Adds sweep and new version of path_sweep to skin.scad, which probably

needs a name change.  Adds apply(), apply_list() and
affine_frame_map() to affine.scad.  Adds derivative calcluation to
math.scad.  Adds path_tangent, path_normal, path_curvature and
path_torsion functions.  Adds path_length_fraction().
Fixed bug in reindex_polygon where it randomly reverses a 3d path (due
to clockwise check that is bogus in 3d) and put a check in
polygon_is_clockwise to trap this case.

affine.scad

@@ -379,4 +379,66 @@ function affine3d_apply(pts, affines) =
 
 
 
+// Function: apply()
+// Usage: apply(transform, points)
+// Description:
+//   Applies the specified transformation matrix to a point list (or single point).  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.  
+// Examples:
+//   transformed = apply(xrot(45), path3d(circle(r=3)));  // Rotates 3d circle data around x axis
+//   transformed = apply(rot(45), circle(r=3));           // Rotates 2d circle data by 45 deg
+//   transformed = apply(rot(45)*right(4)*scale(3), circle(r=3));  // Scales, translates and rotates 2d circle data
+function apply(transform,points) =
+  is_vector(points) ? apply(transform, [points])[0] :
+  let(
+    tdim = len(transform[0])-1,
+    datadim = len(points[0])
+  )
+  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 ? 
+    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));
+
+
+// Function: apply_list()
+// Usage: apply_list(points, transform_list)
+// Description:
+//   Transforms the specified point list (or single point) using a list of transformation matrices.  Transformations on
+//   the list are applied in the order they appear in the list (as in right multiplication of matrices).  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.  All transformations on `transform_list` must have the same dimension: you cannot mix 2d and 3d transformations
+//   even when acting on 2d data.  
+// Examples:
+//   transformed = apply_list(path3d(circle(r=3)),[xrot(45)]);        // Rotates 3d circle data around x axis
+//   transformed = apply_list(circle(r=3), [scale(3), right(4), rot(45)]); // Scales, then translates, and then rotates 2d circle data
+function apply_list(points,transform_list) =
+  is_vector(points) ? apply_list([points],transform_list)[0] :
+  let(
+      tdims = array_dim(transform_list),
+      datadim = len(points[0])
+  )
+  assert(len(tdims)==3 || tdims[1]!=tdims[2], "Invalid transformation list")
+  let( tdim = tdims[1]-1 )
+  tdim==2 && datadim == 2 ? apply(affine2d_chain(transform_list), points) :
+  tdim==3 && datadim == 3 ? apply(affine3d_chain(transform_list), points) :
+  tdim==3 && datadim == 2 ? 
+    let(
+        badlist = [for(i=idx(transform_list)) if (!is_2d_transform(transform_list[i])) i]
+    )
+    assert(badlist==[],str("Transforms with indices ",badlist," are 3d but points are 2d"))
+    apply(affine3d_chain(transform_list), points) :
+  assert(false,str("Unsupported combination: transform with dimension ",tdim,", data of dimension ",datadim));    
+    
+
+// Function: is_2d_transform()
+// Usage: is_2d_transform(t)
+// Description: Checks if the input is a 3d transform that does not act on the z coordinate, except
+//   possibly for a simple scaling of z.  Note that an input which is only a zscale returns false.  
+function is_2d_transform(t) =    // z-parameters are zero, except we allow t[2][2]!=1 so scale() works
+  t[2][0]==0 && t[2][1]==0 && t[2][3]==0 && t[0][2] == 0 && t[1][2]==0 &&  
+  (t[2][2]==1 || !(t[0][0]==1 && t[0][1]==0 && t[1][0]==0 && t[1][1]==1));   // But rule out zscale()
+
+
 // vim: noexpandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap