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+/*
+Open Asset Import Library (assimp)
+----------------------------------------------------------------------
+
+Copyright (c) 2006-2022, assimp team
+
+
+All rights reserved.
+
+Redistribution and use of this software in source and binary forms,
+with or without modification, are permitted provided that the
+following conditions are met:
+
+* Redistributions of source code must retain the above
+ copyright notice, this list of conditions and the
+ following disclaimer.
+
+* Redistributions in binary form must reproduce the above
+ copyright notice, this list of conditions and the
+ following disclaimer in the documentation and/or other
+ materials provided with the distribution.
+
+* Neither the name of the assimp team, nor the names of its
+ contributors may be used to endorse or promote products
+ derived from this software without specific prior
+ written permission of the assimp team.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+----------------------------------------------------------------------
+*/
+
+#include <assimp/Subdivision.h>
+#include <assimp/SceneCombiner.h>
+#include <assimp/SpatialSort.h>
+#include <assimp/Vertex.h>
+#include <assimp/ai_assert.h>
+
+#include "PostProcessing/ProcessHelper.h"
+
+#include <stdio.h>
+
+using namespace Assimp;
+void mydummy() {}
+
+#ifdef _MSC_VER
+#pragma warning(disable : 4709)
+#endif // _MSC_VER
+// ------------------------------------------------------------------------------------------------
+/** Subdivider stub class to implement the Catmull-Clarke subdivision algorithm. The
+ * implementation is basing on recursive refinement. Directly evaluating the result is also
+ * possible and much quicker, but it depends on lengthy matrix lookup tables. */
+// ------------------------------------------------------------------------------------------------
+class CatmullClarkSubdivider : public Subdivider {
+public:
+ void Subdivide(aiMesh *mesh, aiMesh *&out, unsigned int num, bool discard_input);
+ void Subdivide(aiMesh **smesh, size_t nmesh,
+ aiMesh **out, unsigned int num, bool discard_input);
+
+ // ---------------------------------------------------------------------------
+ /** Intermediate description of an edge between two corners of a polygon*/
+ // ---------------------------------------------------------------------------
+ struct Edge {
+ Edge() :
+ ref(0) {}
+ Vertex edge_point, midpoint;
+ unsigned int ref;
+ };
+
+ typedef std::vector<unsigned int> UIntVector;
+ typedef std::map<uint64_t, Edge> EdgeMap;
+
+ // ---------------------------------------------------------------------------
+ // Hashing function to derive an index into an #EdgeMap from two given
+ // 'unsigned int' vertex coordinates (!!distinct coordinates - same
+ // vertex position == same index!!).
+ // NOTE - this leads to rare hash collisions if a) sizeof(unsigned int)>4
+ // and (id[0]>2^32-1 or id[0]>2^32-1).
+ // MAKE_EDGE_HASH() uses temporaries, so INIT_EDGE_HASH() needs to be put
+ // at the head of every function which is about to use MAKE_EDGE_HASH().
+ // Reason is that the hash is that hash construction needs to hold the
+ // invariant id0<id1 to identify an edge - else two hashes would refer
+ // to the same edge.
