Nested<CircleArc> canonicalize_circle_arcs(Nested<const CircleArc> polys) {
// Find the minimal point in each polygon under lexicographic order
Array<int> mins(polys.size());
for (int p=0;p<polys.size();p++) {
const auto poly = polys[p];
for (int i=1;i<poly.size();i++)
if (lex_less(poly[i].x,poly[mins[p]].x))
mins[p] = i;
}
// Sort the polygons
struct Order {
Nested<const CircleArc> polys;
RawArray<const int> mins;
Order(Nested<const CircleArc> polys, RawArray<const int> mins)
: polys(polys), mins(mins) {}
bool operator()(int i,int j) const {
return lex_less(polys(i,mins[i]).x,polys(j,mins[j]).x);
}
};
Array<int> order = arange(polys.size()).copy();
sort(order,Order(polys,mins));
// Copy into new array
Nested<CircleArc> new_polys(polys.sizes().subset(order).copy(),uninit);
for (int p=0;p<polys.size();p++) {
const int base = mins[order[p]];
const auto poly = polys[order[p]];
const auto new_poly = new_polys[p];
for (int i=0;i<poly.size();i++)
new_poly[i] = poly[(i+base)%poly.size()];
}
return new_polys;
}
Ref<SparseMatrix> TriangleSubdivision::loop_matrix() const {
if (loop_matrix_)
return ref(loop_matrix_);
// Build matrix of Loop subdivision weights
Hashtable<Vector<int,2>,T> A;
int offset = coarse_mesh->nodes();
RawArray<const Vector<int,2> > segments = coarse_mesh->segment_soup()->elements;
Nested<const int> neighbors = coarse_mesh->sorted_neighbors();
Nested<const int> boundary_neighbors = coarse_mesh->boundary_mesh()->neighbors();
unordered_set<int> corners_set(corners.begin(),corners.end());
// Fill in node weights
for (int i=0;i<offset;i++){
if (!neighbors.valid(i) || !neighbors.size(i) || corners_set.count(i) || (boundary_neighbors.valid(i) && boundary_neighbors.size(i) && boundary_neighbors.size(i)!=2))
A.set(vec(i,i),1);
else if (boundary_neighbors.valid(i) && boundary_neighbors.size(i)==2) { // Regular boundary node
A.set(vec(i,i),(T).75);
for (int a=0;a<2;a++)
A.set(vec(i,boundary_neighbors(i,a)),(T).125);
} else { // Interior node
RawArray<const int> ni = neighbors[i];
T alpha = new_loop_alpha(ni.size());
A.set(vec(i,i),alpha);
T other = (1-alpha)/ni.size();
for (int j : ni)
A.set(vec(i,j),other);
}
}
// Fill in edge values
for (int s=0;s<segments.size();s++) {
int i = offset+s;
Vector<int,2> e = segments[s];
RawArray<const int> n[2] = {neighbors.valid(e[0])?neighbors[e[0]]:RawArray<const int>(),
neighbors.valid(e[1])?neighbors[e[1]]:RawArray<const int>()};
if (boundary_neighbors.valid(e[0]) && boundary_neighbors.valid(e[1]) && boundary_neighbors.size(e[0]) && boundary_neighbors.size(e[1]) && boundary_neighbors[e[0]].contains(e[1])) // Boundary edge
for (int a=0;a<2;a++)
A.set(vec(i,e[a]),(T).5);
else if (n[0].size()==6 && n[1].size()==6) { // Edge between regular vertices
int j = n[0].find(e[1]);
int c[2] = {n[0][(j-1+n[0].size())%n[0].size()],
n[0][(j+1)%n[0].size()]};
for (int a=0;a<2;a++) {
A.set(vec(i,e[a]),(T).375);
A.set(vec(i,c[a]),(T).125);
}
} else { // Edge between one or two irregular vertices
T factor = n[0].size()!=6 && n[1].size()!=6 ?.5:1;
for (int k=0;k<2;k++)
if (n[k].size()!=6) {
A[vec(i,e[k])] += factor*(1-new_loop_beta(n[k].size()));
int start = n[k].find(e[1-k]);
for (int j=0;j<n[k].size();j++)
