#include "voxel_mesher_dmc.h" #include "../cube_tables.h" #include "hermite_value.h" #include "marching_cubes_tables.h" #include "mesh_builder.h" #include "octree_utility.h" #include // Dual marching cubes // Algorithm taken from https://www.volume-gfx.com/volume-rendering/dual-marching-cubes/ namespace dmc { // Surface is defined when isolevel crosses 0 const float SURFACE_ISO_LEVEL = 0.0; const float NEAR_SURFACE_FACTOR = 2.0; const float SQRT3 = 1.7320508075688772; // Octree used only for dual grid construction struct OctreeNode { Vector3i origin; int size; // Nodes are cubic HermiteValue center_value; OctreeNode *children[8]; OctreeNode() { for (int i = 0; i < 8; ++i) { children[i] = nullptr; } } ~OctreeNode() { for (int i = 0; i < 8; ++i) { if (children[i]) { memdelete(children[i]); } } } inline bool has_children() const { return children[0] != nullptr; } }; void split(OctreeNode *node) { CRASH_COND(node->has_children()); CRASH_COND(node->size == 1); for (int i = 0; i < 8; ++i) { OctreeNode *child = memnew(OctreeNode); const int *v = OctreeUtility::g_octant_position[i]; child->size = node->size / 2; child->origin = node->origin + Vector3i(v[0], v[1], v[2]) * child->size; node->children[i] = child; } } struct VoxelAccess { const VoxelBuffer &buffer; const Vector3i offset; VoxelAccess(const VoxelBuffer &p_buffer, Vector3i p_offset) : buffer(p_buffer), offset(p_offset) {} inline HermiteValue get_hermite_value(int x, int y, int z) const { return dmc::get_hermite_value(buffer, x + offset.x, y + offset.y, z + offset.z); } inline HermiteValue get_interpolated_hermite_value(Vector3 pos) const { pos.x += offset.x; pos.y += offset.y; pos.z += offset.z; return dmc::get_interpolated_hermite_value(buffer, pos); } }; bool can_split(Vector3i node_origin, int node_size, const VoxelAccess &voxels, float geometric_error) { if (node_size == 1) { // Voxel resolution, can't split further return false; } Vector3i origin = node_origin + voxels.offset; int step = node_size; int channel = VoxelBuffer::CHANNEL_ISOLEVEL; // Don't split if nothing is inside, i.e isolevel distance is greater than the size of the cube we are in Vector3i center_pos = node_origin + Vector3i(node_size / 2); HermiteValue center_value = voxels.get_hermite_value(center_pos.x, center_pos.y, center_pos.z); if (Math::abs(center_value.value) > SQRT3 * (float)node_size) { return false; } // Fighting with Clang-format here /**/ float v0 = voxels.buffer.get_voxel_iso(origin.x, /* */ origin.y, /* */ origin.z, /* */ channel); // 0 float v1 = voxels.buffer.get_voxel_iso(origin.x + step, origin.y, /* */ origin.z, /* */ channel); // 1 float v2 = voxels.buffer.get_voxel_iso(origin.x + step, origin.y, /* */ origin.z + step, channel); // 2 float v3 = voxels.buffer.get_voxel_iso(origin.x, /* */ origin.y, /* */ origin.z + step, channel); // 3 float v4 = voxels.buffer.get_voxel_iso(origin.x, /* */ origin.y + step, origin.z, /* */ channel); // 4 float v5 = voxels.buffer.get_voxel_iso(origin.x + step, origin.y + step, origin.z, /* */ channel); // 5 float v6 = voxels.buffer.get_voxel_iso(origin.x + step, origin.y + step, origin.z + step, channel); // 6 float v7 = voxels.buffer.get_voxel_iso(origin.x, /* */ origin.y + step, origin.z + step, channel); // 7 int hstep = step / 2; Vector3i positions[19] = { // Starting from point 8 Vector3i(origin.x + hstep, /**/ origin.y, /* */ origin.z), // 8 Vector3i(origin.x + step, /* */ origin.y, /* */ origin.z + hstep), // 9 Vector3i(origin.x + hstep, /**/ origin.y, /* */ origin.z + step), // 10 Vector3i(origin.x, /* */ origin.y, /* */ origin.z + hstep), // 11 Vector3i(origin.x, /* */ origin.y + hstep, /**/ origin.z), // 12 Vector3i(origin.x + step, /* */ origin.y + hstep, /**/ origin.z), // 13 Vector3i(origin.x + step, /* */ origin.y + hstep, /**/ origin.z + step), // 14 Vector3i(origin.x, /* */ origin.y + hstep, /**/ origin.z + step), // 15 Vector3i(origin.x + hstep, /**/ origin.y + step, /* */ origin.z), // 16 Vector3i(origin.x + step, /* */ origin.y + step, /* */ origin.z + hstep), // 17 Vector3i(origin.x + hstep, /**/ origin.y + step, /* */ origin.z + step), // 18 Vector3i(origin.x, /* */ origin.y + step, /* */ origin.z + hstep), // 19 Vector3i(origin.x + hstep, /**/ origin.y, /* */ origin.z + hstep), // 20 Vector3i(origin.x + hstep, /**/ origin.y + hstep, /**/ origin.z), // 21 Vector3i(origin.x + step, /* */ origin.y + hstep, /**/ origin.z + hstep), // 22 Vector3i(origin.x + hstep, /**/ origin.y + hstep, /**/ origin.z + step), // 23 Vector3i(origin.x, /* */ origin.y + hstep, /**/ origin.z + hstep), // 24 Vector3i(origin.x + hstep, /**/ origin.y + step, /* */ origin.z + hstep), // 25 Vector3i(origin.x + hstep, /**/ origin.y + hstep, /**/ origin.z + hstep) // 26 }; Vector3 positions_ratio[19] = { Vector3(0.5, 0.0, 0.0), Vector3(1.0, 0.0, 0.5), Vector3(0.5, 0.0, 1.0), Vector3(0.0, 0.0, 0.5), Vector3(0.0, 0.5, 0.0), Vector3(1.0, 0.5, 0.0), Vector3(1.0, 0.5, 1.0), Vector3(0.0, 0.5, 1.0), Vector3(0.5, 1.0, 0.0), Vector3(1.0, 1.0, 0.5), Vector3(0.5, 1.0, 1.0), Vector3(0.0, 1.0, 0.5), Vector3(0.5, 0.0, 0.5), Vector3(0.5, 0.5, 0.0), Vector3(1.0, 0.5, 0.5), Vector3(0.5, 0.5, 1.0), Vector3(0.0, 0.5, 0.5), Vector3(0.5, 1.0, 0.5), Vector3(0.5, 0.5, 0.5) }; float error = 0.0; for (int i = 0; i < 19; ++i) { Vector3i pos = positions[i]; HermiteValue value = get_hermite_value(voxels.buffer, pos.x, pos.y, pos.z); float interpolated_value = ::interpolate(v0, v1, v2, v3, v4, v5, v6, v7, positions_ratio[i]); float gradient_magnitude = value.gradient.length(); if (gradient_magnitude < FLT_EPSILON) { gradient_magnitude = 1.0; } error += Math::abs(value.value - interpolated_value) / gradient_magnitude; if (error >= geometric_error) { return true; } } return false; } inline Vector3 get_center(const OctreeNode *node) { return node->origin.to_vec3() + 0.5 * Vector3(node->size, node->size, node->size); } void generate_octree_top_down(OctreeNode *node, const VoxelAccess &voxels, float geometric_error) { if (can_split(node->origin, node->size, voxels, geometric_error)) { split(node); for (int i = 0; i < 8; ++i) { generate_octree_top_down(node->children[i], voxels, geometric_error); } } else { node->center_value = voxels.get_interpolated_hermite_value(get_center(node)); } } // Builds the octree bottom-up, to ensure that no detail can be missed by a top-down approach. class OctreeBuilderBottomUp { public: OctreeBuilderBottomUp(const VoxelAccess &voxels, float geometry_error) : _voxels(voxels), _geometry_error(geometry_error) { } OctreeNode *build(Vector3i node_origin, int node_size) const { OctreeNode *children[8] = { nullptr }; bool any_node = false; // Go all the way down, except leaves because we can't reason bottom-up on them if (node_size > 2) { for (int i = 0; i < 8; ++i) { const int *dir = OctreeUtility::g_octant_position[i]; int child_size = node_size / 2; children[i] = build(node_origin + child_size * Vector3i(dir[0], dir[1], dir[2]), child_size); any_node |= children[i] != nullptr; } } OctreeNode *node = nullptr; if (!any_node) { // No nodes, test if the 8 octants are worth existing (this could be leaves) if (can_split(node_origin, node_size, _voxels, _geometry_error)) { node = memnew(OctreeNode); node->origin = node_origin; node->size = node_size; // Create all 8 children for (int i = 0; i < 8; ++i) { node->children[i] = create_child(node_origin, node_size, i); } } // If no splitting... then we return null. // If the parent iteration gets all children null this way, // it will allow detail reduction recursively upwards. } else { // Some child nodes were deemed worthy of existence, // create their siblings at the same detail level node = memnew(OctreeNode); node->origin = node_origin; node->size = node_size; for (int i = 0; i < 8; ++i) { if (children[i] != nullptr) { node->children[i] = children[i]; } else { node->children[i] = create_child(node_origin, node_size, i); } } } return node; } private: inline OctreeNode *create_child(Vector3i parent_origin, int parent_size, int i) const { const int *dir = OctreeUtility::g_octant_position[i]; OctreeNode *child = memnew(OctreeNode); child->size = parent_size / 2; child->origin = parent_origin + child->size * Vector3i(dir[0], dir[1], dir[2]); child->center_value = _voxels.get_interpolated_hermite_value(get_center(child)); return child; } private: const VoxelAccess &_voxels; const float _geometry_error; }; template void foreach_node(OctreeNode *root, Action_T &a, int depth = 0) { a(root, depth); for (int i = 0; i < 8; ++i) { if (root->children[i]) { foreach_node(root->children[i], a, depth + 1); } } } Ref generate_debug_octree_mesh(OctreeNode *root) { struct GetMaxDepth { int max_depth; void operator()(OctreeNode *_, int depth) { if (depth > max_depth) { max_depth = depth; } } }; struct Arrays { PoolVector3Array positions; PoolColorArray colors; PoolIntArray indices; }; struct AddCube { Arrays *arrays; int max_depth; void operator()(OctreeNode *node, int depth) { float shrink = depth * 0.005; Vector3 o = node->origin.to_vec3() + Vector3(shrink, shrink, shrink); float s = node->size - 2.0 * shrink; Color col(1.0, (float)depth / (float)max_depth, 0.0); int vi = arrays->positions.size(); for (int i = 0; i < Cube::CORNER_COUNT; ++i) { arrays->positions.push_back(o + s * Cube::g_corner_position[i]); arrays->colors.push_back(col); } for (int i = 0; i < Cube::EDGE_COUNT; ++i) { arrays->indices.push_back(vi + Cube::g_edge_corners[i][0]); arrays->indices.push_back(vi + Cube::g_edge_corners[i][1]); } } }; GetMaxDepth get_max_depth; foreach_node(root, get_max_depth); Arrays arrays; AddCube add_cube; add_cube.arrays = &arrays; add_cube.max_depth = get_max_depth.max_depth; foreach_node(root, add_cube); if (arrays.positions.size() == 0) { return Ref(); } Array surface; surface.resize(Mesh::ARRAY_MAX); surface[Mesh::ARRAY_VERTEX] = arrays.positions; surface[Mesh::ARRAY_COLOR] = arrays.colors; surface[Mesh::ARRAY_INDEX] = arrays.indices; Ref mesh; mesh.instance(); mesh->add_surface_from_arrays(Mesh::PRIMITIVE_LINES, surface); return mesh; } struct DualCell { Vector3 corners[8]; HermiteValue values[8]; bool has_values; DualCell() : has_values(false) {} inline void set_corner(int i, Vector3 vertex, HermiteValue