+ // ---------------------------------------------------------------------------
+#define MAKE_EDGE_HASH(id0, id1) (eh_tmp0__ = id0, eh_tmp1__ = id1, \
+ (eh_tmp0__ < eh_tmp1__ ? std::swap(eh_tmp0__, eh_tmp1__) : mydummy()), (uint64_t)eh_tmp0__ ^ ((uint64_t)eh_tmp1__ << 32u))
+
+#define INIT_EDGE_HASH_TEMPORARIES() \
+ unsigned int eh_tmp0__, eh_tmp1__;
+
+private:
+ void InternSubdivide(const aiMesh *const *smesh,
+ size_t nmesh, aiMesh **out, unsigned int num);
+};
+
+// ------------------------------------------------------------------------------------------------
+// Construct a subdivider of a specific type
+Subdivider *Subdivider::Create(Algorithm algo) {
+ switch (algo) {
+ case CATMULL_CLARKE:
+ return new CatmullClarkSubdivider();
+ };
+
+ ai_assert(false);
+
+ return nullptr; // shouldn't happen
+}
+
+// ------------------------------------------------------------------------------------------------
+// Call the Catmull Clark subdivision algorithm for one mesh
+void CatmullClarkSubdivider::Subdivide(
+ aiMesh *mesh,
+ aiMesh *&out,
+ unsigned int num,
+ bool discard_input) {
+ ai_assert(mesh != out);
+
+ Subdivide(&mesh, 1, &out, num, discard_input);
+}
+
+// ------------------------------------------------------------------------------------------------
+// Call the Catmull Clark subdivision algorithm for multiple meshes
+void CatmullClarkSubdivider::Subdivide(
+ aiMesh **smesh,
+ size_t nmesh,
+ aiMesh **out,
+ unsigned int num,
+ bool discard_input) {
+ ai_assert(nullptr != smesh);
+ ai_assert(nullptr != out);
+
+ // course, both regions may not overlap
+ ai_assert(smesh < out || smesh + nmesh > out + nmesh);
+ if (!num) {
+ // No subdivision at all. Need to copy all the meshes .. argh.
+ if (discard_input) {
+ for (size_t s = 0; s < nmesh; ++s) {
+ out[s] = smesh[s];
+ smesh[s] = nullptr;
+ }
+ } else {
+ for (size_t s = 0; s < nmesh; ++s) {
+ SceneCombiner::Copy(out + s, smesh[s]);
+ }
+ }
+ return;
+ }
+
+ std::vector<aiMesh *> inmeshes;
+ std::vector<aiMesh *> outmeshes;
+ std::vector<unsigned int> maptbl;
+
+ inmeshes.reserve(nmesh);
+ outmeshes.reserve(nmesh);
+ maptbl.reserve(nmesh);
+
+ // Remove pure line and point meshes from the working set to reduce the
+ // number of edge cases the subdivider is forced to deal with. Line and
+ // point meshes are simply passed through.
+ for (size_t s = 0; s < nmesh; ++s) {
+ aiMesh *i = smesh[s];
+ // FIX - mPrimitiveTypes might not yet be initialized
+ if (i->mPrimitiveTypes && (i->mPrimitiveTypes & (aiPrimitiveType_LINE | aiPrimitiveType_POINT)) == i->mPrimitiveTypes) {
+ ASSIMP_LOG_VERBOSE_DEBUG("Catmull-Clark Subdivider: Skipping pure line/point mesh");
+
+ if (discard_input) {
+ out[s] = i;
+ smesh[s] = nullptr;
+ } else {
+ SceneCombiner::Copy(out + s, i);
+ }
+ continue;
+ }
+
+ outmeshes.push_back(nullptr);
+ inmeshes.push_back(i);
+ maptbl.push_back(static_cast<unsigned int>(s));
+ }
+
+ // Do the actual subdivision on the preallocated storage. InternSubdivide
+ // *always* assumes that enough storage is available, it does not bother
+ // checking any ranges.
+ ai_assert(inmeshes.size() == outmeshes.size());
+ ai_assert(inmeshes.size() == maptbl.size());
+ if (inmeshes.empty()) {
+ ASSIMP_LOG_WARN("Catmull-Clark Subdivider: Pure point/line scene, I can't do anything");
+ return;
+ }
+ InternSubdivide(&inmeshes.front(), inmeshes.size(), &outmeshes.front(), num);
+ for (unsigned int i = 0; i < maptbl.size(); ++i) {
+ ai_assert(nullptr != outmeshes[i]);
+ out[maptbl[i]] = outmeshes[i];
+ }
+
+ if (discard_input) {
+ for (size_t s = 0; s < nmesh; ++s) {
+ delete smesh[s];
+ }
+ }
+}
+
+// ------------------------------------------------------------------------------------------------
+// Note - this is an implementation of the standard (recursive) Cm-Cl algorithm without further
+// optimizations (except we're using some nice LUTs). A description of the algorithm can be found
+// here: http://en.wikipedia.org/wiki/Catmull-Clark_subdivision_surface
+//
+// The code is mostly O(n), however parts are O(nlogn) which is therefore the algorithm's
+// expected total runtime complexity. The implementation is able to work in-place on the same
+// mesh arrays. Calling #InternSubdivide() directly is not encouraged. The code can operate
+// in-place unless 'smesh' and 'out' are equal (no strange overlaps or reorderings).
