Triply-nested spiral! And more notes.

README.md

@@ -1,8 +1,21 @@
-To-do items, wanted features, bugs:
+# To-do items, wanted features, bugs:
 
+## Cool
 - Examples of branching. This will probably need recursion via functions
-  (or an explicit stack some other way).
-- I need to figure out winding order.  It is consistent through seemingly
+  (or an explicit stack some other way).  If I simply
+  split a boundary into sub-boundaries per the rules I already
+  have in my notes, then this still lets me split any way I want
+  to without having to worry about joining N boundaries instead
+  of 2, doesn't it?
+- More complicated: Examples of *merging*. I'm not sure on the theory
+  behind this.
+  
+## Annoying
+- I really need to standardize some of the behavior of fundamental
+  operations (with regard to things like sizes they generate). This
+  is behavior that, if it changes, will change a lot of things that I'm
+  trying to keep consistent so that my examples still work.
+- Winding order.  It is consistent through seemingly
   everything, except for reflection and close_boundary_simple.
   (When there are two parallel boundaries joined with something like
   join_boundary_simple, traversing these boundaries in their actual order
@@ -10,17 +23,11 @@ To-do items, wanted features, bugs:
   opposite winding order on each. Imagine a transparent clock: seen from the
   front, it moves clockwise, but seen from the back, it moves
   counter-clockwise.)
-- Make it easier to build up meshes a bit at a time?
-- Factor out recursive/iterative stuff to be a bit more concise
-- Embed this in Blender?
 - File that bug that I've seen in trimesh/three.js
   (see trimesh_fail.ipynb)
-  
-- Parametrize gen_twisted_boundary over boundaries and
-do my nested spiral
 - Why do I get the weird zig-zag pattern on the triangles,
-despite larger numbers of them? Is it something in how I
-twist the frames?
+  despite larger numbers of them? Is it something in how I
+  twist the frames?
   - How can I compute the *torsion* on a quad? I think it
     comes down to this: torsion applied across the quad I'm
     triangulating leading to neither diagonal being a
@@ -29,26 +36,33 @@ twist the frames?
     quad to 4 triangles by adding the centroid) could be good
     too.
   - Facets/edges are just oriented the wrong way...
-- I need an actual example of branching/forking. If I simply
-split a boundary into sub-boundaries per the rules I already
-have in my notes, then this still lets me split any way I want
-to without having to worry about joining N boundaries instead
-of 2, doesn't it?
-
-Other notes:
-- Picking at random the diagonal on the quad to triangulate with
+  - Picking at random the diagonal on the quad to triangulate with
     does seem to turn 'error' just to noise, and in its own way this
     is preferable.
 
-# Abstractions
+## Abstractions
 
 - Encode the notions of "generator which transforms an
-existing list of boundaries", "generator which transforms
-another generator"
+  existing list of boundaries", "generator which transforms
+  another generator"
 - This has a lot of functions parametrized over a lot
-of functions.  Need to work with this somehow.  (e.g. should
-it subdivide this boundary? should it merge opening/closing
-boundaries?)
+  of functions.  Need to work with this somehow.  (e.g. should
+  it subdivide this boundary? should it merge opening/closing
+  boundaries?)
 - Work directly with lists of boundaries. The only thing
-I ever do with them is apply transforms to all of them, or
-join adjacent ones with corresponding elements.
+  I ever do with them is apply transforms to all of them, or
+  join adjacent ones with corresponding elements.
+
+- Some generators produce boundaries that can be directly merged
+  and produce sensible geometry.  Some generators produce
+  boundaries that are only usable when they are further
+  transformed (and would produce degenerate geometry).  What sort
+  of nomenclature captures this?
+
+- How can I capture the idea of a group of parameters which, if
+  they are all scaled in the correct way (some linearly, others
+  inversely perhaps), generated geometry that is more or less
+  identical except that it is higher-resolution?
+## ????
+- Embed this in Blender?
+  

examples.py

@@ -1,7 +1,9 @@
 #!/usr/bin/env python3
 
-import stl.mesh
+import itertools
+
 import numpy
+import stl.mesh
 import trimesh
 
 import meshutil
@@ -171,7 +173,9 @@ def twist_from_gen():
     b = meshutil.subdivide_boundary(b)
     b = meshutil.subdivide_boundary(b)
     bs = [b]
-    gen = meshgen.gen_inc_y(meshgen.gen_twisted_boundary(bs))
+    # since it needs a generator:
+    gen_inner = itertools.repeat(bs)
+    gen = meshgen.gen_inc_y(meshgen.gen_twisted_boundary(gen_inner))
     mesh = meshgen.gen2mesh(gen, 100, True)
     return mesh
 