value) { CRASH_COND(i < 0 || i >= 8); corners[i] = vertex; values[i] = value; } }; struct DualGrid { std::vector cells; inline void add_cell( const Vector3 c0, const Vector3 c1, const Vector3 c2, const Vector3 c3, const Vector3 c4, const Vector3 c5, const Vector3 c6, const Vector3 c7) { DualCell cell; cell.corners[0] = c0; cell.corners[1] = c1; cell.corners[2] = c2; cell.corners[3] = c3; cell.corners[4] = c4; cell.corners[5] = c5; cell.corners[6] = c6; cell.corners[7] = c7; cells.push_back(cell); } }; Ref generate_debug_dual_grid_mesh(const DualGrid &grid) { PoolVector3Array positions; PoolIntArray indices; for (int i = 0; i < grid.cells.size(); ++i) { const DualCell &cell = grid.cells[i]; int vi = positions.size(); for (int j = 0; j < 8; ++j) { // Vector3 p = Vector3(g_octant_position[j][0], g_octant_position[j][1], g_octant_position[j][2]); // Vector3 n = (Vector3(0.5, 0.5, 0.5) - p).normalized(); positions.push_back(cell.corners[j]); // + n * 0.01); } for (int j = 0; j < Cube::EDGE_COUNT; ++j) { indices.push_back(vi + Cube::g_edge_corners[j][0]); indices.push_back(vi + Cube::g_edge_corners[j][1]); } } if (positions.size() == 0) { return Ref(); } Array surface; surface.resize(Mesh::ARRAY_MAX); surface[Mesh::ARRAY_VERTEX] = positions; surface[Mesh::ARRAY_INDEX] = indices; Ref mesh; mesh.instance(); mesh->add_surface_from_arrays(Mesh::PRIMITIVE_LINES, surface); return mesh; } inline bool is_border_left(const OctreeNode *node) { return node->origin.x == 0; } inline bool is_border_right(const OctreeNode *node, int rootSize) { return node->origin.x + node->size == rootSize; } inline bool is_border_bottom(const OctreeNode *node) { return node->origin.y == 0; } inline bool is_border_top(const OctreeNode *node, int rootSize) { return node->origin.y + node->size == rootSize; } inline bool is_border_back(const OctreeNode *node) { return node->origin.z == 0; } inline bool is_border_front(const OctreeNode *node, int rootSize) { return node->origin.z + node->size == rootSize; } inline Vector3 get_center_back(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size * 0.5; p.y += node->size * 0.5; return p; } inline Vector3 get_center_front(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size * 0.5; p.y += node->size * 0.5; p.z += node->size; return p; } inline Vector3 get_center_left(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.y += node->size * 0.5; p.z += node->size * 0.5; return p; } inline Vector3 get_center_right(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size; p.y += node->size * 0.5; p.z += node->size * 0.5; return p; } inline Vector3 get_center_top(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size * 0.5; p.y += node->size; p.z += node->size * 0.5; return p; } inline Vector3 get_center_bottom(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size * 0.5; p.z += node->size * 0.5; return p; } inline Vector3 get_center_back_top(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size * 0.5; p.y += node->size; return p; } inline Vector3 get_center_back_bottom(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size * 0.5; return p; } inline Vector3 get_center_front_top(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size * 0.5; p.y += node->size; p.z += node->size; return p; } inline Vector3 get_center_front_bottom(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size * 0.5; p.z += node->size; return p; } inline Vector3 get_center_left_top(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.y += node->size; p.z += node->size * 0.5; return p; } inline Vector3 get_center_left_bottom(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.z += node->size * 0.5; return p; } inline Vector3 get_center_right_top(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size; p.y += node->size; p.z += node->size * 0.5; return p; } inline Vector3 get_center_right_bottom(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size; p.z += node->size * 0.5; return p; } inline Vector3 get_center_back_left(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.y += node->size * 0.5; return p; } inline Vector3 get_center_front_left(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.y += node->size * 0.5; p.z += node->size; return p; } inline Vector3 get_center_back_right(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size; p.y += node->size * 0.5; return p; } inline Vector3 get_center_front_right(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size; p.y += node->size * 0.5; p.z += node->size; return p; } inline Vector3 get_corner1(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size; return p; } inline Vector3 get_corner2(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size; p.z += node->size; return p; } inline Vector3 get_corner3(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.z += node->size; return p; } inline Vector3 get_corner4(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.y += node->size; return p; } inline Vector3 get_corner5(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size; p.y += node->size; return p; } inline Vector3 