+// Previous data is replaced/deleted then.
+// ------------------------------------------------------------------------------------------------
+void CatmullClarkSubdivider::InternSubdivide(
+ const aiMesh *const *smesh,
+ size_t nmesh,
+ aiMesh **out,
+ unsigned int num) {
+ ai_assert(nullptr != smesh);
+ ai_assert(nullptr != out);
+
+ INIT_EDGE_HASH_TEMPORARIES();
+
+ // no subdivision requested or end of recursive refinement
+ if (!num) {
+ return;
+ }
+
+ UIntVector maptbl;
+ SpatialSort spatial;
+
+ // ---------------------------------------------------------------------
+ // 0. Offset table to index all meshes continuously, generate a spatially
+ // sorted representation of all vertices in all meshes.
+ // ---------------------------------------------------------------------
+ typedef std::pair<unsigned int, unsigned int> IntPair;
+ std::vector<IntPair> moffsets(nmesh);
+ unsigned int totfaces = 0, totvert = 0;
+ for (size_t t = 0; t < nmesh; ++t) {
+ const aiMesh *mesh = smesh[t];
+
+ spatial.Append(mesh->mVertices, mesh->mNumVertices, sizeof(aiVector3D), false);
+ moffsets[t] = IntPair(totfaces, totvert);
+
+ totfaces += mesh->mNumFaces;
+ totvert += mesh->mNumVertices;
+ }
+
+ spatial.Finalize();
+ const unsigned int num_unique = spatial.GenerateMappingTable(maptbl, ComputePositionEpsilon(smesh, nmesh));
+
+#define FLATTEN_VERTEX_IDX(mesh_idx, vert_idx) (moffsets[mesh_idx].second + vert_idx)
+#define FLATTEN_FACE_IDX(mesh_idx, face_idx) (moffsets[mesh_idx].first + face_idx)
+
+ // ---------------------------------------------------------------------
+ // 1. Compute the centroid point for all faces
+ // ---------------------------------------------------------------------
+ std::vector<Vertex> centroids(totfaces);
+ unsigned int nfacesout = 0;
+ for (size_t t = 0, n = 0; t < nmesh; ++t) {
+ const aiMesh *mesh = smesh[t];
+ for (unsigned int i = 0; i < mesh->mNumFaces; ++i, ++n) {
+ const aiFace &face = mesh->mFaces[i];
+ Vertex &c = centroids[n];
+
+ for (unsigned int a = 0; a < face.mNumIndices; ++a) {
+ c += Vertex(mesh, face.mIndices[a]);
+ }
+
+ c /= static_cast<float>(face.mNumIndices);
+ nfacesout += face.mNumIndices;
+ }
+ }
+
+ {
+ // we want edges to go away before the recursive calls so begin a new scope
+ EdgeMap edges;
+
+ // ---------------------------------------------------------------------
+ // 2. Set each edge point to be the average of all neighbouring
+ // face points and original points. Every edge exists twice
+ // if there is a neighboring face.
