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-rw-r--r--core/math/basis.cpp25
-rw-r--r--core/math/basis.h4
-rw-r--r--core/math/face3.cpp40
-rw-r--r--core/math/face3.h5
-rw-r--r--core/math/geometry_2d.cpp35
-rw-r--r--core/math/geometry_2d.h1
-rw-r--r--core/math/geometry_3d.cpp145
-rw-r--r--core/math/geometry_3d.h2
-rw-r--r--core/math/plane.h2
-rw-r--r--core/math/transform_2d.cpp6
-rw-r--r--core/math/transform_2d.h1
-rw-r--r--core/math/triangle_mesh.cpp196
-rw-r--r--core/math/triangle_mesh.h2
13 files changed, 2 insertions, 462 deletions
diff --git a/core/math/basis.cpp b/core/math/basis.cpp
index 39e383fb49..234a4ddb79 100644
--- a/core/math/basis.cpp
+++ b/core/math/basis.cpp
@@ -36,23 +36,6 @@
#define cofac(row1, col1, row2, col2) \
(rows[row1][col1] * rows[row2][col2] - rows[row1][col2] * rows[row2][col1])
-void Basis::from_z(const Vector3 &p_z) {
- if (Math::abs(p_z.z) > (real_t)Math_SQRT12) {
- // choose p in y-z plane
- real_t a = p_z[1] * p_z[1] + p_z[2] * p_z[2];
- real_t k = 1.0f / Math::sqrt(a);
- rows[0] = Vector3(0, -p_z[2] * k, p_z[1] * k);
- rows[1] = Vector3(a * k, -p_z[0] * rows[0][2], p_z[0] * rows[0][1]);
- } else {
- // choose p in x-y plane
- real_t a = p_z.x * p_z.x + p_z.y * p_z.y;
- real_t k = 1.0f / Math::sqrt(a);
- rows[0] = Vector3(-p_z.y * k, p_z.x * k, 0);
- rows[1] = Vector3(-p_z.z * rows[0].y, p_z.z * rows[0].x, a * k);
- }
- rows[2] = p_z;
-}
-
void Basis::invert() {
real_t co[3] = {
cofac(1, 1, 2, 2), cofac(1, 2, 2, 0), cofac(1, 0, 2, 1)
@@ -271,14 +254,6 @@ float Basis::get_uniform_scale() const {
return (rows[0].length() + rows[1].length() + rows[2].length()) / 3.0f;
}
-void Basis::make_scale_uniform() {
- float l = (rows[0].length() + rows[1].length() + rows[2].length()) / 3.0f;
- for (int i = 0; i < 3; i++) {
- rows[i].normalize();
- rows[i] *= l;
- }
-}
-
Basis Basis::scaled_local(const Vector3 &p_scale) const {
return (*this) * Basis::from_scale(p_scale);
}
diff --git a/core/math/basis.h b/core/math/basis.h
index b3197dbc84..bbc1d40469 100644
--- a/core/math/basis.h
+++ b/core/math/basis.h
@@ -56,8 +56,6 @@ struct _NO_DISCARD_ Basis {
_FORCE_INLINE_ real_t determinant() const;
- void from_z(const Vector3 &p_z);
-
void rotate(const Vector3 &p_axis, real_t p_angle);
Basis rotated(const Vector3 &p_axis, real_t p_angle) const;
@@ -101,8 +99,6 @@ struct _NO_DISCARD_ Basis {
void scale_orthogonal(const Vector3 &p_scale);
Basis scaled_orthogonal(const Vector3 &p_scale) const;
-
- void make_scale_uniform();
float get_uniform_scale() const;
Vector3 get_scale() const;
diff --git a/core/math/face3.cpp b/core/math/face3.cpp
index e53bbf872b..1dff0ee4a6 100644
--- a/core/math/face3.cpp
+++ b/core/math/face3.cpp
@@ -120,36 +120,6 @@ bool Face3::is_degenerate() const {
return (normal.length_squared() < (real_t)CMP_EPSILON2);
}
-Face3::Side Face3::get_side_of(const Face3 &p_face, ClockDirection p_clock_dir) const {
- int over = 0, under = 0;
-
- Plane plane = get_plane(p_clock_dir);
-
- for (int i = 0; i < 3; i++) {
- const Vector3 &v = p_face.vertex[i];
-
- if (plane.has_point(v)) { //coplanar, don't bother
- continue;
- }
-
- if (plane.is_point_over(v)) {
- over++;
- } else {
- under++;
- }
- }
-
- if (over > 0 && under == 0) {
- return SIDE_OVER;
- } else if (under > 0 && over == 0) {
- return SIDE_UNDER;
- } else if (under == 0 && over == 0) {
- return SIDE_COPLANAR;
- } else {
- return SIDE_SPANNING;
- }
-}
-
Vector3 Face3::get_random_point_inside() const {
real_t a = Math::random(0.0, 1.0);
real_t b = Math::random(0.0, 1.0);
@@ -164,20 +134,10 @@ Plane Face3::get_plane(ClockDirection p_dir) const {
return Plane(vertex[0], vertex[1], vertex[2], p_dir);
}
-Vector3 Face3::get_median_point() const {
- return (vertex[0] + vertex[1] + vertex[2]) / 3.0f;
-}
-
real_t Face3::get_area() const {
return vec3_cross(vertex[0] - vertex[1], vertex[0] - vertex[2]).length() * 0.5f;
}
-ClockDirection Face3::get_clock_dir() const {
- Vector3 normal = vec3_cross(vertex[0] - vertex[1], vertex[0] - vertex[2]);
- //printf("normal is %g,%g,%g x %g,%g,%g- wtfu is %g\n",tofloat(normal.x),tofloat(normal.y),tofloat(normal.z),tofloat(vertex[0].x),tofloat(vertex[0].y),tofloat(vertex[0].z),tofloat( normal.dot( vertex[0] ) ) );
- return (normal.dot(vertex[0]) >= 0) ? CLOCKWISE : COUNTERCLOCKWISE;
-}
-
bool Face3::intersects_aabb(const AABB &p_aabb) const {
/** TEST PLANE **/
if (!p_aabb.intersects_plane(get_plane())) {
diff --git a/core/math/face3.h b/core/math/face3.h
index 3d87de03dc..3dd47d0226 100644
--- a/core/math/face3.h
+++ b/core/math/face3.h
@@ -57,19 +57,14 @@ struct _NO_DISCARD_ Face3 {
Plane get_plane(ClockDirection p_dir = CLOCKWISE) const;
Vector3 get_random_point_inside() const;
- Side get_side_of(const Face3 &p_face, ClockDirection p_clock_dir = CLOCKWISE) const;
-
bool is_degenerate() const;
real_t get_area() const;
- Vector3 get_median_point() const;
Vector3 get_closest_point_to(const Vector3 &p_point) const;
bool intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *p_intersection = nullptr) const;
bool intersects_segment(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *p_intersection = nullptr) const;
- ClockDirection get_clock_dir() const; ///< todo, test if this is returning the proper clockwisity
-
void get_support(const Vector3 &p_normal, const Transform3D &p_transform, Vector3 *p_vertices, int *p_count, int p_max) const;
void project_range(const Vector3 &p_normal, const Transform3D &p_transform, real_t &r_min, real_t &r_max) const;
diff --git a/core/math/geometry_2d.cpp b/core/math/geometry_2d.cpp
index a0b76d31cb..74cb92539a 100644
--- a/core/math/geometry_2d.cpp
+++ b/core/math/geometry_2d.cpp
@@ -320,41 +320,6 @@ Vector<Vector<Point2>> Geometry2D::_polypath_offset(const Vector<Point2> &p_poly
return polypaths;
}
-Vector<Point2i> Geometry2D::pack_rects(const Vector<Size2i> &p_sizes, const Size2i &p_atlas_size) {
- Vector<stbrp_node> nodes;
- nodes.resize(p_atlas_size.width);
-
- stbrp_context context;
- stbrp_init_target(&context, p_atlas_size.width, p_atlas_size.height, nodes.ptrw(), p_atlas_size.width);
-
- Vector<stbrp_rect> rects;
- rects.resize(p_sizes.size());
-
- for (int i = 0; i < p_sizes.size(); i++) {
- rects.write[i].id = 0;
- rects.write[i].w = p_sizes[i].width;
- rects.write[i].h = p_sizes[i].height;
- rects.write[i].x = 0;
- rects.write[i].y = 0;
- rects.write[i].was_packed = 0;
- }
-
- int res = stbrp_pack_rects(&context, rects.ptrw(), rects.size());
- if (res == 0) { //pack failed
- return Vector<Point2i>();
- }
-
- Vector<Point2i> ret;
- ret.resize(p_sizes.size());
-
- for (int i = 0; i < p_sizes.size(); i++) {
- Point2i r(rects[i].x, rects[i].y);
- ret.write[i] = r;
- }
-
- return ret;
-}
-
Vector<Vector3i> Geometry2D::partial_pack_rects(const Vector<Vector2i> &p_sizes, const Size2i &p_atlas_size) {
Vector<stbrp_node> nodes;
nodes.resize(p_atlas_size.width);
diff --git a/core/math/geometry_2d.h b/core/math/geometry_2d.h
index b55aecf85e..0e5702e0af 100644
--- a/core/math/geometry_2d.h
+++ b/core/math/geometry_2d.h
@@ -464,7 +464,6 @@ public:
static Vector<Vector<Vector2>> decompose_polygon_in_convex(Vector<Point2> polygon);
static void make_atlas(const Vector<Size2i> &p_rects, Vector<Point2i> &r_result, Size2i &r_size);
- static Vector<Point2i> pack_rects(const Vector<Size2i> &p_sizes, const Size2i &p_atlas_size);
static Vector<Vector3i> partial_pack_rects(const Vector<Vector2i> &p_sizes, const Size2i &p_atlas_size);
private:
diff --git a/core/math/geometry_3d.cpp b/core/math/geometry_3d.cpp
index 3ac78e0709..51523ea296 100644
--- a/core/math/geometry_3d.cpp
+++ b/core/math/geometry_3d.cpp
@@ -198,149 +198,6 @@ struct _FaceClassify {
_FaceClassify() {}
};
-static bool _connect_faces(_FaceClassify *p_faces, int len, int p_group) {
- // Connect faces, error will occur if an edge is shared between more than 2 faces.
- // Clear connections.
-
- bool error = false;
-
- for (int i = 0; i < len; i++) {
- for (int j = 0; j < 3; j++) {
- p_faces[i].links[j].clear();
- }
- }
-
- for (int i = 0; i < len; i++) {
- if (p_faces[i].group != p_group) {
- continue;
- }
- for (int j = i + 1; j < len; j++) {
- if (p_faces[j].group != p_group) {
- continue;
- }
-
- for (int k = 0; k < 3; k++) {
- Vector3 vi1 = p_faces[i].face.vertex[k];
- Vector3 vi2 = p_faces[i].face.vertex[(k + 1) % 3];
-
- for (int l = 0; l < 3; l++) {
- Vector3 vj2 = p_faces[j].face.vertex[l];
- Vector3 vj1 = p_faces[j].face.vertex[(l + 1) % 3];
-
- if (vi1.distance_to(vj1) < 0.00001f &&
- vi2.distance_to(vj2) < 0.00001f) {
- if (p_faces[i].links[k].face != -1) {
- ERR_PRINT("already linked\n");
- error = true;
- break;
- }
- if (p_faces[j].links[l].face != -1) {
- ERR_PRINT("already linked\n");
- error = true;
- break;
- }
-
- p_faces[i].links[k].face = j;
- p_faces[i].links[k].edge = l;
- p_faces[j].links[l].face = i;
- p_faces[j].links[l].edge = k;
- }
- }
- if (error) {
- break;
- }
- }
- if (error) {
- break;
- }
- }
- if (error) {
- break;
- }
- }
-
- for (int i = 0; i < len; i++) {
- p_faces[i].valid = true;
- for (int j = 0; j < 3; j++) {
- if (p_faces[i].links[j].face == -1) {
- p_faces[i].valid = false;
- }
- }
- }
- return error;
-}
-
-static bool _group_face(_FaceClassify *p_faces, int len, int p_index, int p_group) {
- if (p_faces[p_index].group >= 0) {
- return false;
- }
-
- p_faces[p_index].group = p_group;
-
- for (int i = 0; i < 3; i++) {
- ERR_FAIL_INDEX_V(p_faces[p_index].links[i].face, len, true);
- _group_face(p_faces, len, p_faces[p_index].links[i].face, p_group);
- }
-
- return true;
-}
-
-Vector<Vector<Face3>> Geometry3D::separate_objects(Vector<Face3> p_array) {
- Vector<Vector<Face3>> objects;
-
- int len = p_array.size();
-
- const Face3 *arrayptr = p_array.ptr();
-
- Vector<_FaceClassify> fc;
-
- fc.resize(len);
-
- _FaceClassify *_fcptr = fc.ptrw();
-
- for (int i = 0; i < len; i++) {
- _fcptr[i].face = arrayptr[i];
- }
-
- bool error = _connect_faces(_fcptr, len, -1);
-
- ERR_FAIL_COND_V_MSG(error, Vector<Vector<Face3>>(), "Invalid geometry.");
-
- // Group connected faces in separate objects.
-
- int group = 0;
- for (int i = 0; i < len; i++) {
- if (!_fcptr[i].valid) {
- continue;
- }
- if (_group_face(_fcptr, len, i, group)) {
- group++;
- }
- }
-
- // Group connected faces in separate objects.
-
- for (int i = 0; i < len; i++) {
- _fcptr[i].face = arrayptr[i];
- }
-
- if (group >= 0) {
- objects.resize(group);
- Vector<Face3> *group_faces = objects.ptrw();
-
- for (int i = 0; i < len; i++) {
- if (!_fcptr[i].valid) {
- continue;
- }
- if (_fcptr[i].group >= 0 && _fcptr[i].group < group) {
- group_faces[_fcptr[i].group].push_back(_fcptr[i].face);
- }
- }
- }
-
- return objects;
-}
-
/*** GEOMETRY WRAPPER ***/
enum _CellFlags {
@@ -748,7 +605,7 @@ Geometry3D::MeshData Geometry3D::build_convex_mesh(const Vector<Plane> &p_planes
Vector3 right = p.normal.cross(ref).normalized();
Vector3 up = p.normal.cross(right).normalized();
- Vector3 center = p.center();
+ Vector3 center = p.get_center();
// make a quad clockwise
LocalVector<Vector3> vertices = {
diff --git a/core/math/geometry_3d.h b/core/math/geometry_3d.h
index 6759db5766..99c554fe05 100644
--- a/core/math/geometry_3d.h
+++ b/core/math/geometry_3d.h
@@ -532,8 +532,6 @@ public:
return clipped;
}
- static Vector<Vector<Face3>> separate_objects(Vector<Face3> p_array);
-
// Create a "wrap" that encloses the given geometry.
static Vector<Face3> wrap_geometry(Vector<Face3> p_array, real_t *p_error = nullptr);
diff --git a/core/math/plane.h b/core/math/plane.h
index 3bc7c54b9d..8159f25342 100644
--- a/core/math/plane.h
+++ b/core/math/plane.h
@@ -47,7 +47,7 @@ struct _NO_DISCARD_ Plane {
/* Plane-Point operations */
- _FORCE_INLINE_ Vector3 center() const { return normal * d; }
+ _FORCE_INLINE_ Vector3 get_center() const { return normal * d; }
Vector3 get_any_perpendicular_normal() const;
_FORCE_INLINE_ bool is_point_over(const Vector3 &p_point) const; ///< Point is over plane
diff --git a/core/math/transform_2d.cpp b/core/math/transform_2d.cpp
index 6a7ee32230..910995d717 100644
--- a/core/math/transform_2d.cpp
+++ b/core/math/transform_2d.cpp
@@ -221,12 +221,6 @@ Transform2D Transform2D::operator*(const Transform2D &p_transform) const {
return t;
}
-Transform2D Transform2D::basis_scaled(const Size2 &p_scale) const {
- Transform2D copy = *this;
- copy.scale_basis(p_scale);
- return copy;
-}
-
Transform2D Transform2D::scaled(const Size2 &p_scale) const {
// Equivalent to left multiplication
Transform2D copy = *this;
diff --git a/core/math/transform_2d.h b/core/math/transform_2d.h
index 2a0917c63f..4a17a9db37 100644
--- a/core/math/transform_2d.h
+++ b/core/math/transform_2d.h
@@ -85,7 +85,6 @@ struct _NO_DISCARD_ Transform2D {
_FORCE_INLINE_ const Vector2 &get_origin() const { return columns[2]; }
_FORCE_INLINE_ void set_origin(const Vector2 &p_origin) { columns[2] = p_origin; }
- Transform2D basis_scaled(const Size2 &p_scale) const;
Transform2D scaled(const Size2 &p_scale) const;
Transform2D scaled_local(const Size2 &p_scale) const;
Transform2D translated(const Vector2 &p_offset) const;
diff --git a/core/math/triangle_mesh.cpp b/core/math/triangle_mesh.cpp
index 4b6921d38b..0da1b8c7ad 100644
--- a/core/math/triangle_mesh.cpp
+++ b/core/math/triangle_mesh.cpp
@@ -182,90 +182,6 @@ void TriangleMesh::create(const Vector<Vector3> &p_faces, const Vector<int32_t>
valid = true;
}
-Vector3 TriangleMesh::get_area_normal(const AABB &p_aabb) const {
- uint32_t *stack = (uint32_t *)alloca(sizeof(int) * max_depth);
-
- enum {
- TEST_AABB_BIT = 0,
- VISIT_LEFT_BIT = 1,
- VISIT_RIGHT_BIT = 2,
- VISIT_DONE_BIT = 3,
- VISITED_BIT_SHIFT = 29,
- NODE_IDX_MASK = (1 << VISITED_BIT_SHIFT) - 1,
- VISITED_BIT_MASK = ~NODE_IDX_MASK,
-
- };
-
- int n_count = 0;
- Vector3 n;
-
- int level = 0;
-
- const Triangle *triangleptr = triangles.ptr();
- // const Vector3 *verticesr = vertices.ptr();
- const BVH *bvhptr = bvh.ptr();
-
- int pos = bvh.size() - 1;
-
- stack[0] = pos;
- while (true) {
- uint32_t node = stack[level] & NODE_IDX_MASK;
- const BVH &b = bvhptr[node];
- bool done = false;
-
- switch (stack[level] >> VISITED_BIT_SHIFT) {
- case TEST_AABB_BIT: {
- if (!b.aabb.intersects(p_aabb)) {
- stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
- } else {
- if (b.face_index >= 0) {
- const Triangle &s = triangleptr[b.face_index];
- n += s.normal;
- n_count++;
-
- stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
-
- } else {
- stack[level] = (VISIT_LEFT_BIT << VISITED_BIT_SHIFT) | node;
- }
- }
- continue;
- }
- case VISIT_LEFT_BIT: {
- stack[level] = (VISIT_RIGHT_BIT << VISITED_BIT_SHIFT) | node;
- level++;
- stack[level] = b.left | TEST_AABB_BIT;
- continue;
- }
- case VISIT_RIGHT_BIT: {
- stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
- level++;
- stack[level] = b.right | TEST_AABB_BIT;
- continue;
- }
- case VISIT_DONE_BIT: {
- if (level == 0) {
- done = true;
- break;
- } else {
- level--;
- }
- continue;
- }
- }
-
- if (done) {
- break;
- }
- }
-
- if (n_count > 0) {
- n /= n_count;
- }
-
- return n;
-}
-
bool TriangleMesh::intersect_segment(const Vector3 &p_begin, const Vector3 &p_end, Vector3 &r_point, Vector3 &r_normal, int32_t *r_surf_index) const {
uint32_t *stack = (uint32_t *)alloca(sizeof(int) * max_depth);
@@ -468,118 +384,6 @@ bool TriangleMesh::intersect_ray(const Vector3 &p_begin, const Vector3 &p_dir, V
return inters;
}
-bool TriangleMesh::intersect_convex_shape(const Plane *p_planes, int p_plane_count, const Vector3 *p_points, int p_point_count) const {
- uint32_t *stack = (uint32_t *)alloca(sizeof(int) * max_depth);
-
- //p_fully_inside = true;
-
- enum {
- TEST_AABB_BIT = 0,
- VISIT_LEFT_BIT = 1,
- VISIT_RIGHT_BIT = 2,
- VISIT_DONE_BIT = 3,
- VISITED_BIT_SHIFT = 29,
- NODE_IDX_MASK = (1 << VISITED_BIT_SHIFT) - 1,
- VISITED_BIT_MASK = ~NODE_IDX_MASK,
-
- };
-
- int level = 0;
-
- const Triangle *triangleptr = triangles.ptr();
- const Vector3 *vertexptr = vertices.ptr();
- const BVH *bvhptr = bvh.ptr();
-
- int pos = bvh.size() - 1;
-
- stack[0] = pos;
- while (true) {
- uint32_t node = stack[level] & NODE_IDX_MASK;
- const BVH &b = bvhptr[node];
- bool done = false;
-
- switch (stack[level] >> VISITED_BIT_SHIFT) {
- case TEST_AABB_BIT: {
- if (!b.aabb.intersects_convex_shape(p_planes, p_plane_count, p_points, p_point_count)) {
- stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
- } else {
- if (b.face_index >= 0) {
- const Triangle &s = triangleptr[b.face_index];
-
- for (int j = 0; j < 3; ++j) {
- const Vector3 &point = vertexptr[s.indices[j]];
- const Vector3 &next_point = vertexptr[s.indices[(j + 1) % 3]];
- Vector3 res;
- bool over = true;
- for (int i = 0; i < p_plane_count; i++) {
- const Plane &p = p_planes[i];
-
- if (p.intersects_segment(point, next_point, &res)) {
- bool inisde = true;
- for (int k = 0; k < p_plane_count; k++) {
- if (k == i) {
- continue;
- }
- const Plane &pp = p_planes[k];
- if (pp.is_point_over(res)) {
- inisde = false;
- break;
- }
- }
- if (inisde) {
- return true;
- }
- }
-
- if (p.is_point_over(point)) {
- over = false;
- break;
- }
- }
- if (over) {
- return true;
- }
- }
-
- stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
-
- } else {
- stack[level] = (VISIT_LEFT_BIT << VISITED_BIT_SHIFT) | node;
- }
- }
- continue;
- }
- case VISIT_LEFT_BIT: {
- stack[level] = (VISIT_RIGHT_BIT << VISITED_BIT_SHIFT) | node;
- level++;
- stack[level] = b.left | TEST_AABB_BIT;
- continue;
- }
- case VISIT_RIGHT_BIT: {
- stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
- level++;
- stack[level] = b.right | TEST_AABB_BIT;
- continue;
- }
- case VISIT_DONE_BIT: {
- if (level == 0) {
- done = true;
- break;
- } else {
- level--;
- }
- continue;
- }
- }
-
- if (done) {
- break;
- }
- }
-
- return false;
-}
-
bool TriangleMesh::inside_convex_shape(const Plane *p_planes, int p_plane_count, const Vector3 *p_points, int p_point_count, Vector3 p_scale) const {
uint32_t *stack = (uint32_t *)alloca(sizeof(int) * max_depth);
diff --git a/core/math/triangle_mesh.h b/core/math/triangle_mesh.h
index 728fd600d5..24fc12dda9 100644
--- a/core/math/triangle_mesh.h
+++ b/core/math/triangle_mesh.h
@@ -84,9 +84,7 @@ public:
bool is_valid() const;
bool intersect_segment(const Vector3 &p_begin, const Vector3 &p_end, Vector3 &r_point, Vector3 &r_normal, int32_t *r_surf_index = nullptr) const;
bool intersect_ray(const Vector3 &p_begin, const Vector3 &p_dir, Vector3 &r_point, Vector3 &r_normal, int32_t *r_surf_index = nullptr) const;
- bool intersect_convex_shape(const Plane *p_planes, int p_plane_count, const Vector3 *p_points, int p_point_count) const;
bool inside_convex_shape(const Plane *p_planes, int p_plane_count, const Vector3 *p_points, int p_point_count, Vector3 p_scale = Vector3(1, 1, 1)) const;
- Vector3 get_area_normal(const AABB &p_aabb) const;
Vector<Face3> get_faces() const;
const Vector<Triangle> &get_triangles() const { return triangles; }