get_corner6(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.x += node->size; p.y += node->size; p.z += node->size; return p; } inline Vector3 get_corner7(const OctreeNode *node) { Vector3 p = node->origin.to_vec3(); p.y += node->size; p.z += node->size; return p; } class DualGridGenerator { public: DualGridGenerator(DualGrid &grid, int octree_root_size) : _grid(grid), _octree_root_size(octree_root_size) {} void node_proc(OctreeNode *node); private: DualGrid &_grid; int _octree_root_size; void create_border_cells( const OctreeNode *n0, const OctreeNode *n1, const OctreeNode *n2, const OctreeNode *n3, const OctreeNode *n4, const OctreeNode *n5, const OctreeNode *n6, const OctreeNode *n7); void vert_proc(OctreeNode *n0, OctreeNode *n1, OctreeNode *n2, OctreeNode *n3, OctreeNode *n4, OctreeNode *n5, OctreeNode *n6, OctreeNode *n7); void edge_proc_x(OctreeNode *n0, OctreeNode *n1, OctreeNode *n2, OctreeNode *n3); void edge_proc_y(OctreeNode *n0, OctreeNode *n1, OctreeNode *n2, OctreeNode *n3); void edge_proc_z(OctreeNode *n0, OctreeNode *n1, OctreeNode *n2, OctreeNode *n3); void face_proc_xy(OctreeNode *n0, OctreeNode *n1); void face_proc_zy(OctreeNode *n0, OctreeNode *n1); void face_proc_xz(OctreeNode *n0, OctreeNode *n1); }; void DualGridGenerator::create_border_cells( const OctreeNode *n0, const OctreeNode *n1, const OctreeNode *n2, const OctreeNode *n3, const OctreeNode *n4, const OctreeNode *n5, const OctreeNode *n6, const OctreeNode *n7) { DualGrid &grid = _grid; // Most boring function ever if (is_border_back(n0) && is_border_back(n1) && is_border_back(n4) && is_border_back(n5)) { grid.add_cell( get_center_back(n0), get_center_back(n1), get_center(n1), get_center(n0), get_center_back(n4), get_center_back(n5), get_center(n5), get_center(n4)); // Generate back edge border cells if (is_border_top(n4, _octree_root_size) && is_border_top(n5, _octree_root_size)) { grid.add_cell( get_center_back(n4), get_center_back(n5), get_center(n5), get_center(n4), get_center_back_top(n4), get_center_back_top(n5), get_center_top(n5), get_center_top(n4)); // Generate back top corner cells if (is_border_left(n4)) { grid.add_cell( get_center_back_left(n4), get_center_back(n4), get_center(n4), get_center_left(n4), get_corner4(n4), get_center_back_top(n4), get_center_top(n4), get_center_left_top(n4)); } if (is_border_right(n4, _octree_root_size)) { grid.add_cell( get_center_back(n5), get_center_back_right(n5), get_center_right(n5), get_center(n5), get_center_back_top(n5), get_corner5(n5), get_center_right_top(n5), get_center_top(n5)); } } if (is_border_bottom(n0) && is_border_bottom(n1)) { grid.add_cell( get_center_back_bottom(n0), get_center_back_bottom(n1), get_center_bottom(n1), get_center_bottom(n0), get_center_back(n0), get_center_back(n1), get_center(n1), get_center(n0)); // Generate back bottom corner cells if (is_border_left(n0)) { grid.add_cell(n0->origin.to_vec3(), get_center_back_bottom(n0), get_center_bottom(n0), get_center_left_bottom(n0), get_center_back_left(n0), get_center_back(n0), get_center(n0), get_center_left(n0)); } if (is_border_right(n1, _octree_root_size)) { grid.add_cell(get_center_back_bottom(n1), get_corner1(n1), get_center_right_bottom(n1), get_center_bottom(n1), get_center_back(n1), get_center_back_right(n1), get_center_right(n1), get_center(n1)); } } } if (is_border_front(n2, _octree_root_size) && is_border_front(n3, _octree_root_size) && is_border_front(n6, _octree_root_size) && is_border_front(n7, _octree_root_size)) { grid.add_cell( get_center(n3), get_center(n2), get_center_front(n2), get_center_front(n3), get_center(n7), get_center(n6), get_center_front(n6), get_center_front(n7)); // Generate front edge border cells if (is_border_top(n6, _octree_root_size) && is_border_top(n7, _octree_root_size)) { grid.add_cell( get_center(n7), get_center(n6), get_center_front(n6), get_center_front(n7), get_center_top(n7), get_center_top(n6), get_center_front_top(n6), get_center_front_top(n7)); // Generate back bottom corner cells if (is_border_left(n7)) { grid.add_cell( get_center_left(n7), get_center(n7), get_center_front(n7), get_center_front_left(n7), get_center_left_top(n7), get_center_top(n7), get_center_front_top(n7), get_corner7(n7)); } if (is_border_right(n6, _octree_root_size)) { grid.add_cell( get_center(n6), get_center_right(n6), get_center_front_right(n6), get_center_front(n6), get_center_top(n6), get_center_right_top(n6), get_corner6(n6), get_center_front_top(n6)); } } if (is_border_bottom(n3) && is_border_bottom(n2)) { grid.add_cell( get_center_bottom(n3), get_center_bottom(n2), get_center_front_bottom(n2), get_center_front_bottom(n3), get_center(n3), get_center(n2), get_center_front(n2), get_center_front(n3)); // Generate back bottom corner cells if (is_border_left(n3)) { grid.add_cell( get_center_left_bottom(n3), get_center_bottom(n3), get_center_front_bottom(n3), get_corner3(n3), get_center_left(n3), get_center(n3), get_center_front(n3), get_center_front_left(n3)); } if (is_border_right(n2, _octree_root_size)) { grid.add_cell(get_center_bottom(n2), get_center_right_bottom(n2), get_corner2(n2), get_center_front_bottom(n2), get_center(n2), get_center_right(n2), get_center_front_right(n2), get_center_front(n2)); } } } if (is_border_left(n0) && is_border_left(n3) && is_border_left(n4) && is_border_left(n7)) { grid.add_cell( get_center_left(n0), get_center(n0), get_center(n3), get_center_left(n3), get_center_left(n4), get_center(n4), get_center(n7), get_center_left(n7)); // Generate left edge border cells if (is_border_top(n4, _octree_root_size) && is_border_top(n7, _octree_root_size)) { grid.add_cell( get_center_left(n4), get_center(n4), get_center(n7), get_center_left(n7), get_center_left_top(n4), get_center_top(n4), get_center_top(n7), get_center_left_top(n7)); } if (is_border_bottom(n0) && is_border_bottom(n3)) { grid.add_cell( get_center_left_bottom(n0), get_center_bottom(n0), get_center_bottom(n3), get_center_left_bottom(n3), get_center_left(n0), get_center(n0), get_center(n3), get_center_left(n3)); } if (is_border_back(n0) && is_border_back(n4)) { grid.add_cell( get_center_back_left(n0), get_center_back(n0), get_center(n0), get_center_left(n0), get_center_back_left(n4), get_center_back(n4), get_center(n4), get_center_left(n4)); } if (is_border_front(n3, _octree_root_size) && is_border_front(n7, _octree_root_size)) { grid.add_cell( get_center_left(n3), get_center(n3), get_center_front(n3), get_center_front_left(n3), get_center_left(n7), get_center(n7), get_center_front(n7), get_center_front_left(n7)); } } if (is_border_right(n1, _octree_root_size) && is_border_right(n2, _octree_root_size) && is_border_right(n5, _octree_root_size) && is_border_right(n6, _octree_root_size)) { grid.add_cell( get_center(n1), get_center_right(n1), get_center_right(n2), get_center(n2), get_center(n5), get_center_right(n5), get_center_right(n6), get_center(n6)); // Generate right edge border cells if (is_border_top(n5, _octree_root_size) && is_border_top(n6, _octree_root_size)) { grid.add_cell( get_center(n5), get_center_right(n5), get_center_right(n6), get_center(n6), get_center_top(n5), get_center_right_top(n5), get_center_right_top(n6), get_center_top(n6)); } if (is_border_bottom(n1) && is_border_bottom(n2)) { grid.add_cell( get_center_bottom(n1), get_center_right_bottom(n1), get_center_right_bottom(n2), get_center_bottom(n2), get_center(n1), get_center_right(n1), get_center_right(n2), get_center(n2)); } if (is_border_back(n1) && is_border_back(n5)) { grid.add_cell( get_center_back(n1), get_center_back_right(n1), get_center_right(n1), get_center(n1), get_center_back(n5), get_center_back_right(n5), get_center_right(n5), get_center(n5)); } if (is_border_front(n2, _octree_root_size) && is_border_front(n6, _octree_root_size)) { grid.add_cell( get_center(n2), get_center_right(n2), get_center_front_right(n2), get_center_front(n2), get_center(n6), get_center_right(n6), get_center_front_right(n6), get_center_front(n6)); } } if (is_border_top(n4, _octree_root_size) && is_border_top(n5, _octree_root_size) && is_border_top(n6, _octree_root_size) && is_border_top(n7, _octree_root_size)) { grid.add_cell( get_center(n4), get_center(n5), get_center(n6), get_center(n7), get_center_top(n4), get_center_top(n5), get_center_top(n6), get_center_top(n7)); } if (is_border_bottom(n0) && is_border_bottom(n1) && is_border_bottom(n2) && is_border_bottom(n3)) { grid.add_cell( get_center_bottom(n0), get_center_bottom(n1), get_center_bottom(n2), get_center_bottom(n3), get_center(n0), get_center(n1), get_center(n2), get_center(n3)); } } inline bool is_surface_near(OctreeNode *node) { if (node->center_value.value == 0) { return true; } return Math::abs(node->center_value.value) < node->size * SQRT3 * NEAR_SURFACE_FACTOR; } void DualGridGenerator::vert_proc( OctreeNode *n0, OctreeNode *n1, OctreeNode *n2, OctreeNode *n3, OctreeNode *n4, OctreeNode *n5, OctreeNode *n6, OctreeNode *n7) { const bool n0_has_children = n0->has_children(); const bool n1_has_children = n1->has_children(); const bool n2_has_children = n2->has_children(); const bool n3_has_children = n3->has_children(); const bool n4_has_children = n4->has_children(); const bool n5_has_children = n5->has_children(); const bool n6_has_children = n6->has_children(); const bool n7_has_children = n7->has_children(); if ( n0_has_children || n1_has_children || n2_has_children || n3_has_children || n4_has_children || n5_has_children || n6_has_children || n7_has_children) { OctreeNode *c0 = n0_has_children ? n0->children[6] : n0; OctreeNode *c1 = n1_has_children ? n1->children[7] : n1; OctreeNode *c2 = n2_has_children ? n2->children[4] : n2; OctreeNode *c3 = n3_has_children ? n3->children[5] : n3; OctreeNode *c4 = n4_has_children ? n4->children[2] : n4; OctreeNode *c5 = n5_has_children ? n5->children[3] : n5; OctreeNode *c6 = n6_has_children ? n6->children[0] : n6; OctreeNode *c7 = n7_has_children ? n7->children[1] : n7; vert_proc(c0, c1, c2, c3, c4, c5, c6, c7); } else { if (!