+ // ---------------------------------------------------------------------
+ for (size_t t = 0; t < nmesh; ++t) {
+ const aiMesh *mesh = smesh[t];
+
+ for (unsigned int i = 0; i < mesh->mNumFaces; ++i) {
+ const aiFace &face = mesh->mFaces[i];
+
+ for (unsigned int p = 0; p < face.mNumIndices; ++p) {
+ const unsigned int id[] = {
+ face.mIndices[p],
+ face.mIndices[p == face.mNumIndices - 1 ? 0 : p + 1]
+ };
+ const unsigned int mp[] = {
+ maptbl[FLATTEN_VERTEX_IDX(t, id[0])],
+ maptbl[FLATTEN_VERTEX_IDX(t, id[1])]
+ };
+
+ Edge &e = edges[MAKE_EDGE_HASH(mp[0], mp[1])];
+ e.ref++;
+ if (e.ref <= 2) {
+ if (e.ref == 1) { // original points (end points) - add only once
+ e.edge_point = e.midpoint = Vertex(mesh, id[0]) + Vertex(mesh, id[1]);
+ e.midpoint *= 0.5f;
+ }
+ e.edge_point += centroids[FLATTEN_FACE_IDX(t, i)];
+ }
+ }
+ }
+ }
+
+ // ---------------------------------------------------------------------
+ // 3. Normalize edge points
+ // ---------------------------------------------------------------------
+ {
+ unsigned int bad_cnt = 0;
+ for (EdgeMap::iterator it = edges.begin(); it != edges.end(); ++it) {
+ if ((*it).second.ref < 2) {
+ ai_assert((*it).second.ref);
+ ++bad_cnt;
+ }
+ (*it).second.edge_point *= 1.f / ((*it).second.ref + 2.f);
+ }
+
+ if (bad_cnt) {
+ // Report the number of bad edges. bad edges are referenced by less than two
+ // faces in the mesh. They occur at outer model boundaries in non-closed
+ // shapes.
+ ASSIMP_LOG_VERBOSE_DEBUG("Catmull-Clark Subdivider: got ", bad_cnt, " bad edges touching only one face (totally ",
+ static_cast<unsigned int>(edges.size()), " edges). ");
+ }
+ }
+
+ // ---------------------------------------------------------------------
+ // 4. Compute a vertex-face adjacency table. We can't reuse the code
+ // from VertexTriangleAdjacency because we need the table for multiple
+ // meshes and out vertex indices need to be mapped to distinct values
+ // first.
+ // ---------------------------------------------------------------------
+ UIntVector faceadjac(nfacesout), cntadjfac(maptbl.size(), 0), ofsadjvec(maptbl.size() + 1, 0);
+ {
+ for (size_t t = 0; t < nmesh; ++t) {
+ const aiMesh *const minp = smesh[t];
+ for (unsigned int i = 0; i < minp->mNumFaces; ++i) {
+
+ const aiFace &f = minp->mFaces[i];
+ for (unsigned int n = 0; n < f.mNumIndices; ++n) {
+ ++cntadjfac[maptbl[FLATTEN_VERTEX_IDX(t, f.mIndices[n])]];
+ }
+ }
+ }
+ unsigned int cur = 0;
+ for (size_t i = 0; i < cntadjfac.size(); ++i) {
+ ofsadjvec[i + 1] = cur;
+ cur += cntadjfac[i];
+ }
+ for (size_t t = 0; t < nmesh; ++t) {
+ const aiMesh *const minp = smesh[t];
+ for (unsigned int i = 0; i < minp->mNumFaces; ++i) {
+
+ const aiFace &f = minp->mFaces[i];
+ for (unsigned int n = 0; n < f.mNumIndices; ++n) {
+ faceadjac[ofsadjvec[1 + maptbl[FLATTEN_VERTEX_IDX(t, f.mIndices[n])]]++] = FLATTEN_FACE_IDX(t, i);
+ }
+ }
+ }
+
+ // check the other way round for consistency
+#ifdef ASSIMP_BUILD_DEBUG
+
+ for (size_t t = 0; t < ofsadjvec.size() - 1; ++t) {
+ for (unsigned int m = 0; m < cntadjfac[t]; ++m) {
+ const unsigned int fidx = faceadjac[ofsadjvec[t] + m];
+ ai_assert(fidx < totfaces);
+ for (size_t n = 1; n < nmesh; ++n) {
+
+ if (moffsets[n].first > fidx) {
+ const aiMesh *msh = smesh[--n];
+ const aiFace &f = msh->mFaces[fidx - moffsets[n].first];
+
+ bool haveit = false;
+ for (unsigned int i = 0; i < f.mNumIndices; ++i) {
+ if (maptbl[FLATTEN_VERTEX_IDX(n, f.mIndices[i])] == (unsigned int)t) {
+ haveit = true;
+ break;
+ }
+ }
+ ai_assert(haveit);
+ if (!haveit) {
+ ASSIMP_LOG_VERBOSE_DEBUG("Catmull-Clark Subdivider: Index not used");
+ }
+ break;
+ }
+ }
+ }
+ }
+
+#endif
+ }
+
+#define GET_ADJACENT_FACES_AND_CNT(vidx, fstartout, numout) \
+ fstartout = &faceadjac[ofsadjvec[vidx]], numout = cntadjfac[vidx]
+
+ typedef std::pair<bool, Vertex> TouchedOVertex;
+ std::vector<TouchedOVertex> new_points(num_unique, TouchedOVertex(false, Vertex()));
+ // ---------------------------------------------------------------------
+ // 5. Spawn a quad from each face point to the corresponding edge points
+ // the original points being the fourth quad points.