A[vec(i,n[k][(start+j)%n[k].size()])] += factor*new_loop_weight(n[k].size(),j);
}
}
}
// Finalize construction
loop_matrix_ = new_<SparseMatrix>(A,vec(offset+segments.size(),offset));
return ref(loop_matrix_);
}
static void random_circle_quantize_test(int seed) {
auto r = new_<Random>(seed);
{
// First check that we can split without hitting any asserts
const auto sizes = vec(1.e-3,1.e1,1.e3,1.e7);
Nested<CircleArc, false> arcs;
arcs.append(make_circle(Vec2(0,0),Vec2(1,0)));
for(const auto& s : sizes) {
for(int i = 0; i < 200; ++i) {
arcs.append(make_circle(s*r->unit_ball<Vec2>(),s*r->unit_ball<Vec2>()));
}
}
// Take the union and make sure we don't hit any asserts
circle_arc_union(arcs);
}
{
// Build a bunch of arcs that don't touch
const auto log_options = vec(1.e-3,1.e-1,1.e1,1.e3);
const auto max_bounds = Box<Vec2>(Vec2(0.,0.)).thickened(1.e1 * log_options.max());
const real spacing = 1e-5*max_bounds.sizes().max();
const real max_x = max_bounds.max.x;
real curr_x = max_bounds.min.x;
Nested<CircleArc, false> arcs;
for(int i = 0; i < 50; ++i) {
const real remaining = max_x - curr_x;
if(remaining < spacing)
break;
const real log_choice = log_options[r->uniform<int>(0, log_options.size())];
real next_r = r->uniform<real>(0., min(log_choice, remaining));
arcs.append(make_circle(Vec2(curr_x, 0.),Vec2(curr_x+next_r, 0.)));
curr_x += next_r + spacing;
}
// Take the union and make sure we don't hit any asserts
auto unioned = circle_arc_union(arcs);
// If range of sizes is very large, some arcs could be filtered out if they are smaller than quantization threshold...
GEODE_ASSERT(unioned.size() <= arcs.size());
}
}
Nested<EV> exact_split_polygons(Nested<const EV> polys, const int depth) {
IntervalScope scope;
RawArray<const EV> X = polys.flat;
// We index segments by the index of their first point in X. For convenience, we make an array to keep track of wraparounds.
Array<int> next = (arange(X.size())+1).copy();
for (int i=0;i<polys.size();i++) {
GEODE_ASSERT(polys.size(i)>=3,"Degenerate polygons are not allowed");
next[polys.offsets[i+1]-1] = polys.offsets[i];
}
// Compute all nontrivial intersections between segments
struct Pairs {
const BoxTree<EV>& tree;
RawArray<const int> next;
RawArray<const EV> X;
Array<Vector<int,2>> pairs;
Pairs(const BoxTree<EV>& tree, RawArray<const int> next, RawArray<const EV> X)
: tree(tree), next(next), X(X) {}
bool cull(const int n) const { return false; }
bool cull(const int n0, const int box1) const { return false; }
void leaf(const int n) const { assert(tree.prims(n).size()==1); }
void leaf(const int n0, const int n1) {
assert(tree.prims(n0).size()==1 && tree.prims(n1).size()==1);
const int i0 = tree.prims(n0)[0], i1 = next[i0],
j0 = tree.prims(n1)[0], j1 = next[j0];
if (!(i0==j0 || i0==j1 || i1==j0 || i1==j1)) {
const auto a0 = Perturbed2(i0,X[i0]), a1 = Perturbed2(i1,X[i1]),
b0 = Perturbed2(j0,X[j0]), b1 = Perturbed2(j1,X[j1]);
if (segments_intersect(a0,a1,b0,b1))
pairs.append(vec(i0,j0));
}
}
};
const auto tree = new_<BoxTree<EV>>(segment_boxes(next,X),1);
Pairs pairs(tree,next,X);
double_traverse(*tree,pairs);
// Group intersections by segment. Each pair is added twice: once for each order.