( is_surface_near(n0) || is_surface_near(n1) || is_surface_near(n2) || is_surface_near(n3) || is_surface_near(n4) || is_surface_near(n5) || is_surface_near(n6) || is_surface_near(n7))) { return; } DualCell cell; cell.set_corner(0, get_center(n0), n0->center_value); cell.set_corner(1, get_center(n1), n1->center_value); cell.set_corner(2, get_center(n2), n2->center_value); cell.set_corner(3, get_center(n3), n3->center_value); cell.set_corner(4, get_center(n4), n4->center_value); cell.set_corner(5, get_center(n5), n5->center_value); cell.set_corner(6, get_center(n6), n6->center_value); cell.set_corner(7, get_center(n7), n7->center_value); cell.has_values = true; _grid.cells.push_back(cell); create_border_cells(n0, n1, n2, n3, n4, n5, n6, n7); } } void DualGridGenerator::edge_proc_x(OctreeNode *n0, OctreeNode *n1, OctreeNode *n2, OctreeNode *n3) { const bool n0_has_children = n0->has_children(); const bool n1_has_children = n1->has_children(); const bool n2_has_children = n2->has_children(); const bool n3_has_children = n3->has_children(); if (!(n0_has_children || n1_has_children || n2_has_children || n3_has_children)) { return; } OctreeNode *c0 = n0_has_children ? n0->children[7] : n0; OctreeNode *c1 = n0_has_children ? n0->children[6] : n0; OctreeNode *c2 = n1_has_children ? n1->children[5] : n1; OctreeNode *c3 = n1_has_children ? n1->children[4] : n1; OctreeNode *c4 = n3_has_children ? n3->children[3] : n3; OctreeNode *c5 = n3_has_children ? n3->children[2] : n3; OctreeNode *c6 = n2_has_children ? n2->children[1] : n2; OctreeNode *c7 = n2_has_children ? n2->children[0] : n2; edge_proc_x(c0, c3, c7, c4); edge_proc_x(c1, c2, c6, c5); vert_proc(c0, c1, c2, c3, c4, c5, c6, c7); } void DualGridGenerator::edge_proc_y(OctreeNode *n0, OctreeNode *n1, OctreeNode *n2, OctreeNode *n3) { const bool n0_has_children = n0->has_children(); const bool n1_has_children = n1->has_children(); const bool n2_has_children = n2->has_children(); const bool n3_has_children = n3->has_children(); if (!(n0_has_children || n1_has_children || n2_has_children || n3_has_children)) { return; } OctreeNode *c0 = n0_has_children ? n0->children[2] : n0; OctreeNode *c1 = n1_has_children ? n1->children[3] : n1; OctreeNode *c2 = n2_has_children ? n2->children[0] : n2; OctreeNode *c3 = n3_has_children ? n3->children[1] : n3; OctreeNode *c4 = n0_has_children ? n0->children[6] : n0; OctreeNode *c5 = n1_has_children ? n1->children[7] : n1; OctreeNode *c6 = n2_has_children ? n2->children[4] : n2; OctreeNode *c7 = n3_has_children ? n3->children[5] : n3; edge_proc_y(c0, c1, c2, c3); edge_proc_y(c4, c5, c6, c7); vert_proc(c0, c1, c2, c3, c4, c5, c6, c7); } void DualGridGenerator::edge_proc_z(OctreeNode *n0, OctreeNode *n1, OctreeNode *n2, OctreeNode *n3) { const bool n0_has_children = n0->has_children(); const bool n1_has_children = n1->has_children(); const bool n2_has_children = n2->has_children(); const bool n3_has_children = n3->has_children(); if (!(n0_has_children || n1_has_children || n2_has_children || n3_has_children)) { return; } OctreeNode *c0 = n3_has_children ? n3->children[5] : n3; OctreeNode *c1 = n2_has_children ? n2->children[4] : n2; OctreeNode *c2 = n2_has_children ? n2->children[7] : n2; OctreeNode *c3 = n3_has_children ? n3->children[6] : n3; OctreeNode *c4 = n0_has_children ? n0->children[1] : n0; OctreeNode *c5 = n1_has_children ? n1->children[0] : n1; OctreeNode *c6 = n1_has_children ? n1->children[3] : n1; OctreeNode *c7 = n0_has_children ? n0->children[2] : n0; edge_proc_z(c7, c6, c2, c3); edge_proc_z(c4, c5, c1, c0); vert_proc(c0, c1, c2, c3, c4, c5, c6, c7); } void DualGridGenerator::face_proc_xy(OctreeNode *n0, OctreeNode *n1) { const bool n0_has_children = n0->has_children(); const bool n1_has_children = n1->has_children(); if (!(n0_has_children || n1_has_children)) { return; } OctreeNode *c0 = n0_has_children ? n0->children[3] : n0; OctreeNode *c1 = n0_has_children ? n0->children[2] : n0; OctreeNode *c2 = n1_has_children ? n1->children[1] : n1; OctreeNode *c3 = n1_has_children ? n1->children[0] : n1; OctreeNode *c4 = n0_has_children ? n0->children[7] : n0; OctreeNode *c5 = n0_has_children ? n0->children[6] : n0; OctreeNode *c6 = n1_has_children ? n1->children[5] : n1; OctreeNode *c7 = n1_has_children ? n1->children[4] : n1; face_proc_xy(c0, c3); face_proc_xy(c1, c2); face_proc_xy(c4, c7); face_proc_xy(c5, c6); edge_proc_x(c0, c3, c7, c4); edge_proc_x(c1, c2, c6, c5); edge_proc_y(c0, c1, c2, c3); edge_proc_y(c4, c5, c6, c7); vert_proc(c0, c1, c2, c3, c4, c5, c6, c7); } void DualGridGenerator::face_proc_zy(OctreeNode *n0, OctreeNode *n1) { const bool n0_has_children = n0->has_children(); const bool n1_has_children = n1->has_children(); if (!(n0_has_children || n1_has_children)) { return; } OctreeNode *c0 = n0_has_children ? n0->children[1] : n0; OctreeNode *c1 = n1_has_children ? n1->children[0] : n1; OctreeNode *c2 = n1_has_children ? n1->children[3] : n1; OctreeNode *c3 = n0_has_children ? n0->children[2] : n0; OctreeNode *c4 = n0_has_children ? n0->children[5] : n0; OctreeNode *c5 = n1_has_children ? n1->children[4] : n1; OctreeNode *c6 = n1_has_children ? n1->children[7] : n1; OctreeNode *c7 = n0_has_children ? n0->children[6] : n0; face_proc_zy(c0, c1); face_proc_zy(c3, c2); face_proc_zy(c4, c5); face_proc_zy(c7, c6); edge_proc_y(c0, c1, c2, c3); edge_proc_y(c4, c5, c6, c7); edge_proc_z(c7, c6, c2, c3); edge_proc_z(c4, c5, c1, c0); vert_proc(c0, c1, c2, c3, c4, c5, c6, c7); } void DualGridGenerator::face_proc_xz(OctreeNode *n0, OctreeNode *n1) { const bool n0_has_children = n0->has_children(); const bool n1_has_children = n1->has_children(); if (!