+ // ---------------------------------------------------------------------
+ for (size_t t = 0; t < nmesh; ++t) {
+ const aiMesh *const minp = smesh[t];
+ aiMesh *const mout = out[t] = new aiMesh();
+
+ for (unsigned int a = 0; a < minp->mNumFaces; ++a) {
+ mout->mNumFaces += minp->mFaces[a].mNumIndices;
+ }
+
+ // We need random access to the old face buffer, so reuse is not possible.
+ mout->mFaces = new aiFace[mout->mNumFaces];
+
+ mout->mNumVertices = mout->mNumFaces * 4;
+ mout->mVertices = new aiVector3D[mout->mNumVertices];
+
+ // quads only, keep material index
+ mout->mPrimitiveTypes = aiPrimitiveType_POLYGON;
+ mout->mMaterialIndex = minp->mMaterialIndex;
+
+ if (minp->HasNormals()) {
+ mout->mNormals = new aiVector3D[mout->mNumVertices];
+ }
+
+ if (minp->HasTangentsAndBitangents()) {
+ mout->mTangents = new aiVector3D[mout->mNumVertices];
+ mout->mBitangents = new aiVector3D[mout->mNumVertices];
+ }
+
+ for (unsigned int i = 0; minp->HasTextureCoords(i); ++i) {
+ mout->mTextureCoords[i] = new aiVector3D[mout->mNumVertices];
+ mout->mNumUVComponents[i] = minp->mNumUVComponents[i];
+ }
+
+ for (unsigned int i = 0; minp->HasVertexColors(i); ++i) {
+ mout->mColors[i] = new aiColor4D[mout->mNumVertices];
+ }
+
+ mout->mNumVertices = mout->mNumFaces << 2u;
+ for (unsigned int i = 0, v = 0, n = 0; i < minp->mNumFaces; ++i) {
+
+ const aiFace &face = minp->mFaces[i];
+ for (unsigned int a = 0; a < face.mNumIndices; ++a) {
+
+ // Get a clean new face.
+ aiFace &faceOut = mout->mFaces[n++];
+ faceOut.mIndices = new unsigned int[faceOut.mNumIndices = 4];
+
+ // Spawn a new quadrilateral (ccw winding) for this original point between:
+ // a) face centroid
+ centroids[FLATTEN_FACE_IDX(t, i)].SortBack(mout, faceOut.mIndices[0] = v++);
+
+ // b) adjacent edge on the left, seen from the centroid
+ const Edge &e0 = edges[MAKE_EDGE_HASH(maptbl[FLATTEN_VERTEX_IDX(t, face.mIndices[a])],
+ maptbl[FLATTEN_VERTEX_IDX(t, face.mIndices[a == face.mNumIndices - 1 ? 0 : a + 1])])]; // fixme: replace with mod face.mNumIndices?
+
+ // c) adjacent edge on the right, seen from the centroid
+ const Edge &e1 = edges[MAKE_EDGE_HASH(maptbl[FLATTEN_VERTEX_IDX(t, face.mIndices[a])],
+ maptbl[FLATTEN_VERTEX_IDX(t, face.mIndices[!a ? face.mNumIndices - 1 : a - 1])])]; // fixme: replace with mod face.mNumIndices?
