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Use tighter initialization during computation of subdivided faces' local bounds

This commit is contained in:
Mael Rouxel-Labbé 2022-03-31 12:48:44 +02:00
parent fe21d98345
commit bd29b976f5
1 changed files with 11 additions and 13 deletions
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24
Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
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@ -1670,22 +1670,20 @@ bounded_error_squared_Hausdorff_distance_impl(const TriangleMesh1& tm1,
// (We also have that error_bound is a lower bound.)
const Bbox_3 sub_t1_bbox = sub_triangles[i].bbox();
// Because:
// The lower bound is:
// h_lower(t1, TM2) := max_{v in t1} min_{t2 in TM2} d(v, t2)
// adding more vertices can only increase the max (and the lower bound).
//
// The upper bound is:
// h_upper(t1, TM2) := min_{t2 in TM2} max_{v in t1} d(v, t2)
// If t2m is the face of TM2 realizing the minimum of max_{v in t1} d(v, t2),
// then subdividing t1 can only decrease this upper bound: let v' be a new vertex v'
// of a triangle subdividing t1 is such that
// min_{t2 in TM2} d(v', t2) > h_upper(t1, TM2)
// Because the maximum of the distance over t1 is necessarily reached at a vertex,
// there must exist a vertex v1 in t1 such that d(v1, t2) > d(v', t2), which contradicts
// the definition of v'.
// Thus, subdivision can only decrease the upper bound.
// @FIXME using 'triangle_bounds' actually create bugs?...
Local_bounds<Kernel, Face_handle_1, Face_handle_2> bounds(infinity_value);
// The value max_{p in t1} d(p, t2) is realized at a vertex of t1.
// Thus, when splitting t1 into four subtriangles, the distance at the three new vertices
// is smaller than max_{v in t1} d(v, t2)
// Thus, subdivision can only decrease the min, and the upper bound.
Local_bounds<Kernel, Face_handle_1, Face_handle_2> bounds(triangle_bounds.upper);
// Ensure 'uface' is initialized in case the upper bound is not changed by the subdivision
bounds.tm2_uface = triangle_bounds.tm2_uface;
TM2_hd_traits traversal_traits_tm2(sub_t1_bbox, tm2, vpm2, bounds, global_bounds, infinity_value);
tm2_tree.traversal_with_priority(sub_triangles[i], traversal_traits_tm2);