fix(Geometry): new distance functions between triangles

Author: panquez

include/geode/geometry/distance.hpp

@@ -136,6 +136,33 @@ namespace geode
         opengeode_geometry_api segment_triangle_distance(
             const Segment3D& segment, const Triangle3D& triangle );
 
+    /*!
+     * Compute the smallest distance between two triangles
+     * @return a tuple containing:
+     * - the smallest distance.
+     * - the closest point on the first triangle.
+     * - the closest point on the second triangle.
+     */
+    [[nodiscard]] std::tuple< double, Point3D, Point3D >
+        opengeode_geometry_api triangle_triangle_distance(
+            const Triangle3D& triangle0, const Triangle3D& triangle1 );
+
+    /*!
+     * Compute the smallest distance between two triangles
+     * @details if the two triangles are the same, return nullopt. Only non
+     * conformal part of triangles are considered in computation of distance,
+     * i.e. if the triangle have a common point, it iterates on opposite
+     * segment, if the triangle have a common edge, it computes distance with
+     * the opposite point
+     * @return a tuple containing:
+     * - the smallest distance.
+     * - the closest point on the first triangle.
+     * - the closest point on the second triangle.
+     */
+    [[nodiscard]] std::optional< std::tuple< double, Point3D, Point3D > >
+        opengeode_geometry_api triangle_triangle_non_conformal_distance(
+            const Triangle3D& triangle0, const Triangle3D& triangle1 );
+
     /*!
      * Compute the distance between a point and a tetrahedron
      * @return a tuple containing:

src/geode/geometry/distance.cpp

@@ -339,6 +339,79 @@ namespace
             geode::point_point_distance( point, closest_point );
         return std::make_tuple( distance, std::move( closest_point ) );
     }
+
+    std::pair< std::vector< geode::local_index_t >,
+        std::vector< geode::local_index_t > >
+        find_non_colocated_triangles_points( const geode::Triangle3D& triangle0,
+            const geode::Triangle3D& triangle1 )
+    {
+        std::pair< std::array< bool, 3 >, std::array< bool, 3 > > colocated{
+            { false, false, false }, { false, false, false }
+        };
+        const auto& vertices0 = triangle0.vertices();
+        const auto& vertices1 = triangle1.vertices();
+        for( const auto vertex0 : geode::LRange{ 3 } )
+        {
+            for( const auto vertex1 : geode::LRange{ 3 } )
+            {
+                if( geode::point_point_distance(
+                        vertices0[vertex0].get(), vertices1[vertex1].get() )
+                    <= geode::GLOBAL_EPSILON )
+                {
+                    colocated.first[vertex0] = true;
+                    colocated.second[vertex1] = true;
+                }
+            }
+        }
+
+        std::pair< std::vector< geode::local_index_t >,
+            std::vector< geode::local_index_t > >
+            result;
+        for( const auto v : geode::LRange{ 3 } )
+        {
+            if( !colocated.first[v] )
+            {
+                result.first.push_back( v );
+            }
+            if( !colocated.second[v] )
+            {
+                result.second.push_back( v );
+            }
+        }
+        return result;
+    }
+
+    std::tuple< double, geode::Point3D, geode::Point3D > test_close_triangles(
+        const std::vector< geode::local_index_t >& non_colocated_points,
+        const geode::Triangle3D& base_triangle,
+        const geode::Triangle3D& other_triangle )
+    {
+        const auto& base_vertices = base_triangle.vertices();
+        double min_distance{ std::numeric_limits< double >::max() };
+        geode::Point3D point0;
+        geode::Point3D point1;
+        for( const auto vertex0 : non_colocated_points )
+        {
+            for( const auto vertex1 : non_colocated_points )
+            {
+                if( vertex0 == vertex1 )
+                {
+                    continue;
+                }
+                const geode::Segment3D edge{ base_vertices[vertex0],
+                    base_vertices[vertex1] };
+                auto [cur_distance, cur_pt0, cur_pt1] =
+                    geode::segment_triangle_distance( edge, other_triangle );
+                if( cur_distance < min_distance )
+                {
+                    min_distance = cur_distance;
+                    point0 = cur_pt0;
+                    point1 = cur_pt1;
+                }
+            }
+        }
+        return std::make_tuple( min_distance, point0, point1 );
+    }
 } // namespace
 
 namespace geode
@@ -923,6 +996,112 @@ namespace geode
             closest_on_segment, closest_on_triangle );
     }
 
+    std::tuple< double, Point3D, Point3D >
+        opengeode_geometry_api triangle_triangle_distance(
+            const Triangle3D& triangle0, const Triangle3D& triangle1 )
+    {
+        const auto non_colocated_points =
+            find_non_colocated_triangles_points( triangle0, triangle1 );
+        if( non_colocated_points.first.size() < 3 )
+        {
+            for( const auto v : LRange{ 3 } )
+            {
+                if( !absl::c_contains( non_colocated_points.first, v ) )
+                {
+                    auto& pt0 = triangle0.vertices()[v].get();
+                    auto [distance, pt1] =
+                        point_triangle_distance( pt0, triangle1 );
+                    return std::make_tuple( distance, pt0, pt1 );
+                }
+            }
+        }
+        if( non_colocated_points.second.size() < 3 )
+        {
+            for( const auto v : LRange{ 3 } )
+            {
+                if( !absl::c_contains( non_colocated_points.second, v ) )
+                {
+                    auto& pt1 = triangle1.vertices()[v].get();
+                    auto [distance, pt0] =
+                        point_triangle_distance( pt1, triangle0 );
+                    return std::make_tuple( distance, pt0, pt1 );
+                }
+            }
+        }
+        auto [cur_distance0, cur_pt00, cur_pt01] = test_close_triangles(
+            non_colocated_points.first, triangle0, triangle1 );
+        auto [cur_distance1, cur_pt11, cur_pt10] = test_close_triangles(
+            non_colocated_points.second, triangle1, triangle0 );
+        if( cur_distance0 < cur_distance1 )
+        {
+            return std::make_tuple( cur_distance0, cur_pt00, cur_pt01 );
+        }
+        return std::make_tuple( cur_distance1, cur_pt10, cur_pt11 );
+    }
+
+    std::optional< std::tuple< double, Point3D, Point3D > >
+        triangle_triangle_non_conformal_distance(
+            const Triangle3D& triangle0, const Triangle3D& triangle1 )
+    {
+        const auto non_colocated_points =
+            find_non_colocated_triangles_points( triangle0, triangle1 );
+        if( non_colocated_points.first.size() == 0
+            || non_colocated_points.second.size() == 0 )
+        {
+            return std::nullopt;
+        }
+        const auto& vertices0 = triangle0.vertices();
+        const auto& vertices1 = triangle1.vertices();
+        double min_distance{ std::numeric_limits< double >::max() };
+        Point3D point0;
+        Point3D point1;
+        if( non_colocated_points.first.size() == 1 )
+        {
+            auto [cur_distance, cur_pt] = point_triangle_distance(
+                vertices0[non_colocated_points.first[0]].get(), triangle1 );
+            if( cur_distance < min_distance )
+            {
+                min_distance = cur_distance;
+                point0 = vertices0[non_colocated_points.first[0]].get();
+                point1 = cur_pt;
+            }
+        }
+        if( non_colocated_points.second.size() == 1 )
+        {
+            auto [cur_distance, cur_pt] = point_triangle_distance(
+                vertices1[non_colocated_points.second[0]].get(), triangle0 );
+            if( cur_distance < min_distance )
+            {
+                min_distance = cur_distance;
+                point0 = cur_pt;
+                point1 = vertices1[non_colocated_points.second[0]].get();
+            }
+        }
+        if( non_colocated_points.first.size() > 1 )
+        {
+            auto [cur_distance, cur_pt0, cur_pt1] = test_close_triangles(
+                non_colocated_points.first, triangle0, triangle1 );
+            if( cur_distance < min_distance )
+            {
+                min_distance = cur_distance;
+                point0 = cur_pt0;
+                point1 = cur_pt1;
+            }
+        }
+        if( non_colocated_points.second.size() > 1 )
+        {
+            auto [cur_distance, cur_pt1, cur_pt0] = test_close_triangles(
+                non_colocated_points.second, triangle1, triangle0 );
+            if( cur_distance < min_distance )
+            {
+                min_distance = cur_distance;
+                point0 = cur_pt0;
+                point1 = cur_pt1;
+            }
+        }
+        return std::make_tuple( min_distance, point0, point1 );
+    }
+
     std::tuple< double, Point3D > point_tetrahedron_distance(
         const Point3D& point, const Tetrahedron& tetra )
     {
@@ -1048,7 +1227,8 @@ namespace geode
             }
             OPENGEODE_ASSERT(
                 !circle.plane().normal().inexact_equal( other_direction ),
-                "[point_circle_distance] Problem while getting circle nearest "
+                "[point_circle_distance] Problem while getting circle "
+                "nearest "
                 "point" );
             const Vector3D other_projected_on_plane =
                 other_direction