+
+ e0.edge_point.SortBack(mout, faceOut.mIndices[3] = v++);
+ e1.edge_point.SortBack(mout, faceOut.mIndices[1] = v++);
+
+ // d= original point P with distinct index i
+ // F := 0
+ // R := 0
+ // n := 0
+ // for each face f containing i
+ // F := F+ centroid of f
+ // R := R+ midpoint of edge of f from i to i+1
+ // n := n+1
+ //
+ // (F+2R+(n-3)P)/n
+ const unsigned int org = maptbl[FLATTEN_VERTEX_IDX(t, face.mIndices[a])];
+ TouchedOVertex &ov = new_points[org];
+
+ if (!ov.first) {
+ ov.first = true;
+
+ const unsigned int *adj;
+ unsigned int cnt;
+ GET_ADJACENT_FACES_AND_CNT(org, adj, cnt);
+
+ if (cnt < 3) {
+ ov.second = Vertex(minp, face.mIndices[a]);
+ } else {
+
+ Vertex F, R;
+ for (unsigned int o = 0; o < cnt; ++o) {
+ ai_assert(adj[o] < totfaces);
+ F += centroids[adj[o]];
+
+ // adj[0] is a global face index - search the face in the mesh list
+ const aiMesh *mp = nullptr;
+ size_t nidx;
+
+ if (adj[o] < moffsets[0].first) {
+ mp = smesh[nidx = 0];
+ } else {
+ for (nidx = 1; nidx <= nmesh; ++nidx) {
+ if (nidx == nmesh || moffsets[nidx].first > adj[o]) {
+ mp = smesh[--nidx];
+ break;
+ }
+ }
+ }
+
+ ai_assert(adj[o] - moffsets[nidx].first < mp->mNumFaces);
+ const aiFace &f = mp->mFaces[adj[o] - moffsets[nidx].first];
+ bool haveit = false;
+
+ // find our original point in the face
+ for (unsigned int m = 0; m < f.mNumIndices; ++m) {
+ if (maptbl[FLATTEN_VERTEX_IDX(nidx, f.mIndices[m])] == org) {
+
+ // add *both* edges. this way, we can be sure that we add
+ // *all* adjacent edges to R. In a closed shape, every
+ // edge is added twice - so we simply leave out the
+ // factor 2.f in the amove formula and get the right
+ // result.
+
+ const Edge &c0 = edges[MAKE_EDGE_HASH(org, maptbl[FLATTEN_VERTEX_IDX(
+ nidx, f.mIndices[!m ? f.mNumIndices - 1 : m - 1])])];
+ // fixme: replace with mod face.mNumIndices?
+
+ const Edge &c1 = edges[MAKE_EDGE_HASH(org, maptbl[FLATTEN_VERTEX_IDX(
+ nidx, f.mIndices[m == f.mNumIndices - 1 ? 0 : m + 1])])];
+ // fixme: replace with mod face.mNumIndices?
+ R += c0.midpoint + c1.midpoint;
+
+ haveit = true;
+ break;
+ }
+ }
+
+ // this invariant *must* hold if the vertex-to-face adjacency table is valid
+ ai_assert(haveit);
+ if (!haveit) {
+ ASSIMP_LOG_WARN("OBJ: no name for material library specified.");
+ }
+ }
+
+ const float div = static_cast<float>(cnt), divsq = 1.f / (div * div);
+ ov.second = Vertex(minp, face.mIndices[a]) * ((div - 3.f) / div) + R * divsq + F * divsq;
+ }
+ }
+ ov.second.SortBack(mout, faceOut.mIndices[2] = v++);
+ }
+ }
+ }
+ } // end of scope for edges, freeing its memory
+
+ // ---------------------------------------------------------------------
+ // 7. Apply the next subdivision step.
+ // ---------------------------------------------------------------------
+ if (num != 1) {
+ std::vector<aiMesh *> tmp(nmesh);
+ InternSubdivide(out, nmesh, &tmp.front(), num - 1);
+ for (size_t i = 0; i < nmesh; ++i) {
+ delete out[i];
+ out[i] = tmp[i];
+ }
+ }
+}