(n0_has_children || n1_has_children)) { return; } OctreeNode *c0 = n1_has_children ? n1->children[4] : n1; OctreeNode *c1 = n1_has_children ? n1->children[5] : n1; OctreeNode *c2 = n1_has_children ? n1->children[6] : n1; OctreeNode *c3 = n1_has_children ? n1->children[7] : n1; OctreeNode *c4 = n0_has_children ? n0->children[0] : n0; OctreeNode *c5 = n0_has_children ? n0->children[1] : n0; OctreeNode *c6 = n0_has_children ? n0->children[2] : n0; OctreeNode *c7 = n0_has_children ? n0->children[3] : n0; face_proc_xz(c4, c0); face_proc_xz(c5, c1); face_proc_xz(c7, c3); face_proc_xz(c6, c2); edge_proc_x(c0, c3, c7, c4); edge_proc_x(c1, c2, c6, c5); edge_proc_z(c7, c6, c2, c3); edge_proc_z(c4, c5, c1, c0); vert_proc(c0, c1, c2, c3, c4, c5, c6, c7); } void DualGridGenerator::node_proc(OctreeNode *node) { if (!node->has_children()) { return; } OctreeNode **children = node->children; for (int i = 0; i < 8; ++i) { node_proc(children[i]); } face_proc_xy(children[0], children[3]); face_proc_xy(children[1], children[2]); face_proc_xy(children[4], children[7]); face_proc_xy(children[5], children[6]); face_proc_zy(children[0], children[1]); face_proc_zy(children[3], children[2]); face_proc_zy(children[4], children[5]); face_proc_zy(children[7], children[6]); face_proc_xz(children[4], children[0]); face_proc_xz(children[5], children[1]); face_proc_xz(children[7], children[3]); face_proc_xz(children[6], children[2]); edge_proc_x(children[0], children[3], children[7], children[4]); edge_proc_x(children[1], children[2], children[6], children[5]); edge_proc_y(children[0], children[1], children[2], children[3]); edge_proc_y(children[4], children[5], children[6], children[7]); edge_proc_z(children[7], children[6], children[2], children[3]); edge_proc_z(children[4], children[5], children[1], children[0]); vert_proc(children[0], children[1], children[2], children[3], children[4], children[5], children[6], children[7]); } inline Vector3 interpolate(const Vector3 &v0, const Vector3 &v1, const HermiteValue &val0, const HermiteValue &val1, Vector3 &out_normal) { if (Math::abs(val0.value - SURFACE_ISO_LEVEL) <= FLT_EPSILON) { out_normal = val0.gradient; return v0; } if (Math::abs(val1.value - SURFACE_ISO_LEVEL) <= FLT_EPSILON) { out_normal = val1.gradient; return v1; } if (Math::abs(val1.value - val0.value) <= FLT_EPSILON) { out_normal = val0.gradient; return v0; } float mu = (SURFACE_ISO_LEVEL - val0.value) / (val1.value - val0.value); out_normal = val0.gradient + mu * (val1.gradient - val0.gradient); out_normal.normalize(); return v0 + mu * (v1 - v0); } void polygonize_dual_grid(const DualGrid &grid, const VoxelAccess &voxels, MeshBuilder &mesh_builder) { for (int dci = 0; dci < grid.cells.size(); ++dci) { const DualCell &cell = grid.cells[dci]; const Vector3 *corners = cell.corners; // Polygonize using regular marching cubes unsigned char case_index = 0; HermiteValue values[8]; for (int i = 0; i < 8; ++i) { if (cell.has_values) { values[i] = cell.values[i]; } else { values[i] = voxels.get_interpolated_hermite_value(corners[i]); } if (values[i].value >= SURFACE_ISO_LEVEL) { case_index |= 1 << i; } } int edge = MarchingCubes::mc_edges[case_index]; if (!edge) { // Nothing intersects continue; } // Find the intersection vertices Vector3 intersection_points[12]; Vector3 intersection_normals[12]; if (edge & 1) { intersection_points[0] = interpolate(corners[0], corners[1], values[0], values[1], intersection_normals[0]); } if (edge & 2) { intersection_points[1] = interpolate(corners[1], corners[2], values[1], values[2], intersection_normals[1]); } if (edge & 4) { intersection_points[2] = interpolate(corners[2], corners[3], values[2], values[3], intersection_normals[2]); } if (edge & 8) { intersection_points[3] = interpolate(corners[3], corners[0], values[3], values[0], intersection_normals[3]); } if (edge & 16) { intersection_points[4] = interpolate(corners[4], corners[5], values[4], values[5], intersection_normals[4]); } if (edge & 32) { intersection_points[5] = interpolate(corners[5], corners[6], values[5], values[6], intersection_normals[5]); } if (edge & 64) { intersection_points[6] = interpolate(corners[6], corners[7], values[6], values[7], intersection_normals[6]); } if (edge & 128) { intersection_points[7] = interpolate(corners[7], corners[4], values[7], values[4], intersection_normals[7]); } if (edge & 256) { intersection_points[8] = interpolate(corners[0], corners[4], values[0], values[4], intersection_normals[8]); } if (edge & 512) { intersection_points[9] = interpolate(corners[1], corners[5], values[1], values[5], intersection_normals[9]); } if (edge & 1024) { intersection_points[10] = interpolate(corners[2], corners[6], values[2], values[6], intersection_normals[10]); } if (edge & 2048) { intersection_points[11] = interpolate(corners[3], corners[7], values[3], values[7], intersection_normals[11]); } // Create the triangles according to the table. for (int i = 0; MarchingCubes::mc_triangles[case_index][i] != -1; i += 3) { mesh_builder.add_vertex( intersection_points[MarchingCubes::mc_triangles[case_index][i]], intersection_normals[MarchingCubes::mc_triangles[case_index][i]]); mesh_builder.add_vertex( intersection_points[MarchingCubes::mc_triangles[case_index][i + 1]], intersection_normals[MarchingCubes::mc_triangles[case_index][i + 1]]); mesh_builder.add_vertex( intersection_points[MarchingCubes::mc_triangles[case_index][i + 2]], intersection_normals[MarchingCubes::mc_triangles[case_index][i + 2]]); } } } } // namespace dmc #define BUILD_OCTREE_BOTTOM_UP Ref VoxelMesherDMC::build_mesh(const VoxelBuffer &voxels, real_t geometric_error, Mode mode) { // Requirements: // - Voxel data must be padded // - Gradients must be precalculated // - The non-padded area size is cubic and power of two int padding = 1; const Vector3i buffer_size = voxels.get_size(); // Taking previous power of two because the algorithm uses an integer cubic octree, and data should be padded int chunk_size = previous_power_of_2(MIN(MIN(buffer_size.x, buffer_size.y), buffer_size.z)); ERR_FAIL_COND_V(voxels.get_size().x < chunk_size + padding * 2, Ref()); ERR_FAIL_COND_V(voxels.get_size().y < chunk_size + padding * 2, Ref()); ERR_FAIL_COND_V(voxels.get_size().z < chunk_size + padding * 2, Ref()); // Construct an intermediate to handle padding transparently dmc::VoxelAccess voxels_access(voxels, Vector3i(padding)); real_t time_before = OS::get_singleton()->get_ticks_usec(); // In an ideal world, a tiny sphere placed in the middle of an empty SDF volume will // cause corners data to change so that they indicate distance to it. // That means we could build our meshing octree top-down efficiently because corners of the volume will tell if the // distance to any surface is varying. // // For large terrains, 8-bit isolevels with quantification of -1..1 could be enough to represent surfaces. // It compresses well, and we don't need to propagate distance changes to the whole volume as we edit it. // Finally, it's easy to find uniform locations, they will be filled with 0 or 255, and discarded, // or possibly stored in a data octree already. // // Problem: // If you try building the meshing octree top-down in that case, it could see corners all have value of 1, // and will skip everything, assuming the volume contains nothing. // Building the octree bottom-up ensures to always catch voxels of any size, but will be a bit slower // because all voxels are queried. // #ifdef BUILD_OCTREE_BOTTOM_UP dmc::OctreeBuilderBottomUp octree_builder(voxels_access, geometric_error); dmc::OctreeNode *root = octree_builder.build(Vector3i(), chunk_size); #else dmc::OctreeNode *root = memnew(dmc::OctreeNode); root->origin = Vector3i(); root->size = chunk_size; dmc::generate_octree_top_down(root, voxels_access, geometric_error); #endif _stats.octree_build_time = OS::get_singleton()->get_ticks_usec() - time_before; if (root == nullptr) { return Ref(); } // TODO OctreeNode pool to stop allocating. Or, flat octree? if (mode == VoxelMesherDMC::MODE_DEBUG_OCTREE) { Ref mesh = dmc::generate_debug_octree_mesh(root); memdelete(root); return mesh; } time_before = OS::get_singleton()->get_ticks_usec(); dmc::DualGrid grid; dmc::DualGridGenerator dual_grid_generator(grid, root->size); dual_grid_generator.node_proc(root); _stats.dualgrid_derivation_time = OS::get_singleton()->get_ticks_usec() - time_before; memdelete(root); // TODO Handle non-subdivided octree if (mode == VoxelMesherDMC::MODE_DEBUG_DUAL_GRID) { return dmc::generate_debug_dual_grid_mesh(grid); } time_before = OS::get_singleton()->get_ticks_usec(); dmc::polygonize_dual_grid(grid, voxels_access, _mesh_builder); _stats.meshing_time = OS::get_singleton()->get_ticks_usec() - time_before; time_before = OS::get_singleton()->get_ticks_usec(); Ref mesh = _mesh_builder.commit(mode == VoxelMesherDMC::MODE_WIREFRAME); _stats.commit_time = OS::get_singleton()->get_ticks_usec() - time_before; // TODO Marching squares skirts return mesh; } Ref VoxelMesherDMC::_build_mesh_b(Ref voxels, real_t geometric_error, Mode mode) { ERR_FAIL_COND_V(voxels.is_null(), Ref()); return build_mesh(**voxels, geometric_error, mode); } Dictionary VoxelMesherDMC::get_stats() const { Dictionary d; d["octree_build_time"] = _stats.octree_build_time; d["dualgrid_derivation_time"] = _stats.dualgrid_derivation_time; d["meshing_time"] = _stats.meshing_time; d["commit_time"] = _stats.commit_time; return d; } void VoxelMesherDMC::_bind_methods() { ClassDB::bind_method(D_METHOD("build_mesh", "voxel_buffer", "geometric_error", "mode"), &VoxelMesherDMC::_build_mesh_b, DEFVAL(MODE_NORMAL)); ClassDB::bind_method(D_METHOD("get_stats"), &VoxelMesherDMC::get_stats); BIND_ENUM_CONSTANT(MODE_NORMAL); BIND_ENUM_CONSTANT(MODE_WIREFRAME); BIND_ENUM_CONSTANT(MODE_DEBUG_OCTREE); BIND_ENUM_CONSTANT(MODE_DEBUG_DUAL_GRID); }