@@ -189,11 +193,54 @@ def twisty_torus(frames = 200, turns = 4, count = 4, rad = 4):
     b = meshutil.subdivide_boundary(b)
     b = meshutil.subdivide_boundary(b)
     bs = [b]
+    # since it needs a generator:
+    gen_inner = itertools.repeat(bs)
     # In order to make this line up properly:
     angle = numpy.pi * 2 * turns / frames
-    gen = meshgen.gen_torus_xy(meshgen.gen_twisted_boundary(bs=bs, count=count, ang=angle), rad=rad, frames=frames)
+    gen = meshgen.gen_torus_xy(meshgen.gen_twisted_boundary(gen=gen_inner, count=count, ang=angle), rad=rad, frames=frames)
     return meshgen.gen2mesh(gen, 0, flip_order=True, loop=True)
 
+def spiral_nested_2():
+    # Slow.
+    b = numpy.array([
+        [0, 0, 0],
+        [1, 0, 0],
+        [1, 0, 1],
+        [0, 0, 1],
+    ], dtype=numpy.float64) - [0.5, 0, 0.5]
+    b *= 0.3
+    b = meshutil.subdivide_boundary(b)
+    b = meshutil.subdivide_boundary(b)
+    bs = [b]
+    # since it needs a generator:
+    gen1 = itertools.repeat(bs)
+    gen2 = meshgen.gen_twisted_boundary(gen1, ang=-0.2, dx0=0.5)
+    gen3 = meshgen.gen_twisted_boundary(gen2, ang=0.05, dx0=1)
+    gen = meshgen.gen_inc_y(gen3, dy=0.1)
+    return meshgen.gen2mesh(
+        gen, count=250, flip_order=True, close_first=True, close_last=True)
+
+def spiral_nested_3():
+    # Slower.
+    b = numpy.array([
+        [0, 0, 0],
+        [1, 0, 0],
+        [1, 0, 1],
+        [0, 0, 1],
+    ], dtype=numpy.float64) - [0.5, 0, 0.5]
+    b *= 0.3
+    b = meshutil.subdivide_boundary(b)
+    b = meshutil.subdivide_boundary(b)
+    bs = [b]
+    # since it needs a generator:
+    gen1 = itertools.repeat(bs)
+    gen2 = meshgen.gen_twisted_boundary(gen1, ang=-0.2, dx0=0.5)
+    gen3 = meshgen.gen_twisted_boundary(gen2, ang=0.07, dx0=1)
+    gen4 = meshgen.gen_twisted_boundary(gen3, ang=-0.03, dx0=3)
+    gen = meshgen.gen_inc_y(gen4, dy=0.1)
+    return meshgen.gen2mesh(
+        gen, count=500, flip_order=True, close_first=True, close_last=True)
+
 def main():
     fns = {
         ram_horn: "ramhorn.stl",
@@ -202,6 +249,8 @@ def main():
         twist_nonlinear: "twist_nonlinear.stl",
         twist_from_gen: "twist_from_gen.stl",
         twisty_torus: "twisty_torus.stl",
+        spiral_nested_2: "spiral_nested_2.stl",
+        spiral_nested_3: "spiral_nested_3.stl",
     }
     for f in fns:
         fname = fns[f]

meshgen.py

@@ -1,35 +1,34 @@
+import itertools
+
 import meshutil
 import stl.mesh
 import numpy
 import trimesh
 
 # Generate a frame with 'count' boundaries in the XZ plane.
-# Each one rotates by 'ang' as it moves by 'dz'.
+# Each one rotates by 'ang' at each step.
 # dx0 is center-point distance from each to the origin.
 #
-# TODO: This needs to transform an existing generator, not just
-# a boundary!
-def gen_twisted_boundary(bs=None, count=4, dx0=2, dz=0.2, ang=0.1):
-    if bs is None:
+# This doesn't generate usable geometry on its own.
+def gen_twisted_boundary(gen=None, count=4, dx0=2, ang=0.1):
+    if gen is None:
         b = numpy.array([
             [0, 0, 0],
             [1, 0, 0],
             [1, 0, 1],
             [0, 0, 1],
         ], dtype=numpy.float64) - [0.5, 0, 0.5]
-        b = meshutil.subdivide_boundary(b)
-        b = meshutil.subdivide_boundary(b)
-        b = meshutil.subdivide_boundary(b)
-        bs = [b]
+        gen = itertools.repeat([b])
     # Generate 'seed' transformations:
     xfs = [meshutil.Transform().translate(dx0, 0, 0).rotate([0,1,0], numpy.pi * 2 * i / count)
            for i in range(count)]
     # (we'll increment the transforms in xfs as we go)
-    while True:
+    for bs in gen:
         xfs_new = []
+        bs2 = []
         for i, xf in enumerate(xfs):
             # Generate a boundary from running transform:
-            bs2 = [xf.apply_to(b) for b in bs]
+            bs2 += [xf.apply_to(b) for b in bs]
             # Increment transform i:
             xf2 = xf.rotate([0,1,0], ang)
             xfs_new.append(xf2)