more error messages for star()

improve speed and flexibility of apply()
fix triangulation bug
add support for single point 2d solutions in polygon_line_intersection

affine.scad

@@ -142,6 +142,9 @@ function affine3d_to_2d(m) =
 //   Applies the specified transformation matrix to a point, pointlist, bezier patch or VNF.
 //   Both inputs can be 2D or 3D, and it is also allowed to supply 3D transformations with 2D
 //   data as long as the the only action on the z coordinate is a simple scaling.
+//   .
+//   If you construct your own matrices you can also use a transform that acts like a projection
+//   with fewer rows to produce lower dimensional output.  
 // Arguments:
 //   transform = The 2D or 3D transformation matrix to apply to the point/points.
 //   points = The point, pointlist, bezier patch, or VNF to apply the transformation to.
@@ -173,14 +176,15 @@ function apply(transform,points) =
       ? /* BezPatch */ [for (x=points) apply(transform,x)] :
     let(
         tdim = len(transform[0])-1,
-        datadim = len(points[0])
+        datadim = len(points[0]),
+        outdim = min(datadim,len(transform)),
+        matrix = [for(i=[0:1:tdim]) [for(j=[0:1:outdim-1]) transform[j][i]]]
     )
-    tdim == 3 && datadim == 3 ? [for(p=points) point3d(transform*concat(p,[1]))] :
-    tdim == 2 && datadim == 2 ? [for(p=points) point2d(transform*concat(p,[1]))] :
-    tdim == 3 && datadim == 2 ?
+    tdim==datadim && (datadim==3 || datadim==2) ? [for(p=points) concat(p,1)] * matrix
+  : tdim == 3 && datadim == 2 ?
         assert(is_2d_transform(transform), str("Transforms is 3d but points are 2d"))
-        [for(p=points) point2d(transform*concat(p,[0,1]))] :
-        assert(false, str("Unsupported combination: transform with dimension ",tdim,", data of dimension ",datadim));
+        [for(p=points) concat(p,[0,1])]*matrix 
+  : assert(false, str("Unsupported combination: transform with dimension ",tdim,", data of dimension ",datadim));
 
 
 // Function: rot_decode()

geometry.scad

@@ -654,11 +654,24 @@ function polygon_line_intersection(poly, line, bounded=false, nonzero=false, eps
             boundedline = [line[0] + (bounded[0]? 0 : -bound) * linevec,
                            line[1] + (bounded[1]? 0 :  bound) * linevec],
             parts = split_path_at_region_crossings(boundedline, [poly], closed=false),
-            inside = [for (part = parts)
-                        if (point_in_polygon(mean(part), poly,nonzero=nonzero,eps=eps)>=0) part
+            inside = [
+                      if(point_in_polygon(parts[0][0], poly, nonzero=nonzero, eps=eps) == 0)
+                         [parts[0][0]],   // Add starting point if it is on the polygon
+                      for(part = parts)
+                         if (point_in_polygon(mean(part), poly, nonzero=nonzero, eps=eps) >=0 )
+                             part
+                         else if(len(part)==2 && point_in_polygon(part[1], poly, nonzero=nonzero, eps=eps) == 0)
+                             [part[1]]   // Add segment end if it is on the polygon
                      ]
         )
-        len(inside)==0? undef : _merge_segments(inside, [inside[0]], eps)
+        (
+            len(inside)==0 ? undef :
+            let(
+                seglist = [for (entry=_merge_segments(inside, [inside[0]], eps))
+                              same_shape(entry,[[0,0]]) ? entry[0]:entry]
+            )
+            len(seglist)==1 && is_vector(seglist[0]) ? seglist[0] : seglist
+        )
     : // 3d case
        let(indices = noncollinear_triple(poly))
        indices==[] ? undef :   // Polygon is collinear
@@ -681,13 +694,14 @@ function polygon_line_intersection(poly, line, bounded=false, nonzero=false, eps
            )
            segments==undef ? undef : [for(seg=segments) lift_plane(plane,seg)];
 
-
-function _merge_segments(insegs,outsegs, eps, i=1) = //let(f=echo(insegs=insegs, outsegs=outsegs,lo=last(outsegs[1]), fi=insegs[i][0]))
+function _merge_segments(insegs,outsegs, eps, i=1) = 
     i==len(insegs) ? outsegs : 
-    approx(last(outsegs)[1], insegs[i][0], eps) ? _merge_segments(insegs, [each list_head(outsegs),[last(outsegs)[0],insegs[i][1]]], eps, i+1)
+    approx(last(last(outsegs)), insegs[i][0], eps) 
+        ? _merge_segments(insegs, [each list_head(outsegs),[last(outsegs)[0],last(insegs[i])]], eps, i+1)
         : _merge_segments(insegs, [each outsegs, insegs[i]], eps, i+1);
 
     
+
 // Function: plane_intersection()
 // Usage:
 //   line = plane_intersection(plane1, plane2)
@@ -1443,10 +1457,10 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
         ) 2*(len(cross)%2)-1;
 
 
-// Function: polygon_triangulation(poly, [ind], [eps])
+// Function: polygon_triangulate(poly, [ind], [eps])
 // Usage:
-//   triangles = polygon_triangulation(poly)
-//   triangles = polygon_triangulation(poly, ind)
+//   triangles = polygon_triangulate(poly)
+//   triangles = polygon_triangulate(poly, ind)
 // Description:
 //   Given a simple polygon in 2D or 3D, triangulates it and returns a list 
 //   of triples indexing into the polygon vertices. When the optional argument `ind` is 
@@ -1467,7 +1481,7 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
 //   eps = A maximum tolerance in geometrical tests. Default: EPSILON
 // Example:
 //   poly = star(id=10, od=15,n=11);
-//   tris =  polygon_triangulation(poly);
+//   tris =  polygon_triangulate(poly);
 //   polygon(poly);
 //   up(1)
 //   color("blue");
@@ -1477,11 +1491,11 @@ function point_in_polygon(point, poly, nonzero=false, eps=EPSILON) =
 //   include<BOSL2/polyhedra.scad>
 //   vnf = regular_polyhedron_info(name="dodecahedron",side=5,info="vnf");
 //   %vnf_polyhedron(vnf);
-//   vnf_tri = [vnf[0], [for(face=vnf[1]) each polygon_triangulation(vnf[0], face) ] ];
+//   vnf_tri = [vnf[0], [for(face=vnf[1]) each polygon_triangulate(vnf[0], face) ] ];
 //   color("blue")
 //   vnf_wireframe(vnf_tri, d=.15);
 
-function polygon_triangulation(poly, ind, eps=EPSILON) =
+function polygon_triangulate(poly, ind, eps=EPSILON) =
     assert(is_path(poly), "Polygon `poly` should be a list of 2d or 3d points")
     assert(is_undef(ind) 
            || (is_vector(ind) && min(ind)>=0 && max(ind)<len(poly) ),

shapes2d.scad

@@ -1563,7 +1563,9 @@ function star(n, r, ir, d, or, od, id, step, realign=false, align_tip, align_pit
     )
     assert(is_def(n), "Must specify number of points, n")
     assert(count==1, "Must specify exactly one of ir, id, step")
-    assert(stepOK, str("Parameter 'step' must be between 2 and ",floor(n/2-1/2)," for ",n," point star"))
+    assert(stepOK,  n==4 ? "Parameter 'step' not allowed for 4 point stars"
+                  : n==5 || n==6 ? str("Parameter 'step' must be 2 for ",n," point stars")
+                  : str("Parameter 'step' must be between 2 and ",floor(n/2-1/2)," for ",n," point stars"))
     let(
         mat = !is_undef(_mat) ? _mat :
             ( realign? rot(-180/n, planar=true) : affine2d_identity() ) * (

vnf.scad

@@ -211,7 +211,7 @@ function vnf_triangulate(vnf) =
     let(
         vnf = is_vnf_list(vnf)? vnf_merge(vnf) : vnf,
         verts = vnf[0],
-        faces = [for (face=vnf[1]) polygon_triangulation(verts, face)]
+        faces = [for (face=vnf[1]) each polygon_triangulate(verts, face)]
     ) [verts, faces]; 
 
 
@@ -546,6 +546,11 @@ function vnf_volume(vnf) =
     ])/6;
 
 
+function vnf_area(vnf) =
+    let(verts=vnf[0])
+    sum([for(face=vnf[1]) polygon_area(select(verts,face))]);
+
+
 // Function: vnf_centroid()
 // Usage:
 //   vol = vnf_centroid(vnf);