754 lines
24 KiB
C++
754 lines
24 KiB
C++
#ifndef VCG_PIVOT_H
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#define VCG_PIVOT_H
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#include <vector>
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#include <list>
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#include "vcg/space/index/grid_static_ptr.h"
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#include "vcg/complex/algorithms/closest.h"
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namespace vcg {
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namespace tri {
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struct Hinge {
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int v0, v1, v2; //v0, v1 represent the Hinge, v2 the other vertex in the face
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//this Hinge belongs to
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int face; //corresponding face
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Point3f center; //center of the sphere touching the face
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int count; //test delay touch Hinges.
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//the loops in the front are mantained as a double linked list
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std::list<Hinge>::iterator next;
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std::list<Hinge>::iterator previous;
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Hinge() {}
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Hinge(int _v0, int _v1, int _v2, int _face, Point3f &_center):
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v0(_v0), v1(_v1), v2(_v2),
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face(_face), center(_center), count(0) {
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assert(v0 != v1 && v1 != v2 && v0 != v2);
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}
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};
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template <class MESH>
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class Pivot {
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public:
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// typedef CMesh MESH;
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typedef GridStaticPtr<typename MESH::VertexType, typename MESH::ScalarType > StaticGrid;
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float radius; //default 1 (not meaningful
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float mindist; //minimum distance between points in the mesh (% of radius)
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float crease; // -0.5
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Box3f box;
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MESH &mesh;
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StaticGrid grid;
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/* front Hinges of the mesh:
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to expand the front we get the first Hinge
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if an Hinge cannot create a new triangle it is marked dead and moved
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to the end of the list
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the new Hinges are inserted to the back (before dead_begin) */
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std::list<Hinge> front;
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std::list<Hinge> deads;
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std::vector<int> nb; //number of fronts a vertex is into,
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//this is used for the Visited and Border flags
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//but adding topology may not be needed anymode
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Pivot(MESH &_mesh, float _radius, float _mindist = 0.05, float _crease = -0.5):
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mesh(_mesh), radius(_radius), mindist(_mindist), crease(_crease) {
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//Compute bounding box. (this may be passed as a parameter?
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for(int i = 0; i < mesh.vert.size(); i++)
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box.Add(mesh.vert[i].P());
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/* we need to enlarge the grid to allow queries from little outside of the box
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Someone is a bit lazy... */
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box.Offset(4*radius);
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grid.Set(mesh.vert.begin(), mesh.vert.end(), box);
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nb.clear();
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nb.resize(mesh.vert.size(), 0);
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for(int i = 0; i < mesh.vert.size(); i++)
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mesh.vert[i].ClearFlags();
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}
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/* select a vertex at random, a small group of nearby vertices and looks
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for a sphere that touches 3 and contains none.
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Use the center of the box to get a sphere inside (or outside) the model
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You may be unlucky... */
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bool seed(bool outside = true, int start = -1) {
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//pick a random point (well...)
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if(start == -1) start = rand()%mesh.vert.size();
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//get a sphere of neighbours
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std::vector<int> targets;
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std::vector<float> dists;
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int n = getInSphere(mesh.vert[start].P(), 2*radius, targets, dists);
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if(n < 3) {
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//bad luck. we should call seed again (assuming random pick) up to
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//some maximum tries. im lazy.
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return false;
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}
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int v0, v1, v2;
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bool found = false;
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//find a triplet that does not contains any other point
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Point3f center;
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for(int i = 0; i < n; i++) {
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v0 = targets[i];
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CVertex &vv0 = mesh.vert[v0];
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if(vv0.IsD() || vv0.IsB() || vv0.IsV()) continue;
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Point3f &p0 = mesh.vert[v0].P();
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Point3f out = (p0 - box.Center());
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if(!outside) out = -out;
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for(int k = i+1; k < n; k++) {
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v1 = targets[k];
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CVertex &vv1 = mesh.vert[v1];
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if(vv1.IsD() || vv1.IsB() || vv1.IsV()) continue;
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Point3f &p1 = mesh.vert[v1].P();
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if((p1 - p0).Norm() < mindist*radius) continue;
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for(int j = k+1; j < n; j++) {
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v2 = targets[j];
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CVertex &vv2 = mesh.vert[v2];
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if(vv2.IsD() || vv2.IsB() || vv2.IsV()) continue;
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Point3f &p2 = mesh.vert[v2].P();
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if((p2 - p0).Norm() < mindist*radius) continue;
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if((p2 - p1).Norm() < mindist*radius) continue;
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Point3f normal = (p1 - p0)^(p2 - p0);
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//check normal pointing inside
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if(normal * out < 0) continue;
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if(!findSphere(p0, p1, p2, center)) continue;
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bool failed = false;
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//check no other point inside
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for(int t = 0; t < n; t++) {
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Point3f &p = mesh.vert[targets[t]].P();
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if((center - p).Norm() <= radius) {
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failed = true;
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break;
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}
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}
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if(failed) continue;
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found = true;
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i = k = j = n;
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}
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}
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}
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if(!found) //see bad luck above
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return false;
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assert(!front.size());
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//TODO: should i check the Hinges too?
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addFace(v0, v1, v2);
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//create the border of the first face
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std::list<Hinge>::iterator e = front.end();
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std::list<Hinge>::iterator last;
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for(int i = 0; i < 3; i++) {
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int v0 = (int)(mesh.face.back().V0(i));
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int v1 = (int)(mesh.face.back().V1(i));
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int v2 = (int)(mesh.face.back().V2(i));
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nb[v0] = 1;
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assert(!mesh.vert[v0].IsB());
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mesh.vert[v0].SetB();
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Hinge Hinge(v0, v1, v2, 0, center);
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Hinge.previous = e;
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e = front.insert(front.begin(), Hinge);
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if(i == 0) last = e;
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(*Hinge.previous).next = e;
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cluster(v0);
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}
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//connect last and first
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(*e).next = last;
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(*last).previous = e;
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return true;
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}
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/* expand the front adding 1 face. Return false on failure (id when
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all Hinges are dead returns:
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1: added a face
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0: added nothing
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-1: finished */
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int addFace() {
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//We try to seed again
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if(!mesh.face.size()) {
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for(int i = 0; i < 100; i++)
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if(seed()) return 1;
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return -1;
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}
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if(!front.size()) {
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//maybe there are unconnected parts of the mesh:
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//find a non D, V, B point and try to seed if failed D it.
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for(int i = 0; i < mesh.vert.size();i ++) {
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CVertex &v = mesh.vert[i];
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if(v.IsD() || v.IsV() || v.IsB()) continue;
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if(seed(true, i)) return 1;
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v.SetD();
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}
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return -1;
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}
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std::list<Hinge>::iterator ei = front.begin();
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Hinge &e = *ei;
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Hinge &previous = *e.previous;
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Hinge &next = *e.next;
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int v0 = e.v0, v1 = e.v1;
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//last triangle missing. or it is the first?
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if(0 &&next.next == e.previous) {
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int v[3] = { previous.v0, next.v0, e.v0 };
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int c[3] = { 0, 0, 0 };
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for(int k = 0; k < 3; k++) {
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int vert = v[k];
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nb[vert]--;
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if(nb[vert] == 0) {
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mesh.vert[vert].SetV();
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mesh.vert[vert].ClearB();
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}
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}
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assert(previous.previous == e.next);
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addFace(previous.v0, next.v0, e.v0);
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front.erase(e.previous);
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front.erase(e.next);
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front.erase(ei);
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return 1;
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}
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int v2;
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Point3f center;
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std::vector<int> targets;
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bool success = pivot(e, v2, center, targets);
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//if no pivoting move this thing to the end and try again
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//or we are trying to connect to the inside of the mesh. BAD.
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if(!success || mesh.vert[v2].IsV()) {
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killHinge(ei);
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return 0;
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}
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//does v2 belongs to a front? (and which?)
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std::list<Hinge>::iterator touch = touches(v2, ei);
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assert(v2 != v0 && v2 != v1);
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int fn = mesh.face.size();
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if(touch != front.end()) {
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if(!checkHinge(v0, v2) || !checkHinge(v2, v1)) {
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killHinge(ei);
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return 0;
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}
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if(v2 == previous.v0) {
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/*touching previous Hinge (we reuse previous)
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next
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------->v2 -----> v1------>
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\ /
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\ /
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previous \ / e
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\ /
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v0 */
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detach(v0);
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previous.v1 = v1;
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previous.v2 = v0;
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previous.face = fn;
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previous.center = center;
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previous.next = e.next;
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next.previous = e.previous;
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moveBack(e.previous);
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//this checks if we can glue something to e.previous
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trovamiunnome(e.previous);
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front.erase(ei);
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} else if(v2 == next.v1) {
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/*touching previous Hinge (we reuse next)
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previous
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------->v0 -----> v2------>
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\ /
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\ /
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\ / next
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\ /
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v1 */
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detach(v1);
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next.v0 = v0;
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next.v2 = v1;
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next.face = fn;
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next.center = center;
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next.previous = e.previous;
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previous.next = e.next;
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// moveBack(e.next);
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//this checks if we can glue something to e.previous
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trovamiunnome(e.next);
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front.erase(ei);
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} else {
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/* this code would delay the joining Hinge to avoid bad situations not used but..
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if(e.count < 2) {
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e.count++;
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moveBack(ei);
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return true;
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}*/
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//touching some loop: split (or merge it is local does not matter.
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//like this
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/*
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left right
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<--------v2-<------
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/|\
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/ \
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up / \ down
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/ \
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/ V
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----v0 - - - > v1---------
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e */
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std::list<Hinge>::iterator left = touch;
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std::list<Hinge>::iterator right = (*touch).previous;
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std::list<Hinge>::iterator up = ei;
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if(v1 == (*right).v0 || v0 == (*left).v1) {
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// cout << "Bad join.\n";
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killHinge(ei);
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return 0;
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}
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nb[v2]++;
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std::list<Hinge>::iterator down = newHinge(Hinge(v2, v1, v0, fn, center));
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(*right).next = down;
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(*down).previous = right;
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(*down).next = e.next;
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next.previous = down;
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(*left).previous = up;
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(*up).next = left;
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(*up).v2 = v1;
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(*up).v1 = v2;
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(*up).face = fn;
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(*up).center = center;
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moveBack(ei);
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}
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} else {
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assert(!mesh.vert[v2].IsB()); //fatal error! a new point is already a border?
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/* adding a new vertex
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v2
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/|\
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/ \
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up / \ down
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/ \
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/ V
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----v0 - - - > v1--------- */
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cluster(v2);
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nb[v2]++;
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mesh.vert[v2].SetB();
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std::list<Hinge>::iterator down = newHinge(Hinge(v2, v1, v0, fn, center));
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(*down).previous = ei;
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(*down).next = e.next;
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next.previous = down;
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e.v2 = v1;
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e.v1 = v2;
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e.face = fn;
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e.center = center;
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e.next = down;
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moveBack(ei);
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}
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addFace(v0, v2, v1);
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return 1;
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}
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/* return new vertex and the center of the new sphere pivoting from Hinge
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if the vertex belongs to another Hinge, touch points to it. */
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bool pivot(Hinge &Hinge, int &candidate, Point3f &end_pivot, std::vector<int> &targets) {
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Point3f v0 = mesh.vert[Hinge.v0].P();
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Point3f v1 = mesh.vert[Hinge.v1].P();
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Point3f v2 = mesh.vert[Hinge.v2].P();
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/* TODO why using the face normals everything goes wrong? should be
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exactly the same................................................
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Check if the e.face is correct.
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Point3f &normal = mesh.face[Hinge.face].N();
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*/
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Point3f normal = ((v1 - v0)^(v2 - v0)).Normalize();
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Point3f middle = (v0 + v1)/2;
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Point3f start_pivot = Hinge.center - middle;
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Point3f axis = (v1 - v0);
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float axis_len = axis.SquaredNorm();
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if(axis_len > 4*radius*radius) return false;
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axis.Normalize();
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// r is the radius of the thorus of all possible spheres passing throug v0 and v1
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float r = sqrt(radius*radius - axis_len/4);
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std::vector<float> dists;
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getInSphere(middle, r + radius, targets, dists);
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if(targets.size() == 0) return false; //this really would be strange but one never knows.
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candidate = -1;
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float minangle = 0;
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Point3f center; //to be computed for each sample
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for(int i = 0; i < targets.size(); i++) {
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int id = targets[i];
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if(id == Hinge.v0 || id == Hinge.v1 || id == Hinge.v2) continue;
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if(mesh.vert[id].IsD()) {
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continue;
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}
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Point3f p = mesh.vert[id].P();
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/* Prevent 360 Hinges, also often reject ~ 50% points */
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Point3f n = ((p - v0)^(v1 - v0)).Normalize();
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if(n * normal < -0.5) {
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continue;
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}
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/* Find the sphere through v0, p, v1 (store center on end_pivot */
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if(!findSphere(v0, p, v1, center)) {
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continue;
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}
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/* Angle between old center and new center */
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float alpha = angle(start_pivot, center - middle, axis);
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/* adding a small bias to already chosen vertices.
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doesn't solve numerical problems, but helps. */
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if(mesh.vert[id].IsB()) alpha -= 0.001;
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/* Sometimes alpha might be little less then M_PI while it should be 0,
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by numerical errors: happens for example pivoting
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on the diagonal of a square. */
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if(alpha > 2*M_PI - 0.8) {
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// Angle between old center and new *point*
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//TODO is this really overshooting? shouldbe enough to alpha -= 2*M_PI
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Point3f proj = p - axis * (axis * p - axis * middle);
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float beta = angle(start_pivot, proj - middle, axis);
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if(alpha > beta) alpha -= 2*M_PI;
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}
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if(candidate == -1 || alpha < minangle) {
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candidate = id;
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minangle = alpha;
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end_pivot = center;
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}
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}
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//found no point suitable.
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if(candidate == -1) {
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return false;
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}
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assert(candidate != Hinge.v0 && candidate != Hinge.v1);
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return true;
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}
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private:
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//front management:
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//Add a new Hinge to the back of the queue
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std::list<Hinge>::iterator newHinge(Hinge e) {
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return front.insert(front.end(), e);
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}
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//move an Hinge among the dead ones
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void killHinge(std::list<Hinge>::iterator e) {
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deads.splice(deads.end(), front, e);
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}
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//move an Hinge to the back of the queue
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void moveBack(std::list<Hinge>::iterator e) {
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front.splice(front.end(), front, e);
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}
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void moveFront(std::list<Hinge>::iterator e) {
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front.splice(front.begin(), front, e);
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}
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bool checkHinge(int v0, int v1) {
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int tot = 0;
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//HACK to speed up things until i can use a seach structure
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int i = mesh.face.size() - 2*(front.size());
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// i = 0;
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if(i < 0) i = 0;
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for(; i < mesh.face.size(); i++) {
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CFace &f = mesh.face[i];
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for(int k = 0; k < 3; k++) {
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if(v1== (int)f.V(k) && v0 == (int)f.V((k+1)%3)) ++tot;
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else if(v0 == (int)f.V(k) && v1 == (int)f.V((k+1)%3)) { //orientation non constistent
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return false;
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}
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}
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if(tot >= 2) { //non manifold
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return false;
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}
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}
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return true;
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}
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void Pivot::cluster(int v) {
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/* clean up too close points */
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std::vector<int> targets;
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std::vector<float> dists;
|
|
getInSphere(mesh.vert[v].P(), mindist*radius, targets, dists);
|
|
|
|
for(int i = 0; i < targets.size(); i++) {
|
|
int id = targets[i];
|
|
if(id == v) continue;
|
|
|
|
CVertex &v = mesh.vert[id];
|
|
if(v.IsD() || v.IsV() || v.IsB()) continue;
|
|
v.SetD();
|
|
}
|
|
|
|
}
|
|
|
|
void Pivot::trovamiunnome(std::list<Hinge>::iterator e) {
|
|
if(glue((*e).previous, e)) return;
|
|
glue(e, (*e).next);
|
|
}
|
|
|
|
//glue toghether a and b (where a.next = b
|
|
bool Pivot::glue(std::list<Hinge>::iterator a, std::list<Hinge>::iterator b) {
|
|
if((*a).v0 != (*b).v1) return false;
|
|
|
|
std::list<Hinge>::iterator previous = (*a).previous;
|
|
std::list<Hinge>::iterator next = (*b).next;
|
|
(*previous).next = next;
|
|
(*next).previous = previous;
|
|
detach((*a).v1);
|
|
detach((*a).v0);
|
|
front.erase(a);
|
|
front.erase(b);
|
|
return true;
|
|
}
|
|
|
|
void Pivot::detach(int v) {
|
|
assert(nb[v] > 0);
|
|
if(--nb[v] == 0) {
|
|
mesh.vert[v].SetV();
|
|
mesh.vert[v].ClearB();
|
|
}
|
|
}
|
|
|
|
|
|
/* compute angle from p to q, using axis for orientation */
|
|
float angle(Point3f p, Point3f q, Point3f &axis) {
|
|
p.Normalize();
|
|
q.Normalize();
|
|
Point3f vec = p^q;
|
|
float angle = acos(p*q);
|
|
if(vec*axis < 0) angle = -angle;
|
|
if(angle < 0) angle += 2*M_PI;
|
|
return angle;
|
|
}
|
|
/* add a new face. compute normals. */
|
|
void addFace(int a, int b, int c) {
|
|
CFace face;
|
|
face.V(0) = (CVertex *)a;
|
|
face.V(1) = (CVertex *)b;
|
|
face.V(2) = (CVertex *)c;
|
|
Point3f &p0 = mesh.vert[a].P();
|
|
Point3f &p1 = mesh.vert[b].P();
|
|
Point3f &p2 = mesh.vert[c].P();
|
|
face.N() = ((p1 - p0)^(p2 - p0)).Normalize();
|
|
|
|
mesh.face.push_back(face);
|
|
mesh.fn++;
|
|
}
|
|
|
|
|
|
/* intersects segment [v0, v1] with the sphere of radius radius. */
|
|
bool intersect(int v0, int v1, Point3f ¢er) {
|
|
Point3f m = mesh.vert[v1].P() - mesh.vert[v0].P();
|
|
float t = m*(center - mesh.vert[v0].P());
|
|
if(t < 0) return false;
|
|
if(t > m*m) return false;
|
|
return true;
|
|
}
|
|
|
|
|
|
float distance(int v0, int v1, Point3f ¢er) {
|
|
Point3f m = mesh.vert[v1].P() - mesh.vert[v0].P();
|
|
float t = m*(center - mesh.vert[v0].P())/(m*m);
|
|
Point3f p = mesh.vert[v0].P() + m*t;
|
|
return (p - center).Norm();
|
|
}
|
|
|
|
|
|
/* return all point in a given ball, notice as i want the index
|
|
of the vertices not the pointers... this may change in future */
|
|
unsigned int getInSphere(vcg::Point3f &p, float distance,
|
|
std::vector<int> &results,
|
|
std::vector<float> &dists) {
|
|
std::vector<CVertex *> ptr;
|
|
std::vector<Point3f> points;
|
|
int n = vcg::tri::GetInSphereVertex(mesh, grid, p, distance, ptr, dists, points);
|
|
for(int i = 0; i < ptr.size(); i++)
|
|
results.push_back(ptr[i] - &(mesh.vert[0]));
|
|
return n;
|
|
}
|
|
|
|
|
|
|
|
/* returns the sphere touching p0, p1, p2 of radius r such that
|
|
the normal of the face points toward the center of the sphere */
|
|
bool findSphere(Point3f &p0, Point3f &p1, Point3f &p2, Point3f ¢er) {
|
|
Point3f q1 = p1 - p0;
|
|
Point3f q2 = p2 - p0;
|
|
|
|
Point3f up = q1^q2;
|
|
float uplen = up.Norm();
|
|
|
|
//the three points are aligned
|
|
if(uplen < 0.001*q1.Norm()*q2.Norm()) return false;
|
|
up /= uplen;
|
|
|
|
|
|
float a11 = q1*q1;
|
|
float a12 = q1*q2;
|
|
float a22 = q2*q2;
|
|
|
|
float m = 4*(a11*a22 - a12*a12);
|
|
float l1 = 2*(a11*a22 - a22*a12)/m;
|
|
float l2 = 2*(a11*a22 - a12*a11)/m;
|
|
|
|
center = q1*l1 + q2*l2;
|
|
float circle_r = center.Norm();
|
|
if(circle_r > radius) return false; //need too big a sphere
|
|
|
|
float height = sqrt(radius*radius - circle_r*circle_r);
|
|
center += p0 + up*height;
|
|
|
|
return true;
|
|
}
|
|
std::list<Hinge>::iterator touches(int v, std::list<Hinge>::iterator e) {
|
|
//TODO what happens when it touches more than one front?
|
|
//might still work.
|
|
|
|
std::list<Hinge>::iterator touch = front.end();
|
|
if(mesh.vert[v].IsB()) {
|
|
//test nearby Hinges: it is faster
|
|
std::list<Hinge>::iterator p = e;
|
|
p = (*e).previous;
|
|
if(v == (*p).v0) return p;
|
|
e = (*e).next;
|
|
if(v == (*e).v0) return e;
|
|
|
|
p = (*p).previous;
|
|
if(v == (*p).v0) return p;
|
|
e = (*e).next;
|
|
if(v == (*e).v0) return e;
|
|
|
|
//test all. sigh.
|
|
|
|
for(std::list<Hinge>::iterator k = front.begin(); k != front.end(); k++) {
|
|
if(v == (*k).v0) {
|
|
touch = k;
|
|
break;
|
|
}
|
|
}
|
|
for(std::list<Hinge>::iterator k = deads.begin(); k != deads.end(); k++) {
|
|
if(v == (*k).v0) {
|
|
touch = k;
|
|
break;
|
|
}
|
|
}
|
|
assert(touch != front.end());
|
|
}
|
|
|
|
return touch;
|
|
}
|
|
|
|
|
|
public:
|
|
|
|
};
|
|
|
|
|
|
}//namespace
|
|
}//namespace
|
|
/* CODE FOR PIVOTING IN A TOUCH SITUATION not used now.
|
|
|
|
//if touch we want to check the ball could really pivot around that point
|
|
if(touch != front.end() && touch != (*Hinge.next).next && touch != Hinge.previous) {
|
|
Point3f &hinge = mesh.vert[min].P();
|
|
Point3f target = (*touch).center - hinge;
|
|
float d = (target * start_pivot)/(target.Norm()*start_pivot.Norm());
|
|
if(d < -0.8) {
|
|
return false;
|
|
}
|
|
|
|
|
|
|
|
if(d < 0.5) { //they are far enough so test .
|
|
Point3f naxis = (target ^ start_pivot).Normalize();
|
|
Point3f d1 = naxis^start_pivot;
|
|
Point3f d2 = target^naxis;
|
|
|
|
for(int i = 0; i < targets.size(); i++) {
|
|
int id = targets[i];
|
|
if(id == Hinge.v0 || id == Hinge.v1 || id == Hinge.v2 || id == min) continue;
|
|
if(mesh.vert[id].IsD()) {
|
|
continue;
|
|
}
|
|
|
|
Point3f intruder = mesh.vert[targets[i]].P() - hinge;
|
|
float h = intruder*naxis;
|
|
if(fabs(h) > radius) continue;
|
|
intruder -= naxis*h;
|
|
assert(fabs(intruder *naxis) < 0.01);
|
|
float off = radius - intruder.Norm(); //(distance from the center ring of the thorus
|
|
if(h*h + off*off > radius*radius) continue; //outside of thorus
|
|
if(d1*intruder < 0 || d2*intruder < 0) continue; //ouside of sector
|
|
cout << "could not pivot while touching;\n";
|
|
return false;
|
|
}
|
|
|
|
}
|
|
}*/
|
|
|
|
|
|
#endif
|