Array<int> counts(X.size());
for (auto pair : pairs.pairs) {
counts[pair.x]++;
counts[pair.y]++;
}
Nested<int> others(counts,uninit);
for (auto pair : pairs.pairs) {
others(pair.x,--counts[pair.x]) = pair.y;
others(pair.y,--counts[pair.y]) = pair.x;
}
pairs.pairs.clean_memory();
counts.clean_memory();
// Walk all original polygons, recording which subsegments occur in the final result
Hashtable<Vector<int,2>,int> graph; // If (i,j) -> k, the output contains the portion of segment j from ij to jk
for (const int p : range(polys.size())) {
const auto poly = range(polys.offsets[p],polys.offsets[p+1]);
// Compute the depth of the first point in the polygon by firing a ray along the positive x axis.
struct Depth {
const BoxTree<EV>& tree;
RawArray<const int> next;
RawArray<const EV> X;
const Perturbed2 start;
int depth;
Depth(const BoxTree<EV>& tree, RawArray<const int> next, RawArray<const EV> X, const int prev, const int i)
: tree(tree), next(next), X(X)
, start(i,X[i])
// If we intersect no other segments, the depth depends on the orientation of direction = (1,0) relative to segments prev and i
, depth(-!local_outwards_x_axis(Perturbed2(prev,X[prev]),start,Perturbed2(next[i],X[next[i]]))) {}
bool cull(const int n) const {
const auto box = tree.boxes(n);
return box.max.x<start.value().x || box.max.y<start.value().y || box.min.y>start.value().y;
}
void leaf(const int n) {
assert(tree.prims(n).size()==1);
const int i0 = tree.prims(n)[0], i1 = next[i0];
if (start.seed()!=i0 && start.seed()!=i1) {
const auto a0 = Perturbed2(i0,X[i0]),
a1 = Perturbed2(i1,X[i1]);
const bool above0 = upwards(start,a0),
above1 = upwards(start,a1);
if (above0!=above1 && above1==triangle_oriented(a0,a1,start))
depth += above1 ? 1 : -1;
}
}
};
Depth ray(tree,next,X,poly.back(),poly[0]);
single_traverse(*tree,ray);
// Walk around the polygon, recording all subsegments at the desired depth
int delta = ray.depth-depth;
int prev = poly.back();
for (const int i : poly) {
const int j = next[i];
const Vector<Perturbed2,2> segment(Perturbed2(i,X[i]),Perturbed2(j,X[j]));
const auto other = others[i];
// Sort intersections along this segment
if (other.size() > 1) {
struct PairOrder {
RawArray<const int> next;
RawArray<const EV> X;
const Vector<Perturbed2,2> segment;
PairOrder(RawArray<const int> next, RawArray<const EV> X, const Vector<Perturbed2,2>& segment)
: next(next), X(X), segment(segment) {}
bool operator()(const int j, const int k) const {
if (j==k)
return false;
const int jn = next[j],
kn = next[k];
return segment_intersections_ordered(segment.x,segment.y,
Perturbed2(j,X[j]),Perturbed2(jn,X[jn]),
Perturbed2(k,X[k]),Perturbed2(kn,X[kn]));
}
};
sort(other,PairOrder(next,X,segment));
}
// Walk through each intersection of this segment, updating delta as we go and remembering the subsegment if it has the right depth
for (const int o : other) {
if (!delta)
graph.set(vec(prev,i),o);
const int on = next[o];
delta += segment_directions_oriented(segment.x,segment.y,Perturbed2(o,X[o]),Perturbed2(on,X[on])) ? -1 : 1;
prev = o;
}
if (!delta)
graph.set(vec(prev,i),next[i]);
// Advance to the next segment
prev = i;
}
}
// Walk the graph to produce output polygons
Hashtable<Vector<int,2>> seen;
Nested<EV,false> output;
for (const auto& start : graph)
if (seen.set(start.x)) {
auto ij = start.x;
for (;;) {
const int i = ij.x, j = ij.y, in = next[i], jn = next[j];
output.flat.append(j==next[i] ? X[j] : segment_segment_intersection(Perturbed2(i,X[i]),Perturbed2(in,X[in]),Perturbed2(j,X[j]),Perturbed2(jn,X[jn])));
ij = vec(j,graph.get(ij));
if (ij == start.x)
break;
seen.set(ij);
}
output.offsets.append(output.flat.size());
}
return output;
}
