prosha/src/dcel.rs

753 lines
28 KiB
Rust

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,
}
}
}