+	(i<len(face)-1)?
+		let(
+			prev=point_in_ear(points, face, tests, i+1),
+			test=check_point_in_ear(points[face[i]], tests)
+		)
+		(test>prev[0])? [test, i] : prev
+	:
+		[check_point_in_ear(points[face[i]], tests), i]
+;
+
+
+function check_point_in_ear(point, tests) =
+	let(
+		result=[
+			(point*tests[0][0])-tests[0][1],
+			(point*tests[1][0])-tests[1][1],
+			(point*tests[2][0])-tests[2][1]
+		]
+	)
+	(result[0]>0 && result[1]>0 && result[2]>0)? result[0] : -1
+;
+
+
+function normalize_vertex_perimeter(v) =
+	(len(v) < 2)? v :
+		(v[len(v)-1] != v[0])? v :
+			[for (i=[0:len(v)-2]) v[i]]
+;
+
+
+function triangulate_faces(points, faces) =
+	[
+		for (i=[0 : len(faces)-1])
+			let(facet = normalize_vertex_perimeter(faces[i]))
+			for (face = triangulate_face(points, facet))
+				if (face[0]!=face[1] && face[1]!=face[2] && face[2]!=face[0]) face
+	]
+;
+
+
+function is_last_off_a_line(points, facelist, vertex) =
+	let(
+		face=wrap_range(facelist, vertex+1, vertex-1),
+		count=len(face),
+		dir=winding_dir(points, face)
+	)
+	0==sum(
+		[
+			for(i=[0:count-1]) norm(
+				cross(
+					points[face[(i+1)%count]]-points[face[0]],
+					points[face[(i+2)%count]]-points[face[(i+1)%count]]
+				)
+			)
+		]
+	)
+;
+
+
+function triangulate_face(points, face) =
+	let(count=len(face))
+	(3==count)?
+		[face]
+	:
+		let(
+			dir=winding_dir(points, face),
+			cv=find_convex_vertex(dir, points, face),
+			pv=(count+cv-1)%count,
+			nv=(cv+1)%count,
+			p0=points[face[pv]],
+			p1=points[face[cv]],
+			p2=points[face[nv]],
+			tests=[
+				[cross(dir, p0-p2), cross(dir, p0-p2)*p0],
+				[cross(dir, p1-p0), cross(dir, p1-p0)*p1],
+				[cross(dir, p2-p1), cross(dir, p2-p1)*p2]
+			],
+			ear_test=point_in_ear(points, face, tests),
+			clipable_ear=(ear_test[0]<0),
+			diagonal_point=ear_test[1]
+		)
+		(clipable_ear)? // There is no point inside the ear.
+			is_last_off_a_line(points, face, cv)?
+				// In the point&line degeneracy clip to somewhere in the middle of the line.
+				flatten([
+					triangulate_face(points, wrap_range(face, cv, (cv+2)%count)),
+					triangulate_face(points, wrap_range(face, (cv+2)%count, cv))
+				])
+			:
+				// Otherwise the ear is safe to clip.
+				flatten([
+					[wrap_range(face, pv, nv)],
+					triangulate_face(points, wrap_range(face, nv, pv))
+				])
+		: // If there is a point inside the ear, make a diagonal and clip along that.
+			flatten([
+				triangulate_face(points, wrap_range(face, cv, diagonal_point)),
+				triangulate_face(points, wrap_range(face, diagonal_point, cv))
+			])
+;
+
+
+// vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap