Misc notes in README; minor fix in tests

Cargo.toml

@@ -1,5 +1,5 @@
 [package]
-name = "mesh_scratch"
+name = "prosha"
 version = "0.1.0"
 authors = ["Chris Hodapp <hodapp87@gmail.com>"]
 edition = "2018"
@@ -16,3 +16,4 @@ euclid = "0.20.7"
 nalgebra = "0.19.0"
 stl_io = "0.4.2"
 rand = "0.7.3"
+itertools = "0.10.0"

README.md

@@ -1,4 +1,16 @@
-# This needs a title
+# Prosha
+
+Experiments in procedural meshes in Rust
+
+More detailed docs and examples forthcoming.
+
+Due to some issues explained a little bit below and a little bit in
+other blog posts, I'm now treating this as maintenance-only and not as
+an active project.
+
+(TODO: Link to these posts)
+
+## General Notes & History
 
 This particular code base was started around 2019 December
 as an attempt to make meshes in a more "generative" style,
@@ -61,7 +73,7 @@ A lot of what I wrote here ended up just being a buggy, half-assed
 interpreter for a buggy, half-assed EDSL/minilanguage.
 (Greenspun's Tenth Rule of Programming, anyone?)
 
-On top of this, my implementation is pretty slow when it is
+On top of this, my implementation was pretty slow when it was
 using a large number of rules each producing small geometry
 (which is almost literally the only way it *can* be used
 if you want to produce a fairly complex mesh). I did some
@@ -69,7 +81,7 @@ profiling some months ago that showed I was spending the
 vast majority of my time in `extend()` and `clone()` for
 `Vec` - and so I could probably see some huge performance
 gains if I could simply pre-allocate vectors and share geometry
-more. Also, I'm pretty sure this code does some very task-parallel
+more. Also, I'm pretty sure this code did some very task-parallel
 elements (e.g. anytime a rule branches), and multithreading should
 be able to exploit this if I care.
 
@@ -86,14 +98,23 @@ branch, thus named because I needed to get rid of my buggy
 implementation of half of Common Lisp. It paid off quite quickly and
 also was vastly faster at generating meshes. 
 
+## What does the name mean?
+
+Nothing, but it's better than its previous name of
+"mesh_scratch". I asked for name suggestions, and someone came up
+with this one.
+
 ## Highest priority:
 
-- Begin converting older examples.
-- Trash all the dead code.
+- Work on abstraction/composition.  Particularly: factor out
+  patterns I use, and be able to *compose* procedural meshes
+  somehow - e.g. the 'context' object I discussed. 
 - Docs on modules
+- Make some examples that are non-deterministic!
 - swept-isocontour stuff from
   `/mnt/dev/graphics_misc/isosurfaces_2018_2019/spiral*.py`.  This
   will probably require that I figure out parametric curves
+  (is this stuff still possible?)
 - Make an example that is more discrete-automata, less
   approximation-of-space-curve.
 
@@ -119,6 +140,7 @@ also was vastly faster at generating meshes.
 - [Geometry and Algorithms for Computer Aided Design (Hartmann)](https://www2.mathematik.tu-darmstadt.de/~ehartmann/cdgen0104.pdf)
 - https://en.wikipedia.org/wiki/Surface_triangulation
 - https://www.cs.cmu.edu/~quake/triangle.html
+- OpenSubdiv!
 
 ## Reflections & Quick Notes
 
@@ -130,3 +152,34 @@ also was vastly faster at generating meshes.
   the current local space. 
 - Don't reinvent subdivision surfaces.
 - Don't reinvent Lisp when you wanted a Lisp!
+
+## Examples
+
+### Barbs
+
+See `examples::Barbs` & "barbs" test in `lib.rs`.
+
+![Barbs](./images/barbs_preview.png)
+
+### Tree Thing
+
+See `examples::TreeThing`.  First one is "tree_thing" test in `lib.rs`:
+
+![tree_thing](./images/tree_thing_preview.jpg)
+
+Second is "tree_thing2" (this was from a larger Blender render):
+
+![tree_thing2](./images/rust_tree_thing_03_smaller.jpg)
+
+### Sierpinski
+
+See `examples::Sierpinski` & "sierpinski" test in `lib.rs`.
+This looks cooler with some randomness added and 3D printed.
+
+![sierpinski](./images/sierpinski_preview.png)
+
+### Triple Nested Spiral
+
+See `examples::NestedSpiral` & "nested_spiral" test in `lib.rs`.
+
+![nested_spiral](./images/nested_spiral.jpg)

src/dcel.rs

@@ -1,752 +0,0 @@
-use std::fmt;
-
-use crate::mesh::{Mesh};
-use crate::xform::{Vertex};
-
-/// Doubly-connected edge list mesh (or a half-edge mesh),
-/// parametrized over some vertex type.
-#[derive(Clone, Debug)]
-pub struct DCELMesh<V: Copy> {
-    pub verts: Vec<DCELVertex<V>>,
-    pub faces: Vec<DCELFace>,
-    pub halfedges: Vec<DCELHalfEdge>,
-
-    pub num_verts: usize,
-    pub num_faces: usize,
-    pub num_halfedges: usize,
-}
-
-/// A vertex of a mesh, combined with an arbitrary half-edge that has
-/// this vertex as its origin.  This is always relative to some parent
-/// Mesh<V>.
-#[derive(Clone, Debug)]
-pub struct DCELVertex<V> {
-    /// The vertex itself.
-    pub v: V,
-    /// A half-edge (given as an index into 'halfedges');
-    /// arbitrary, but `mesh.halfedges[halfedge] = v` must be true
-    pub halfedge: usize,
-}
-
-/// A face, given as a half-edge that lies on its boundary (and must
-/// traverse it counter-clockwise). This is always relative to some
-/// parent Mesh<V>, as in Vertex.
-#[derive(Clone, Debug)]
-pub struct DCELFace {
-    /// A boundary half-edge of this face (given as an index into
-    /// 'halfedges').
-    pub halfedge: usize,
-}
-
-/// A half-edge, given in terms of its origin vertex, the face that the
-/// half-edge lies on the boundary of, its optional "twin" half-edge that
-/// lies on an adjacent face, and previous and next half-edges (to
-/// traverse the boundaries of the face). This is always relative to
-/// some parent Mesh<V>, as in Vertex and Face.
-#[derive(Clone, Debug)]
-pub struct DCELHalfEdge {
-    /// Origin vertex (given as an index into 'verts')
-    pub vert: usize,
-    /// Face this half-edge lies on the boundary of (given as an index
-    /// into 'faces')
-    pub face: usize,
-    /// If false, ignore twin_halfedge.  (If this is true, then it must
-    /// also be true for the twin.)
-    pub has_twin: bool,
-    /// The twin half-edge (given as an index into 'halfedges').
-    /// The twin of the twin must point back to this HalfEdge.
-    pub twin_halfedge: usize,
-    /// The next half-edge on the boundary (given as an index into
-    /// 'halfedges').  'prev_halfedge' of this half-edge must point
-    /// back to this same HalfEdge.  Repeatedly following 'next_halfedge'
-    /// must also lead back to this same HalfEdge.
-    pub next_halfedge: usize,
-    /// The previous half-edge on the boundary (given as an index into
-    /// 'halfedges'). 'next_halfedge' of this half-edge must point
-    /// back to this HalfEdge.  Repeatedly following 'prev_halfedge'
-    /// must also lead back to this same HalfEdge.
-    pub prev_halfedge: usize,
-}
-
-#[derive(Debug)]
-pub enum VertSpec<V> {
-    New(V),
-    Idx(usize),
-}
-
-impl<V: Copy + std::fmt::Debug> fmt::Display for DCELMesh<V> {
-    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
-
-        let v_strs: Vec<String> = self.verts.iter().enumerate().map(|(i,v)| {
-            format!("V{}=e{} {:?}", i, v.halfedge, v.v)
-        }).collect();
-        let v_str = v_strs.join(",");
-
-        let f_strs: Vec<String> = self.faces.iter().enumerate().map(|(i,f)| {
-            format!("F{}=e{}", i, f.halfedge)
-        }).collect();
-        let f_str = f_strs.join(", ");
-
-        let e_strs: Vec<String> = self.halfedges.iter().enumerate().map(|(i,h)| {
-            let twin = if h.has_twin {
-                format!(" tw{}", h.twin_halfedge)
-            } else {
-                String::from("")
-            };
-            format!("E{}=v{} f{}{} n{} p{}", i, h.vert, h.face, twin, h.next_halfedge, h.prev_halfedge)
-        }).collect();
-        let e_str = e_strs.join(", ");
-
-        write!(f, "DCELMesh({} verts, {}; {} faces, {}; {} halfedges, {})",
-               self.num_verts, v_str,
-               self.num_faces, f_str,
-               self.num_halfedges, e_str)
-    }
-}
-
-impl<V: Copy + std::fmt::Debug> DCELMesh<V> {
-
-    pub fn new() -> DCELMesh<V> {
-        DCELMesh {
-            verts: vec![],
-            faces: vec![],
-            halfedges: vec![],
-            num_verts: 0,
-            num_faces: 0,
-            num_halfedges: 0,
-        }
-    }
-
-    pub fn print(&self) {
-
-        println!("DCELMesh has {} verts, {} faces, {} halfedges:",
-               self.num_verts,
-               self.num_faces,
-               self.num_halfedges);
-
-        for (i,v) in self.verts.iter().enumerate() {
-            println!("Vert {}: halfedge {}, {:?}", i, v.halfedge, v.v);
-        }
-
-        for (i,f) in self.faces.iter().enumerate() {
-            println!("Face {}: halfedge {} (halfedges {:?}, verts {:?})",
-                     i, f.halfedge, self.face_to_halfedges(i), self.face_to_verts(i));
-        }
-
-        for (i,h) in self.halfedges.iter().enumerate() {
-            let twin = if h.has_twin {                format!(", twin half-edge {}", h.twin_halfedge)
-            } else {
-                format!(", no twin")
-            };
-            let v1 = self.verts[h.vert].v;
-            let v2 = self.verts[self.halfedges[h.next_halfedge].vert].v;
-            println!("Halfedge {}: vert {} (to {}), face {}, prev: {}, next: {}{}, ({:?} to {:?})",
-                     i, h.vert, self.halfedges[h.next_halfedge].vert, h.face,
-                     h.prev_halfedge, h.next_halfedge, twin,
-                     v1, v2);
-        }
-    }
-
-    /// Runs various checks on the mesh. This will return true if the mesh
-    /// looks okay, and otherwise false. It will print messages as it
-    /// runs.
-    pub fn check(&self) -> bool {
-        let mut pass = true;
-
-        if self.num_halfedges != self.halfedges.len() {
-            pass = false;
-            println!("self.num_halfedges={} != self.halfedges.len()={}",
-                     self.num_halfedges, self.halfedges.len());
-        } else {
-            println!("self.num_halfedges matches self.halfedges.len()");
-        }
-
-        if self.num_faces != self.faces.len() {
-            pass = false;
-            println!("self.faces={} != self.faces.len()={}",
-                     self.num_faces, self.faces.len());
-        } else {
-            println!("self.num_faces matches self.faces.len()");
-        }
-
-        if self.num_verts != self.verts.len() {
-            pass = false;
-            println!("self.verts={} != self.verts.len()={}",
-                     self.num_verts, self.verts.len());
-        } else {
-            println!("self.num_verts matches self.verts.len()");
-        }
-
-        for (i,v) in self.verts.iter().enumerate() {
-            if v.halfedge >= self.halfedges.len() {
-                println!("Vertex {}: halfedge index {} out of range",
-                    i, v.halfedge);
-                pass = false;
-            }
-            if self.halfedges[v.halfedge].vert != i {
-                println!("Vertex {} names halfedge {}, which has a different origin vertex ({})",
-                    i, v.halfedge, self.halfedges[v.halfedge].vert);
-            }
-        }
-
-        for (i,edge) in self.halfedges.iter().enumerate() {
-            if edge.vert >= self.verts.len() {
-                println!("Halfedge {}: vertex index {} out of range", i, edge.vert);
-                pass = false;
-            }
-            if edge.has_twin {
-                let twin = &self.halfedges[edge.twin_halfedge];
-                if !twin.has_twin {
-                    println!("Halfedge {}: twin {} says it has no twin",
-                        i, edge.twin_halfedge);
-                    pass = false;
-                } else if i != twin.twin_halfedge {
-                    println!("Halfedge {} has twin {}, but reverse isn't true",
-                             i, edge.twin_halfedge);
-                    pass = false;
-                } else if edge.vert != self.halfedges[twin.next_halfedge].vert {
-                    println!("Halfedge {} starts at vertex {} but twin {} ends at vertex {}",
-                             i, edge.vert, edge.twin_halfedge, self.halfedges[twin.next_halfedge].vert);
-                    pass = false;
-                }
-            }
-            let p = edge.prev_halfedge;
-            if p >= self.halfedges.len() {
-                println!("Halfedge {}: previous halfedge index {} out of range",
-                    i, p);
-                pass = false;
-            }
-            let n = edge.next_halfedge;
-            if p >= self.halfedges.len() {
-                println!("Halfedge {}: next halfedge index {} out of range",
-                         i, n);
-                pass = false;
-            }
-            let pn = self.halfedges[p].next_halfedge;
-            if pn != i {
-                println!("Halfedge {}: previous halfedge {} has next halfedge of {}, not {}",
-                    i, p, pn, i);
-                pass = false;
-            }
-            let np = self.halfedges[n].prev_halfedge;
-            if np != i {
-                println!("Halfedge {}: next halfedge {} has previous halfedge of {}, not {}",
-                         i, n, np, i);
-                pass = false;
-            }
-            // TODO: Check that following prev always leads back to start
-            // likewise following next
-        }
-
-        for (i,face) in self.faces.iter().enumerate() {
-            if face.halfedge >= self.halfedges.len() {
-                println!("Face {}: halfedge index {} out of range",
-                         i, face.halfedge);
-                pass = false;
-            }
-            let face2 = self.halfedges[face.halfedge].face;
-            if i != face2 {
-                println!("Face {} gives boundary halfedge {}, which gives different face ({})",
-                    i, face.halfedge, face2);
-                pass = false;
-            }
-
-            // TODO: Check that face never visits same vertex twice?
-            // This might belong in halfedge checking
-        }
-
-        if pass {
-            println!("Mesh OK")
-        } else {
-            println!("Mesh has errors!")
-        }
-
-        pass
-    }
-
-    pub fn face_to_halfedges(&self, face_idx: usize) -> Vec<usize> {
-        let mut edges: Vec<usize> = vec![];
-        let start_idx = self.faces[face_idx].halfedge;
-        edges.push(start_idx);
-
-        let mut idx = self.halfedges[start_idx].next_halfedge;
-        while start_idx != idx {
-            edges.push(idx);
-            idx = self.halfedges[idx].next_halfedge;
-        }
-        return edges;
-    }
-
-    pub fn face_to_verts(&self, face_idx: usize) -> Vec<usize> {
-        self.face_to_halfedges(face_idx).iter().map(|e| {
-            self.halfedges[*e].vert
-        }).collect()
-    }
-
-    /// Adds a face that shares no edges with anything else  in the mesh.
-    /// Returns (face index, half-edge indices); half-edge indices are
-    /// given in the order of the vertices (i.e. the first half-edge's
-    /// origin is verts[0], second is verts[1], third is verts[2]).
-    pub fn add_face(&mut self, verts: [VertSpec<V>; 3]) -> (usize, [usize; 3]) {
-        // *New* vertices will be at index v_n onward.
-        let v_n = self.num_verts;
-        // The face will be at index f_n:
-        let f_n = self.num_faces;
-        // The half-edges will be at indices e_n, e_n+1, e_n+2:
-        let e_n = self.num_halfedges;
-
-        // Half-edges and vertices can be inserted both at once:
-        let mut new_verts: usize = 0;
-        for i in 0..3 {
-            let n = (i + 1) % 3;
-            let p = (i + 2) % 3;
-            // Either insert a new vertex, or use an existing one.
-            // In both cases, 'v' is its index.
-            let v = match verts[i] {
-                VertSpec::New(v) => {
-                    self.verts.push(DCELVertex {
-                        v: v,
-                        halfedge: e_n + i,
-                    });
-                    let idx = v_n + new_verts;
-                    new_verts += 1;
-                    idx
-                },
-                VertSpec::Idx(v) => v,
-            };
-            // Note that its half-edge is e_n + i, which technically
-            // doesn't exist yet, but is inserted below:
-            self.halfedges.push(DCELHalfEdge {
-                vert: v,
-                face: f_n,
-                has_twin: false,
-                twin_halfedge: 0,
-                next_halfedge: e_n + n,
-                prev_halfedge: e_n + p,
-            });
-        }
-        self.num_halfedges += 3;
-        self.num_verts += new_verts;
-
-        // Finally, add the face (any halfedge is fine):
-        self.faces.push(DCELFace { halfedge: e_n });
-        self.num_faces += 1;
-
-        (f_n, [e_n, e_n+1, e_n+2])
-    }
-
-    /// Add a face that lies on an existing boundary - i.e. one half-edge
-    /// has a twin half-edge already on the mesh.  As this gives two
-    /// vertices, only one other vertex needs specified.
-    /// Returns (face index, halfedge indices).  Halfedge indices begin
-    /// at the twin half-edge to the one specified.
-    pub fn add_face_twin1(&mut self, twin: usize, vert: V) -> (usize, [usize; 3]) {
-        // 'vert' will be at index v_n:
-        let v_n = self.num_verts;
-        // The half-edges will be at indices e_n, e_n+1, e_n+2:
-        let e_n = self.num_halfedges;
-
-        self.verts.push(DCELVertex {
-            v: vert,
-            halfedge: e_n + 2,
-        });
-        self.num_verts += 1;
-        self.add_face_twin1_ref(twin, v_n)
-    }
-
-    /// Like `add_face_twin1`, but for a vertex already present in the
-    /// mesh rather than a new one.  All else is identical.
-    pub fn add_face_twin1_ref(&mut self, twin: usize, vert_idx: usize) -> (usize, [usize; 3]) {
-        // The face will be at index f_n:
-        let f_n = self.num_faces;
-        // The half-edges will be at indices e_n, e_n+1, e_n+2:
-        let e_n = self.num_halfedges;
-
-        // Note the reversal of direction
-        let twin_halfedge = &self.halfedges[twin];
-        let v1 = self.halfedges[twin_halfedge.next_halfedge].vert;
-        let v2 = twin_halfedge.vert;
-        // twin is: v2 -> v1
-
-        // Insert *its* twin, v1 -> v2, first:
-        self.halfedges.push(DCELHalfEdge {
-            vert: v1,
-            face: f_n,
-            has_twin: true,
-            twin_halfedge: twin,
-            next_halfedge: e_n + 1,
-            prev_halfedge: e_n + 2,
-        });
-        // DEBUG
-        if self.halfedges[twin].has_twin {
-            panic!("Trying to add twin to {}, which already has twin ({})",
-                   twin, self.halfedges[twin].twin_halfedge);
-        }
-        self.halfedges[twin].has_twin = true;
-        self.halfedges[twin].twin_halfedge = e_n;
-        self.halfedges.push(DCELHalfEdge {
-            vert: v2,
-            face: f_n,
-            has_twin: false,
-            twin_halfedge: 0,
-            next_halfedge: e_n + 2,
-            prev_halfedge: e_n,
-        });
-        self.halfedges.push(DCELHalfEdge {
-            vert: vert_idx,
-            face: f_n,
-            has_twin: false,
-            twin_halfedge: 0,
-            next_halfedge: e_n,
-            prev_halfedge: e_n + 1,
-        });
-
-        self.num_halfedges += 3;
-
-        // Finally, add the face (any halfedge is fine):
-        self.faces.push(DCELFace { halfedge: e_n });
-        self.num_faces += 1;
-
-        (f_n, [e_n, e_n+1, e_n+2])
-    }
-
-    /// Add a face that lies on two connected boundaries - i.e. two of its
-    /// half-edges have twins already on the mesh.
-    ///
-    /// Twin half-edges should be given in counter-clockwise order; that
-    /// is, for the resultant face, one half-edge's twin will be twin1, and
-    /// the next half-edge's twin will be twin2.
-    /// Also: halfedge `twin2_idx` must end at the vertex that starts
-    /// `twin1_idx`.
-    ///
-    /// Returns (face index, halfedge indices).  Halfedge indices begin
-    /// at the twin halfedge to twin1, then twin halfedge of
-    /// twin2, then the 'new' halfedge (which starts where twin2 starts,
-    /// and ends where twin1 ends).
-    pub fn add_face_twin2(&mut self, twin1_idx: usize, twin2_idx: usize) -> (usize, [usize; 3]) {
-        // The face will be at index f_n:
-        let f_n = self.num_faces;
-        // The half-edges will be at indices e_n, e_n+1, e_n+2:
-        let e_n = self.num_halfedges;
-
-        // The origin vertex is 'between' the two edges, but because their
-        // order is reversed (as twins), this is twin1's origin:
-        let twin1 = &self.halfedges[twin1_idx];
-        let twin2 = &self.halfedges[twin2_idx];
-        let v1 = twin1.vert;
-        let v2 = self.halfedges[twin1.next_halfedge].vert;
-        // Final vertex is back around to twin2's origin:
-        let v3 = twin2.vert;
-
-        if v1 != self.halfedges[twin2.next_halfedge].vert {
-            panic!("twin2 ({}) must end where twin1 ({}) begins, but does not (vertex {} vs. {})",
-                twin2_idx, twin1_idx, self.halfedges[twin2.next_halfedge].vert, v1);
-        }
-
-        // twin1 is: v1 -> v2, twin2 is: v3 -> v1.
-        // so the twin of twin1 must be: v2 -> v1
-        self.halfedges.push(DCELHalfEdge {
-            vert: v2,
-            face: f_n,
-            has_twin: true,
-            twin_halfedge: twin1_idx,
-            next_halfedge: e_n + 1,
-            prev_halfedge: e_n + 2,
-        }); // index e_n
-        self.halfedges[twin1_idx].has_twin = true;
-        self.halfedges[twin1_idx].twin_halfedge = e_n;
-        // and the twin of twin2 must be: v1 -> v3
-        self.halfedges.push(DCELHalfEdge {
-            vert: v1,
-            face: f_n,
-            has_twin: true,
-            twin_halfedge: twin2_idx,
-            next_halfedge: e_n + 2,
-            prev_halfedge: e_n,
-        }); // index e_n + 1
-        self.halfedges[twin2_idx].has_twin = true;
-        self.halfedges[twin2_idx].twin_halfedge = e_n + 1;
-        // and final edge must be v3 -> v2:
-        self.halfedges.push(DCELHalfEdge {
-            vert: v3,
-            face: f_n,
-            has_twin: false,
-            twin_halfedge: 0,
-            next_halfedge: e_n,
-            prev_halfedge: e_n + 1,
-        }); // index e_n + 2
-        self.num_halfedges += 3;
-
-        // Finally, add the face (any halfedge is fine):
-        self.faces.push(DCELFace { halfedge: e_n });
-        self.num_faces += 1;
-
-        (f_n, [e_n, e_n+1, e_n+2])
-    }
-
-    /// Splits a face (assumed to be a triangle) in this mesh by splitting
-    /// its half-edges, in order, at the vertices given, and then creating
-    /// half-edges between each pair of them.
-    ///
-    /// This returns; (new face indices, updated face indices).  That is,
-    /// the first vector is new face indices that were created, and the
-    /// second is existing face indices that were reused (but the faces
-    /// were updated).
-    ///
-    /// This splits the given face into 4 smaller faces, and it splits the
-    /// three *bordering* faces each into 2 faces.  That is, this
-    /// increases the number of faces by 6 and the number of vertices
-    /// by 3.
-    ///
-    /// Right now, this requires that every halfedge of `face` has a twin.
-    /// If this is not the case, this returns `None` and does not subdivide.
-    /// This behavior will likely be changed in the future.
-    ///
-    /// Disclaimer: This code is completely awful; just don't use it.
-    pub fn full_subdiv_face(&mut self, face: usize, verts: Vec<V>) -> Option<(Vec<usize>, Vec<usize>)> {
-        // 'verts' maps 1:1 to vertices for 'face' (i.e. face_to_verts).
-
-        let mut edge_idx = self.faces[face].halfedge;
-        let n = verts.len();
-
-        let mut faces_new = vec![];
-        let mut faces_upd = vec![];
-
-        let mut fail = false;
-        let new_edges: Vec<(usize, usize)> = verts.iter().map(|v| {
-
-            // As we iterate over every vertex, we walk the half-edges:
-            let mut edge = self.halfedges[edge_idx].clone();
-            if !edge.has_twin {
-                println!("Halfedge {} has no twin, and split_face (for now) requires twins", edge_idx);
-                fail = true;
-                return (0,0);
-            }
-            // TODO: Remove the above limitation and just don't try to split
-            // nonexistent twins. I think all logic works the same way.
-
-            let next_idx = edge.next_halfedge;
-            let twin_idx = edge.twin_halfedge;
-            let mut twin = self.halfedges[twin_idx].clone();
-
-            // This half-edge, and its twin, are both split (at this
-            // vertex). Half-edges i & j will be the new ones created.
-            let i_edge = self.num_halfedges;
-            let j_edge = i_edge + 1;
-            // Half of edge_idx is split into j_edge.
-            // Half of twin_idx (its twin) is split into i_edge.
-
-            // This is where the vertex will be inserted:
-            let v_idx = self.num_verts;
-            self.verts.push(DCELVertex {
-                v: *v,
-                halfedge: i_edge, // j_edge is also fine
-            });
-            self.num_verts += 1;
-
-            edge.twin_halfedge = i_edge;
-            let j_next = edge.next_halfedge;
-
-            twin.twin_halfedge = j_edge;
-            let i_next = twin.next_halfedge;
-
-            self.halfedges.push(DCELHalfEdge {
-                vert: v_idx,
-                face: 0, // This is set properly in the next loop
-                has_twin: true,
-                twin_halfedge: edge_idx,
-                next_halfedge: i_next,
-                prev_halfedge: twin_idx,
-            }); // i_edge
-            self.halfedges.push(DCELHalfEdge {
-                vert: v_idx,
-                face: 0, // This is set properly in the next loop
-                has_twin: true,
-                twin_halfedge: twin_idx,
-                next_halfedge: j_next,
-                prev_halfedge: edge_idx,
-            }); // j_edge
-
-            self.num_halfedges += 2;
-
-            self.halfedges[edge_idx] = edge;
-            self.halfedges[twin_idx] = twin;
-
-            let r = (edge_idx, j_edge);
-
-            edge_idx = next_idx;
-
-            r
-        }).collect();
-
-        if fail {
-            return None;
-        }
-
-        // We then must connect some edges up 'across' vertices
-        // in order to form the smaller face at each vertex.
-        //
-        // This is outside the loop because we need one iteration's
-        // value (any iteration, doesn't matter) to reassign a face:
-        let mut e_twin_idx = 0;
-        let twin_edges: Vec<usize> = (0..n).map(|i0| {
-            let i1 = (i0 + 1) % n;
-
-            let (_, ep_idx) = new_edges[i0];
-            let (en_idx, _) = new_edges[i1];
-
-            // Halfedges will be inserted here:
-            let e_cross_idx = self.num_halfedges;
-            e_twin_idx = e_cross_idx + 1;
-            // And the face here:
-            let face_new = self.num_faces;
-
-            // So, the vertex for i0 had two halfedges (one pointing in,
-            // one pointing out). We split both those half-edges earlier.
-            // en_idx & ep_idx are the halves that are nearest the
-            // vertex. The point of below is to form a smaller triangle
-            // (which includes this vertex, and the point at which both
-            // edges were split).  This requires a half-edge from ep_idx
-            // (which *starts* where the other was split) to en_idx (which
-            // *ends* where one edge was split).
-            self.halfedges.push(DCELHalfEdge {
-                vert: self.halfedges[self.halfedges[en_idx].twin_halfedge].vert,
-                face: face_new,
-                has_twin: true,
-                twin_halfedge: e_twin_idx,
-                next_halfedge: ep_idx,
-                prev_halfedge: en_idx,
-            }); // e_cross_idx
-
-            // It also requires a twin half-edge. These all form a single
-            // central face with each edge sharing a boundary with the
-            // 'cross' edge we just created.
-            self.halfedges.push(DCELHalfEdge {
-                vert: self.halfedges[ep_idx].vert,
-                face: face, // Reuse index for the smaller *central* face
-                has_twin: true,
-                twin_halfedge: e_cross_idx,
-                next_halfedge: 0, // TODO
-                prev_halfedge: 0, // TODO
-            }); // e_twin_idx
-            self.num_halfedges += 2;
-
-            // en/ep also need directed to 'new' edges and each other
-            self.halfedges[en_idx].prev_halfedge = ep_idx;
-            self.halfedges[en_idx].next_halfedge = e_cross_idx;
-
-            self.halfedges[ep_idx].next_halfedge = en_idx;
-            self.halfedges[ep_idx].prev_halfedge = e_cross_idx;
-
-            self.halfedges[ep_idx].face = face_new;
-
-            self.faces.push(DCELFace {
-                halfedge: e_cross_idx, // en_idx or ep_idx is fine too
-            }); // face_new
-            faces_new.push(face_new);
-            self.num_faces += 1;
-
-            // We also need to split the opposite side to make the two
-            // 'side' triangles (which means two new half-edges).
-            // First, we have to find the halfedge that starts the
-            // 'opposite' vertex (outer2):
-            let base1 = self.halfedges[en_idx].twin_halfedge;
-            let base2 = self.halfedges[base1].prev_halfedge;
-            let outer1 = self.halfedges[base1].next_halfedge;
-            let outer2 = self.halfedges[outer1].next_halfedge;
-            let v_opp = self.halfedges[outer2].vert;
-            // One face will reuse the old index:
-            let face1 = self.halfedges[outer2].face;
-            // Another will be inserted at this index:
-            let face2 = self.num_faces;
-            // Half-edges will be inserted here:
-            let edge_side1 = self.num_halfedges;
-            let edge_side2 = edge_side1 + 1;
-            self.halfedges.push(DCELHalfEdge {
-                vert: v_opp,
-                face: face1,
-                has_twin: true,
-                twin_halfedge: edge_side2,
-                next_halfedge: base1,
-                prev_halfedge: outer1,
-            }); // edge_side1
-            self.halfedges.push(DCELHalfEdge {
-                vert: self.halfedges[base1].vert,
-                face: face2,
-                has_twin: true,
-                twin_halfedge: edge_side1,
-                next_halfedge: outer2,
-                prev_halfedge: base2,
-            }); // edge_side2
-            self.num_halfedges += 2;
-
-            self.faces.push(DCELFace {
-                halfedge: outer2, // base2 or edge_side2 is fine too
-            });
-            faces_new.push(self.num_faces);
-            self.num_faces += 1;
-            self.faces[face1].halfedge = outer1; // base1 or edge_side1 is fine too
-            faces_upd.push(face1);
-
-            self.halfedges[outer1].next_halfedge = edge_side1;
-            self.halfedges[outer1].prev_halfedge = base1;
-            self.halfedges[outer1].face = face1;
-            self.halfedges[base1].face = face1;
-            self.halfedges[base1].prev_halfedge = edge_side1;
-            self.halfedges[base1].next_halfedge = outer1;
-
-            self.halfedges[outer2].next_halfedge = base2;
-            self.halfedges[outer2].prev_halfedge = edge_side2;
-            self.halfedges[outer2].face = face2;
-            self.halfedges[base2].face = face2;
-            self.halfedges[base2].prev_halfedge = outer2;
-            self.halfedges[base2].next_halfedge = edge_side2;
-
-            e_twin_idx
-        }).collect();
-
-        for i0 in 0..n {
-            let i1 = (i0 + 1) % n;
-
-            self.halfedges[twin_edges[i0]].next_halfedge = twin_edges[i1];
-            self.halfedges[twin_edges[i1]].prev_halfedge = twin_edges[i0];
-        }
-
-        // We split up original 'face' completely and created four new faces,
-        // We need something at this index, and the other three already have
-        // indices, so reuse it for the smaller central face:
-        self.faces[face].halfedge = e_twin_idx;
-        faces_upd.push(face);
-
-        return Some((faces_new, faces_upd));
-    }
-
-    pub fn convert_mesh<F>(&self, f: F) -> Mesh
-        where F: Fn(V) -> Vertex,
-    {
-        let n = self.faces.len();
-        let mut faces: Vec<usize> = vec![0; 3 * n];
-
-        for i in 0..n {
-
-            let e0 = self.faces[i].halfedge;
-            let h0 = &self.halfedges[e0];
-            faces[3*i + 0] = h0.vert;
-            let e1 = h0.next_halfedge;
-            let h1 = &self.halfedges[e1];
-            faces[3*i + 1] = h1.vert;
-            let e2 = h1.next_halfedge;
-            let h2 = &self.halfedges[e2];
-            faces[3*i + 2] = h2.vert;
-            if h2.next_halfedge != e0 {
-                panic!("Face {}: half-edges {},{},{} return to {}, not {}",
-                       i, e0, e1, e2, h2.next_halfedge, e0);
-            }
-        }
-
-        Mesh {
-            verts: self.verts.iter().map(|e| f(e.v)).collect(),
-            faces: faces,
-        }
-    }
-}

src/lib.rs

@@ -1,12 +1,10 @@
 pub mod mesh;
 #[macro_use]
-pub mod rule;
 pub mod prim;
 #[macro_use]
 pub mod util;
-pub mod xform;
 pub mod examples;
-pub mod dcel;
+pub mod xform;
 
 //pub use crate::examples;
 //pub use crate::openmesh::test_thing;
@@ -14,32 +12,9 @@ pub mod dcel;
 #[cfg(test)]
 mod tests {
     use super::*;
+    use nalgebra::*;
     use std::rc::Rc;
     use std::time::Instant;
-    use rule::Rule;
-    use nalgebra::*;
-
-    fn run_test<S>(rule: Rule<S>, iters: usize, name: &str, use_old: bool) {
-        let r = Rc::new(rule);
-        println!("---------------------------------------------------");
-        println!("Running {} with {}...",
-                 name, if use_old { "to_mesh" } else { "to_mesh_iter" });
-        if false {
-            let start = Instant::now();
-            let n = 5;
-            for _ in 0..n {
-                Rule::to_mesh_iter(r.clone(), iters);
-            }
-            let elapsed = start.elapsed();
-            println!("DEBUG: {} ms per run", elapsed.as_millis() / n);
-        }
-        let mesh_fn = if use_old { Rule::to_mesh } else { Rule::to_mesh_iter };
-        let (mesh, nodes) = mesh_fn(r.clone(), iters);
-        println!("Evaluated {} rules to {} verts", nodes, mesh.verts.len());
-        let fname = format!("{}.stl", name);
-        println!("Writing {}...", fname);
-        mesh.to_mesh().write_stl_file(&fname).unwrap();
-    }
 
     #[test]
     fn xform_order() {
@@ -57,13 +32,27 @@ mod tests {
         let xf2 = rot.translate(dx, 0.0, 0.0);
 
         // Rotate entire space, *then* translate in that rotated plane:
-        geom.transform(&trans).transform(&rot).write_stl_file("xform_apply_trans_rot.stl").unwrap();
-        geom.transform(&(rot * trans)).write_stl_file("xform_mul_rot_trans.stl").unwrap();
-        geom.transform(&xf2).write_stl_file("xform_rot_trans.stl").unwrap();
+        geom.transform(&trans)
+            .transform(&rot)
+            .write_stl_file("xform_apply_trans_rot.stl")
+            .unwrap();
+        geom.transform(&(rot * trans))
+            .write_stl_file("xform_mul_rot_trans.stl")
+            .unwrap();
+        geom.transform(&xf2)
+            .write_stl_file("xform_rot_trans.stl")
+            .unwrap();
         // Translate cube, *then* rotate it:
-        geom.transform(&rot).transform(&trans).write_stl_file("xform_apply_rot_trans.stl").unwrap();
-        geom.transform(&(trans * rot)).write_stl_file("xform_mul_trans_rot.stl").unwrap();
-        geom.transform(&xf1).write_stl_file("xform_trans_rot.stl").unwrap();
+        geom.transform(&rot)
+            .transform(&trans)
+            .write_stl_file("xform_apply_rot_trans.stl")
+            .unwrap();
+        geom.transform(&(trans * rot))
+            .write_stl_file("xform_mul_trans_rot.stl")
+            .unwrap();
+        geom.transform(&xf1)
+            .write_stl_file("xform_trans_rot.stl")
+            .unwrap();
     }
 
     // TODO: These tests don't test any conditions, so this is useful
@@ -80,11 +69,10 @@ mod tests {
         let fname = format!("{}.stl", name);
         println!("Writing {}...", fname);
         m.write_stl_file(&fname).unwrap();
-
     }
 
     #[test]
-    fn tree_thing() {
+    fn tree_thing1() {
         let name = "tree_thing";
         println!("---------------------------------------------------");
         let b = examples::TreeThing::new(0.6, 10);
@@ -95,7 +83,6 @@ mod tests {
         let fname = format!("{}.stl", name);
         println!("Writing {}...", fname);
         m.write_stl_file(&fname).unwrap();
-
     }
 
     #[test]
@@ -110,73 +97,36 @@ mod tests {
         let fname = format!("{}.stl", name);
         println!("Writing {}...", fname);
         m.write_stl_file(&fname).unwrap();
-
     }
 
     #[test]
-    fn sierpinski() { run_test(examples::sierpinski(), 6, "sierpinski", false); }
-    /*
-    #[test]
-    fn twist() {
-        run_test(examples::twist(1.0, 2), 200, "screw", false);
+    fn sierpinski() {
+        let name = "sierpinski";
+        println!("---------------------------------------------------");
+        let b = examples::Sierpinski::new(0.50, 0.10, 0.0);
+        //let b = examples::Sierpinski::new(0.51, 0.10, 0.1);
+        let m = b.run();
+
+        println!("Got {} verts...", m.verts.len());
+
+        let fname = format!("{}.stl", name);
+        println!("Writing {}...", fname);
+        m.write_stl_file(&fname).unwrap();
     }
 
     #[test]
-    fn twisty_torus() {
-        run_test(examples::twisty_torus(), 3000, "twisty_torus", false);
-    }
+    fn nested_spiral() {
+        let name = "nested_spiral";
+        println!("---------------------------------------------------");
+        let b = examples::NestedSpiral::new();
+        //let b = examples::Sierpinski::new(0.51, 0.10, 0.1);
+        let m = b.run();
 
-    #[test]
-    fn twisty_torus_hardcode() {
-        run_test(examples::twisty_torus_hardcode(), 1000, "twisty_torus_hardcode", false);
-    }
+        println!("Got {} verts...", m.verts.len());
 
-    #[test]
-    #[ignore]
-    fn twisty_torus_full() {
-        run_test(examples::twisty_torus(), 40000, "twisty_torus_full", false);
-    }
-
-    #[test]
-    #[ignore]
-    fn wind_chime_mistake_thing() {
-        run_test(examples::wind_chime_mistake_thing(), 400, "wind_chime_mistake_thing", false);
-    }
-
-    #[test]
-    fn nest_spiral_2() {
-        run_test(examples::nest_spiral_2(), 200, "nest_spiral_2", false);
-    }
-
-    // This one is very time-consuming to run:
-    #[test]
-    #[ignore]
-    fn twist_full() {
-        let f = 40;
-        run_test(examples::twist(f as f32, 128), 100*f, "screw_full", false);
-    }
-    */
-    
-    #[test]
-    fn ramhorn() {
-        run_test(examples::ramhorn(), 100, "ram_horn3", false);
-    }
-
-    /*
-    #[test]
-    fn ramhorn_branch_random() {
-        run_test(examples::ramhorn_branch_random(24, 0.25), 32, "ram_horn_branch_random", false);
-    }
-     */
-
-    #[test]
-    fn test_parametric() {
-        examples::test_parametric().write_stl_file("test_parametric.stl").unwrap();
-    }
-
-    #[test]
-    fn test_dcel() {
-        examples::test_dcel("test_dcel.stl");
+        let fname = format!("{}.stl", name);
+        println!("Writing {}...", fname);
+        m.write_stl_file(&fname).unwrap();
     }
 }
 // need this for now:

src/mesh.rs

@@ -1,8 +1,7 @@
 use std::fs::OpenOptions;
 use std::io;
-use std::borrow::Borrow;
 
-use crate::xform::{Vertex, Transform};
+use crate::xform::{Transform, Vertex};
 
 /// Basic face-vertex mesh.  `faces` contains indices of `verts` and is
 /// taken in groups of 3 for each triangle.
@@ -26,19 +25,25 @@ impl Mesh {
     /// Write this mesh as an STL file.  This will fail if any element
     /// of `faces` is `Tag::Parent`.
     pub fn write_stl_file(&self, fname: &str) -> io::Result<()> {
-        let mut file = OpenOptions::new().write(true).create(true).truncate(true).open(fname)?;
+        let mut file = OpenOptions::new()
+            .write(true)
+            .create(true)
+            .truncate(true)
+            .open(fname)?;
         self.write_stl(&mut file)
     }
 
     fn write_stl<W: std::io::Write>(&self, writer: &mut W) -> io::Result<()> {
-
         // Every group of 3 indices in self.faces is one triangle, so
         // pre-allocate in the format stl_io wants:
         let num_faces = self.faces.len() / 3;
-        let mut triangles = vec![stl_io::Triangle {
+        let mut triangles = vec![
+            stl_io::Triangle {
                 normal: [0.0; 3],
                 vertices: [[0.0; 3]; 3],
-        }; num_faces];
+            };
+            num_faces
+        ];
 
         // Turn every face into an stl_io::Triangle:
         for i in 0..num_faces {
@@ -61,185 +66,4 @@ impl Mesh {
 
         stl_io::write_stl(writer, triangles.iter())
     }
-
-    pub fn to_meshfunc(&self) -> MeshFunc {
-        MeshFunc {
-            faces: self.faces.clone(),
-            verts: self.verts.iter().map(|v| VertexUnion::Vertex(*v)).collect(),
-        }
-    }
-}
-
-#[derive(Clone, Debug)]
-pub enum VertexUnion {
-    /// A concrete vertex.
-    Vertex(Vertex),
-    /// A vertex argument - something like an argument to a function with
-    /// the given positional index.
-    ///
-    /// The job of `MeshFunc.connect` is to bind these arguments to concrete
-    /// vertices.
-    Arg(usize),
-}
-
-pub fn vert_args<T: IntoIterator<Item = usize>>(v: T) -> Vec<VertexUnion> {
-    v.into_iter().map(|i| VertexUnion::Arg(i)).collect()
-}
-
-/// A face-vertex mesh, some of whose vertices may be 'vertex arguments'
-/// rather than concrete vertices. The job of `connect()` is to resolve
-/// these.
-#[derive(Clone, Debug)]
-pub struct MeshFunc {
-    pub verts: Vec<VertexUnion>,
-    /// Indices of triangles (taken as every 3 values).
-    pub faces: Vec<usize>,
-}
-
-impl MeshFunc {
-    pub fn to_mesh(&self) -> Mesh {
-        Mesh {
-            faces: self.faces.clone(),
-            verts: self.verts.iter().map(|v| match *v {
-                VertexUnion::Vertex(v) => v,
-                VertexUnion::Arg(_) => panic!("Mesh still has vertex arguments!"),
-            }).collect(),
-        }
-    }
-
-    /// Returns a new `MeshFunc` whose concrete vertices have
-    /// been transformed. Note that alias vertices are left untouched.
-    pub fn transform(&self, xfm: &Transform) -> MeshFunc {
-        let v = self.verts.iter().map(|v| {
-            match v {
-                VertexUnion::Vertex(v) => VertexUnion::Vertex(xfm.mtx * v),
-                a @ _ => a.clone(),
-            }
-        });
-
-        MeshFunc {
-            verts: v.collect(),
-            faces: self.faces.clone(),
-        }
-    }
-
-    /// Appends any number of meshes together.  Returns both a single
-    /// mesh, and a vector which gives the offset by which each
-    /// corresponding input mesh was shifted.  That is, for the i'th
-    /// index in `meshes`, all of its triangle indices were shifted by
-    /// the i'th offset in the resultant mesh.
-    pub fn append<T, U>(meshes: T) -> (MeshFunc, Vec<usize>)
-        where U: Borrow<MeshFunc>,
-              T: IntoIterator<Item=U>
-    {
-        let mut offsets: Vec<usize> = vec![];
-        let mut v: Vec<VertexUnion> = vec![];
-        let mut f: Vec<usize> = vec![];
-        for mesh_ in meshes {
-            let mesh = mesh_.borrow();
-
-            // Position in 'verts' at which we're appending
-            // mesh.verts, which we need to know to shift indices:
-            let offset = v.len();
-            offsets.push(offset);
-
-            // Copy all vertices:
-            v.append(&mut mesh.verts.clone());
-            // Append its faces, applying offset:
-            f.extend(mesh.faces.iter().map(|n| n + offset));
-        }
-
-        (MeshFunc { verts: v, faces: f }, offsets)
-    }
-
-    /// Treat this mesh as a 'parent' mesh to connect with any number
-    /// of 'child' meshes, all of them paired with their respective
-    /// vertex argument values (i.e. `arg_vals` from `Child`).
-    ///
-    /// This returns a tuple of (new `MeshFunc`, new `arg_vals`), where
-    /// `arg_vals[i]` is the new index of `self.verts[i]` in the
-    /// returned `MeshFunc`.
-    pub fn connect<T, U>(&self, children: T) -> (MeshFunc, Vec<Vec<usize>>)
-        where U: Borrow<MeshFunc>,
-              T: IntoIterator<Item=(U, Vec<usize>)>
-    {
-        // TODO: Clean up this description a bit
-        // TODO: Clean up Vec<usize> stuff
-
-        // Copy body vertices & faces:
-        let mut verts: Vec<VertexUnion> = self.verts.clone();
-        let mut faces = self.faces.clone();
-
-        let mut remaps: Vec<Vec<usize>> = vec![];
-
-        for (child_, arg_vals) in children {
-            let child = child_.borrow();
-
-            // 'offset' corresponds to the position in 'verts' at
-            // which we begin appending everything in 'child.verts'.
-            let offset = verts.len();
-
-            // 'remap[i]' - if 'child.verts[i]' is a Vertex, not an Arg -
-            // will contain the index in 'verts' that this vertex was
-            // copied to.  (This is needed because below we copy only
-            // the Vertex elements, not the Arg ones.)
-            let mut remap = vec![0; child.verts.len()];
-            let mut j = 0;
-
-            // Like mentioned, copy just the Vertex in 'child.verts':
-            verts.extend(child.verts.iter().enumerate().filter_map(|(i,v)| {
-                match v {
-                    VertexUnion::Vertex(_) => {
-                        // TODO: A less-side-effectful way?
-                        remap[i] = offset + j;
-                        j += 1;
-                        Some(v.clone())
-                    },
-                    VertexUnion::Arg(_) => None,
-                }
-            }));
-            // So, note that:
-            // 1st Vertex in 'child.verts' went to 'verts[offset + 0]'.
-            // 2nd Vertex in 'child.verts' went to 'verts[offset + 1]'.
-            // 3rd Vertex in 'child.verts' went to 'verts[offset + 2]'.
-            // and so forth.
-            // Since this skips Arg elements, we used 'remap' to
-            // store the mapping: 'child.verts[i]' was copied to
-            // 'verts[remap[i]].'
-
-            // We then use 'remap' below to update the indices in
-            // 'child.faces' to vertices in the returned mesh.
-            //
-            // Also, we didn't copy Arg elements from 'child.verts', but
-            // we do use them below - if 'child.faces' makes a
-            // reference to this Arg, we resolve it with the help of
-            // 'arg_vals', passed in by the caller.
-            faces.extend(child.faces.iter().map(|n| {
-                let f = match child.verts[*n] {
-                    VertexUnion::Vertex(_) => remap[*n],
-                    VertexUnion::Arg(m) => {
-                        println!("remap face: vert {} arg {} = vert {} ({:?})",
-                            *n, m, arg_vals[m], verts[arg_vals[m]]
-                        );
-                        arg_vals[m]
-                    },
-                };
-                if f >= verts.len() {
-                    panic!("face >= num_verts")
-                }
-                f
-            }));
-
-            // Since the caller might need this same remapping (there
-            // could be an Arg that referred to these vertices), we
-            // save this information to return it later:
-            remaps.push(remap);
-        }
-
-        let m = MeshFunc {
-            verts: verts,
-            faces: faces,
-        };
-        (m, remaps)
-    }
 }

src/prim.rs

@@ -1,4 +1,4 @@
-use crate::mesh::{Mesh, MeshFunc};
+use crate::mesh::Mesh;
 use crate::xform::{vertex, Transform};
 
 /// Returns an empty mesh (no vertices, no faces).
@@ -9,14 +9,6 @@ pub fn empty_mesh() -> Mesh {
     }
 }
 
-/// Returns an empty MeshFn (no vertices, no faces, thus no args).
-pub fn empty_meshfunc() -> MeshFunc {
-    MeshFunc {
-        verts: vec![],
-        faces: vec![],
-    }
-}
-
 /// Returns a cube of sidelength one centered at (0,0,0).
 pub fn cube() -> Mesh {
     Mesh {
@@ -31,18 +23,9 @@ pub fn cube() -> Mesh {
             vertex(1.0, 1.0, 1.0),
         ],
         faces: vec![
-            0, 3, 1,
-            0, 2, 3,
-            1, 7, 5,
-            1, 3, 7,
-            5, 6, 4,
-            5, 7, 6,
-            4, 2, 0,
-            4, 6, 2,
-            2, 7, 3,
-            2, 6, 7,
-            0, 1, 5,
-            0, 5, 4,
+            0, 3, 1, 0, 2, 3, 1, 7, 5, 1, 3, 7, 5, 6, 4, 5, 7, 6, 4, 2, 0, 4, 6, 2, 2, 7, 3, 2, 6,
+            7, 0, 1, 5, 0, 5, 4,
         ],
-    }.transform(&Transform::new().translate(-0.5, -0.5, -0.5))
+    }
+    .transform(&Transform::new().translate(-0.5, -0.5, -0.5))
 }

src/rule.rs

@@ -1,498 +0,0 @@
-use std::borrow::Borrow;
-use std::rc::Rc;
-use std::f32;
-
-use crate::mesh::{Mesh, MeshFunc, VertexUnion};
-use crate::xform::{Transform, Vertex};
-
-pub type RuleFn<S> = Rc<dyn Fn(Rc<Rule<S>>) -> RuleEval<S>>;
-
-/// Definition of a rule.  In general, a `Rule`:
-///
-/// - produces geometry when it is evaluated
-/// - tells what other rules to invoke, and what to do with their
-/// geometry
-pub struct Rule<S> {
-    pub eval: RuleFn<S>,
-    pub ctxt: S,
-}
-
-// TODO: It may be possible to have just a 'static' rule that requires
-// no function call.
-// TODO: Do I benefit with Rc<Rule> below so Rule can be shared?
-
-// TODO: Why *can't* I make this FnOnce?
-
-// The above looks like it is going to require a lifetime parameter
-// regardless, in which case I don't really need Box.
-
-/// `RuleEval` supplies the results of evaluating some `Rule` for one
-/// iteration: it contains the geometry produced at this step
-/// (`geom`), and it tells what to do next depending on whether
-/// recursion continues further, or is stopped here (due to hitting
-/// some limit of iterations or some lower limit on overall scale).
-///
-/// That is:
-/// - if recursion stops, `final_geom` is connected with `geom`.
-/// - if recursion continues, the rules of `children` are evaluated,
-/// and the resultant geometry is transformed and then connected with
-/// `geom`.
-pub struct RuleEval<S> {
-    /// The geometry generated at just this iteration
-    pub geom: Rc<MeshFunc>,
-
-    /// The "final" geometry that is merged with `geom` via
-    /// `connect()` in the event that recursion stops.  This must be
-    /// in the same coordinate space as `geom`.
-    ///
-    /// Parent vertex references will be resolved directly to `geom`
-    /// with no mapping.
-    /// (TODO: Does this make sense? Nowhere else do I treat Arg(n) as
-    /// an index - it's always a positional argument.)
-    pub final_geom: Rc<MeshFunc>,
-
-    /// The child invocations (used if recursion continues).  The
-    /// 'parent' mesh, from the perspective of all geometry produced
-    /// by `children`, is `geom`.
-    pub children: Vec<Child<S>>,
-}
-
-/// `Child` evaluations, pairing another `Rule` with the
-/// transformations and parent vertex mappings that should be applied
-/// to it.
-pub struct Child<S> {
-
-    /// Rule to evaluate to produce geometry
-    pub rule: Rc<Rule<S>>,
-
-    /// The transform to apply to all geometry produced by `rule`
-    /// (including its own `geom` and `final_geom` if needed, as well
-    /// as all sub-geometry produced recursively).
-    pub xf: Transform,
-
-    /// The 'argument values' to apply to vertex arguments of a `MeshFunc`
-    /// from `geom` and `final_geom` that `rule` produces when evaluated.
-    /// The values of this are treated as indices into the parent
-    /// `RuleEval` that produced this `Child`.
-    ///
-    /// In specific: if `arg_vals[i] = j` and `rule` produces some `geom` or
-    /// `final_geom`, then any vertex of `VertexUnion::Arg(i)` will be mapped
-    /// to `geom.verts[j]` in the *parent* geometry.
-    pub arg_vals: Vec<usize>,
-}
-
-#[macro_export]
-macro_rules! child {
-    ( $Rule:expr, $Xform:expr, $( $Arg:expr ),* ) => {
-        Child {
-            rule: /*std::rc::Rc::new*/($Rule).clone(),
-            xf: $Xform,
-            arg_vals: vec![$($Arg,)*],
-        }
-    }
-}
-
-#[macro_export]
-macro_rules! child_iter {
-    ( $Rule:expr, $Xform:expr, $Args:expr ) => {
-        Child {
-            rule: /*std::rc::Rc::new*/($Rule).clone(),
-            xf: $Xform,
-            arg_vals: $Args.collect(), // does this even need a macro?
-        }
-    }
-}
-
-#[macro_export]
-macro_rules! rule {
-    ( $RuleFn:expr, $Ctxt:expr ) => {
-        std::rc::Rc::new(Rule {
-            eval: $RuleFn.clone(),
-            ctxt: $Ctxt,
-        })
-    }
-}
-
-#[macro_export]
-macro_rules! rule_fn {
-    ( $Ty:ty => |$Self:ident $(,$x:ident)*| $Body:expr ) => {
-        {
-            $(let $x = $x.clone();)*
-            std::rc::Rc::new(move |$Self: std::rc::Rc<Rule<$Ty>>| -> RuleEval<$Ty> {
-                $(let $x = $x.clone();)*
-                let $Self = $Self.clone();
-                $Body
-            })
-        }
-    }
-}
-// TODO: Shouldn't I fully-qualify Rule & RuleEval?
-// TODO: Document all of the above macros
-// TODO: Why must I clone twice?
-
-impl<S> Rule<S> {
-
-    /// Convert this `Rule` to mesh data, recursively (depth first).
-    /// `iters_left` sets the maximum recursion depth.  This returns
-    /// (geometry, number of rule evaluations).
-    pub fn to_mesh(s: Rc<Rule<S>>, iters_left: usize) -> (MeshFunc, usize) {
-
-        let mut evals = 1;
-
-        let rs: RuleEval<S> = (s.eval)(s.clone());
-        if iters_left <= 0 {
-            return ((*rs.final_geom).clone(), 1);
-            // TODO: This is probably wrong because of the way that
-            // sub.arg_vals is used below.  final_geom is not supposed to
-            // have any vertex mapping applied.
-        }
-
-        // TODO: This logic is more or less right, but it
-        // could perhaps use some un-tupling or something.
-
-        let subgeom: Vec<(MeshFunc, Vec<usize>)> = rs.children.iter().map(|sub| {
-            // Get sub-geometry (still un-transformed):
-            let (submesh, eval) = Rule::to_mesh(sub.rule.clone(), iters_left - 1);
-            // Tally up eval count:
-            evals += eval;
-            
-            let m2 = submesh.transform(&sub.xf);
-            
-            (m2, sub.arg_vals.clone())
-                // TODO: Fix clone?
-        }).collect();
-        
-        // Connect geometry from this rule (not child rules):
-        return (rs.geom.connect(subgeom).0, evals);
-    }
-
-    /// This should be identical to to_mesh, but implemented
-    /// iteratively with an explicit stack rather than with recursive
-    /// function calls.
-    pub fn to_mesh_iter(s: Rc<Rule<S>>, max_depth: usize) -> (MeshFunc, usize) {
-
-        struct State<S> {
-            // The set of rules we're currently handling:
-            rules: Vec<Child<S>>,
-            // The next element of 'children' to handle:
-            next: usize,
-            // World transform of the *parent* of 'rules', that is,
-            // not including any transform of any element of 'rules'.
-            xf: Transform,
-            // How many levels 'deeper' can we recurse?
-            depth: usize,
-        }
-
-        // 'stack' stores at its last element our "current" State in
-        // terms of a current world transform and which Child should
-        // be processed next.  Every element prior to this is previous
-        // states which must be kept around for further backtracking
-        // (usually because they involve multiple rules).
-        //
-        // We evaluate our own rule to initialize the stack:
-        let eval = (s.eval)(s.clone());
-        let mut stack: Vec<State<S>> = vec![State {
-            rules: eval.children,
-            next: 0,
-            xf: Transform::new(),
-            depth: max_depth,
-        }];
-        let mut geom = (*eval.geom).clone();
-
-        // Number of times we've evaluated a Rule:
-        let mut eval_count = 1;
-
-        // Stack depth (update at every push & pop):
-        let mut n = stack.len();
-
-        while !stack.is_empty() {
-
-            // s = the 'current' state:
-            let s = &mut stack[n-1];
-            let depth = s.depth;
-
-            if s.rules.is_empty() {
-                stack.pop();
-                n -= 1;
-                continue;
-            }
-            
-            // Evaluate the rule:
-            let child = &s.rules[s.next];
-            let mut eval = (child.rule.eval)(child.rule.clone());
-            eval_count += 1;
-
-            // Make an updated world transform:
-            let xf = s.xf * child.xf;
-
-            // This rule produced some geometry which we'll
-            // combine with the 'global' geometry:
-            let new_geom = eval.geom.transform(&xf);
-            
-            // See if we can still recurse further:
-            if depth <= 0 {
-                // As we're stopping recursion, we need to connect
-                // final_geom with all else in order to actually close
-                // geometry properly:
-                let final_geom = eval.final_geom.transform(&xf);
-                // TODO: Fix the awful hack below.  I do this only to
-                // generate an identity mapping for arg_vals when I don't
-                // actually need arg_vals.
-                let m = {
-                    let mut m_ = 0;
-                    for v in &final_geom.verts {
-                        match *v {
-                            VertexUnion::Arg(a) => {
-                                if a > m_ {
-                                    m_ = a;
-                                }
-                            },
-                            VertexUnion::Vertex(_) => (),
-                        }
-                    }
-                    m_ + 1
-                };
-                let arg_vals: Vec<usize> = (0..m).collect();
-                let (geom2, _) = new_geom.connect(vec![(final_geom, arg_vals)]);
-                
-                geom = geom.connect(vec![(geom2, child.arg_vals.clone())]).0;
-                // TODO: Fix clone?
-
-                // If we end recursion on one child, we must end it
-                // similarly on every sibling (i.e. get its geometry &
-                // final geometry, and merge it in) - so we increment
-                // s.next and let the loop re-run.
-                s.next += 1;
-                if s.next >= s.rules.len() {
-                    // Backtrack only at the last child:
-                    stack.pop();
-                    n -= 1;
-                }
-                continue;
-            }
-
-            let (g, remaps) = geom.connect(vec![(new_geom, child.arg_vals.clone())]);
-            geom = g;
-
-            // 'eval.children' may contain (via 'arg_vals') references to
-            // indices of 'new_geom'. However, we don't connect() to
-            // 'new_geom', but to the global geometry we just merged it
-            // into.  To account for this, we must remap 'arg_vals' by the
-            // mapping connect() gave us:
-            let remap = &remaps[0];
-            // (We pass a one-element vector to geom.connect() above
-            // so remaps always has just one element.)
-            for child in eval.children.iter_mut() {
-                child.arg_vals = child.arg_vals.iter().map(|n| remap[*n]).collect();
-            }
-
-            // We're done evaluating this rule, so increment 'next'.
-            // If that was the last rule at this level (i.e. ignoring
-            // eval.children), remove it - we're done with it.
-            s.next += 1;
-            if s.next >= s.rules.len() {
-                stack.pop();
-                n -= 1;
-            }
-
-            if !eval.children.is_empty() {
-                // Recurse further (i.e. put more onto stack):
-                stack.push(State {
-                    rules: eval.children,
-                    next: 0,
-                    xf: xf,
-                    depth: depth - 1,
-                });
-                n += 1;
-            }
-        }
-        
-        return (geom, eval_count); 
-    }
-    
-}
-
-impl<S> RuleEval<S> {
-    /// Turn an iterator of (MeshFunc, Child) into a single RuleEval.
-    /// All meshes are merged, and the `arg_vals` in each child has the
-    /// correct offsets applied to account for this merge.
-    ///
-    /// (`final_geom` is passed through to the RuleEval unmodified.)
-    pub fn from_pairs<T, U>(m: T, final_geom: MeshFunc) -> RuleEval<S>
-        where U: Borrow<MeshFunc>,
-              T: IntoIterator<Item = (U, Child<S>)>
-    {
-        let (meshes, children): (Vec<_>, Vec<_>) = m.into_iter().unzip();
-        let (mesh, offsets) = MeshFunc::append(meshes);
-
-        // Patch up arg_vals in each child, and copy everything else:
-        let children2: Vec<Child<S>> = children.iter().zip(offsets.iter()).map(|(c,off)| {
-            Child {
-                rule: c.rule.clone(),
-                xf: c.xf.clone(),
-                // simply add offset:
-                arg_vals: c.arg_vals.iter().map(|i| i + off).collect(),
-            }
-        }).collect();
-
-        RuleEval {
-            geom: Rc::new(mesh),
-            final_geom: Rc::new(final_geom),
-            children: children2,
-        }
-    }
-
-}
-
-// fa001f47d40de989da6963e442f31c278c88abc8
-
-/// Produce a mesh from a starting frame, and a function `f` which produces
-/// transformations that change continuously over its argument (the range
-/// of which is given by `t0` and `t1`).  By convention, `f(t0)` should
-/// always produce an identity transformation.
-///
-/// Facetization is guided by the given error, `max_err`, which is treated
-/// as a distance in 3D space.
-pub fn parametric_mesh<F>(frame: Vec<Vertex>, f: F, t0: f32, t1: f32, max_err: f32) -> Mesh
-    where F: Fn(f32) -> Transform
-{
-    let n = frame.len();
-
-    // Sanity checks:
-    if t1 <= t0 {
-        panic!("t1 must be greater than t0");
-    }
-    if n < 3 {
-        panic!("frame must have at least 3 vertices");
-    }
-
-    struct FrontierVert {
-        vert: Vertex, // Vertex position
-        t: f32, // Parameter value; f(t) should equal vert
-        frame_idx: usize, // Index of 'frame' this sits in the trajectory of
-        mesh_idx: usize, // Index of this vertex in the mesh
-        neighbor1: usize, // Index of 'frontier' of one neighbor
-        neighbor2: usize, // Index of 'frontier' of other neighbor
-    };
-
-    // Init 'frontier' with each 'frame' vertex, and start it at t=t0.
-    let mut frontier: Vec<FrontierVert> = frame.iter().enumerate().map(|(i,v)| FrontierVert {
-        vert: *v,
-        t: t0,
-        frame_idx: i,
-        mesh_idx: i,
-        neighbor1: (i - 1) % n,
-        neighbor2: (i + 1) % n,
-    }).collect();
-    // Every vertex in 'frontier' has a trajectory it follows - which is
-    // simply the position as we transform the original vertex by f(t),
-    // and increment t through the range [t0, t1].
-    //
-    // The goal is to advance the vertices, one at a time, building up
-    // new triangles every time we advance one, until each vertex
-    // reaches t=t1 - in a way that forms the mesh we want.
-
-    // That mesh will be built up here, starting with frame vertices:
-    // (note initial value of mesh_idx)
-    let mut verts: Vec<Vertex> = frame.clone();
-    let mut faces: Vec<usize> = vec![];
-
-    while !frontier.is_empty() {
-
-        // Pick a vertex to advance.
-        //
-        // Heuristic for now: pick the 'furthest back' (lowest t)
-        let (i,v) = frontier.iter().enumerate().min_by(|(_,f), (_, g)|
-            f.t.partial_cmp(&g.t).unwrap_or(std::cmp::Ordering::Equal)).unwrap();
-        // TODO: Make this less ugly?
-
-        if v.t >= t1 {
-            break;
-        }
-
-        println!("DEBUG: Moving vertex {}, {:?} (t={}, frame_idx={})", i, v.vert, v.t, v.frame_idx);
-
-        let mut dt = (t1 - t0) / 100.0;
-        let vf = frame[v.frame_idx];
-        for iter in 0..100 {
-            // Consider an edge from f(v.t)*vf to f(v.t + dt)*vf.
-            // These two endpoints have zero error from the trajectory
-            // (because they are directly on it).
-            //
-            // If we assume some continuity in f, then we can guess that
-            // the worst error occurs at the midpoint of the edge:
-            let edge_mid = 0.5*(f(v.t).mtx + f(v.t + dt).mtx)*vf;
-            // ...relative to the trajectory midpoint:
-            let traj_mid = f(v.t + dt/2.0).mtx * vf;
-            let err = (edge_mid - traj_mid).norm();
-
-            println!("DEBUG iter {}: dt={}, edge_mid={:?}, traj_mid={:?}, err={}", iter, dt, edge_mid, traj_mid, err);
-
-            let r = (err - max_err).abs() / max_err;
-            if r < 0.10 {
-                println!("err close enough");
-                break;
-            } else if err > max_err {
-                dt = dt / 2.0;
-                println!("err > max_err, reducing dt to {}", dt);
-            } else {
-                dt = dt * 1.2;
-                println!("err < max_err, increasing dt to {}", dt);
-            }
-        }
-
-        let t = v.t + dt;
-        let v_next = f(t).mtx * vf;
-
-        // Add this vertex to our mesh:
-        let pos = verts.len();
-        verts.push(v_next);
-        // There are 3 other vertices of interest: the one we started
-        // from (v) and its two neighbors. We make two edges - one on
-        // each side of the edge (v, v_next).
-        faces.append(&mut vec![
-            v.mesh_idx, pos, frontier[v.neighbor1].mesh_idx,
-            pos, v.mesh_idx, frontier[v.neighbor2].mesh_idx,
-        ]);
-
-        // Replace this vertex in the frontier:
-        frontier[i] = FrontierVert {
-            vert: v_next,
-            frame_idx: v.frame_idx,
-            mesh_idx: pos,
-            t: t,
-            neighbor1: v.neighbor1,
-            neighbor2: v.neighbor2,
-        }
-    }
-
-    // Move this vertex further along, i.e. t + dt.  (dt is set by
-    // the furthest we can go while remaining within 'err', i.e. when we
-    // make our connections we look at how far points on the *edges*
-    // diverge from the trajectory of the  continuous transformation).
-
-    // Add this vertex to the mesh, and connect it to: the vertex we
-    // started with, and the two neighbors of that vertex.
-
-    // Repeat at "Pick a vertex...".
-
-    // Don't move t + dt past t1.  Once a frontier vertex is placed at
-    // that value of t, remove it.
-
-
-    // Missing: Anything about when to subdivide an edge.
-    // If I assume a good criterion of "when" to subdivide an edge, the
-    // "how" is straightforward: find the edge's two neighbors in the
-    // frontier. Trace them back to their 'original' vertices at t=t0
-    // (these should just be stored alongside each frontier member),
-    // produce an interpolated vertex. Produce an interpolated t from
-    // respective t of the two neighbors in the frontier; use that t
-    // to move the 'interpolated' vertex along its trajectory.
-    //
-    // Add new vertex to mesh (and make the necessary connections)
-    // and to frontier.
-
-    // But still missing from that: When do I collapse a subdivision
-    // back down?
-    return Mesh { verts, faces };
-}

src/util.rs

@@ -1,6 +1,6 @@
+use crate::mesh::Mesh;
+use crate::xform::Vertex;
 use std::ops::Range;
-use crate::mesh::{Mesh, MeshFunc, VertexUnion};
-use crate::xform::{Vertex};
 
 /// This is like `vec!`, but it can handle elements that are given
 /// with `@var element` rather than `element`, e.g. like
@@ -42,7 +42,8 @@ impl<T> VecExt<T> for Vec<T> {
 /// (thus, the returned length will be `count*p.len()`).
 pub fn subdivide_cycle(p: &Vec<Vertex>, count: usize) -> Vec<Vertex> {
     let n = p.len();
-    (0..n).map(|i| {
+    (0..n)
+        .map(|i| {
             // The inner loop is interpolating between v1 and v2:
             let v1 = &p[i];
             let v2 = &p[(i + 1) % n];
@@ -51,7 +52,9 @@ pub fn subdivide_cycle(p: &Vec<Vertex>, count: usize) -> Vec<Vertex> {
                 let f = (j as f32) / (count as f32);
                 v1 * (1.0 - f) + v2 * f
             })
-    }).flatten().collect()
+        })
+        .flatten()
+        .collect()
 }
 // TODO: This can be generalized to an iterator or to IntoIterator
 // trait bound
@@ -61,28 +64,27 @@ pub fn parallel_zigzag_faces(r1: Range<usize>, r2: Range<usize>) -> Vec<usize> {
     if (r2.end - r2.start) != count {
         panic!("Ranges must have the same size");
     }
-    if (r2.end > r1.start && r2.end < r1.end) ||
-        (r1.end > r2.start && r1.end < r2.end) {
+    if (r2.end > r1.start && r2.end < r1.end) || (r1.end > r2.start && r1.end < r2.end) {
         panic!("Ranges cannot overlap");
     }
 
-    (0..count).map(|i0| {
+    (0..count)
+        .map(|i0| {
             // i0 is an *offset* for the 'current' index.
             // i1 is for the 'next' index, wrapping back to 0.
             let i1 = (i0 + 1) % count;
             vec![
                 // Mind winding order!
-            r1.start + i1, r2.start + i0, r1.start + i0,
-            r2.start + i1, r2.start + i0, r1.start + i1,
+                r1.start + i1,
+                r2.start + i0,
+                r1.start + i0,
+                r2.start + i1,
+                r2.start + i0,
+                r1.start + i1,
             ]
-    }).flatten().collect()
-}
-
-pub fn parallel_zigzag(verts: Vec<VertexUnion>, main: Range<usize>, parent: Range<usize>) -> MeshFunc {
-    MeshFunc {
-        verts: verts,
-        faces: parallel_zigzag_faces(main, parent),
-    }
+        })
+        .flatten()
+        .collect()
 }
 
 pub fn parallel_zigzag_mesh(verts: Vec<Vertex>, main: Range<usize>, parent: Range<usize>) -> Mesh {
@@ -93,7 +95,9 @@ pub fn parallel_zigzag_mesh(verts: Vec<Vertex>, main: Range<usize>, parent: Rang
 }
 
 pub fn parallel_zigzag2<T, U>(main: T, parent: U) -> Vec<usize>
-where T: IntoIterator<Item=usize>, U: IntoIterator<Item=usize>
+where
+    T: IntoIterator<Item = usize>,
+    U: IntoIterator<Item = usize>,
 {
     let m: Vec<usize> = main.into_iter().collect();
     let p: Vec<usize> = parent.into_iter().collect();
@@ -102,16 +106,18 @@ where T: IntoIterator<Item=usize>, U: IntoIterator<Item=usize>
         panic!("Vectors must be the same size!")
     }
 
-    (0..l).map(|i0| {
+    (0..l)
+        .map(|i0| {
             // i0 is an *offset* for the 'current' index.
             // i1 is for the 'next' index, wrapping back to 0.
             let i1 = (i0 + 1) % l;
             vec![
                 // Mind winding order!
-            m[i1], p[i0], m[i0],
-            p[i1], p[i0], m[i1],
+                m[i1], p[i0], m[i0], p[i1], p[i0], m[i1],
             ]
-    }).flatten().collect()
+        })
+        .flatten()
+        .collect()
 }
 
 pub fn centroid(verts: &Vec<Vertex>) -> Vertex {
@@ -125,17 +131,22 @@ pub fn centroid(verts: &Vec<Vertex>) -> Vertex {
 }
 
 pub fn connect_convex(range: Range<usize>, target: usize, as_parent: bool) -> Vec<usize> {
-
     let count = range.end - range.start;
     if as_parent {
-        (0..count).map(|i0| {
+        (0..count)
+            .map(|i0| {
                 let i1 = (i0 + 1) % count;
                 vec![range.start + i1, range.start + i0, target]
-        }).flatten().collect()
+            })
+            .flatten()
+            .collect()
     } else {
-        (0..count).map(|i0| {
+        (0..count)
+            .map(|i0| {
                 let i1 = (i0 + 1) % count;
                 vec![range.start + i0, range.start + i1, target]
-        }).flatten().collect()
+            })
+            .flatten()
+            .collect()
     }
 }