//----------------------------------------------------------------------- bool ConvexBody::hasClosedHull( void ) const { // if this map is returned empty, the body is closed Polygon::EdgeMap edgeMap = getSingleEdges(); return edgeMap.empty(); }
//----------------------------------------------------------------------- bool ConvexBody::findAndEraseEdgePair(const Vector3& vec, Polygon::EdgeMap& intersectionEdges, Vector3& vNext ) const { for (Polygon::EdgeMap::iterator it = intersectionEdges.begin(); it != intersectionEdges.end(); ++it) { if (it->first.positionEquals(vec)) { vNext = it->second; // erase found edge intersectionEdges.erase( it ); return true; // found! } else if (it->second.positionEquals(vec)) { vNext = it->first; // erase found edge intersectionEdges.erase( it ); return true; // found! } } return false; // not found! }
//----------------------------------------------------------------------- Polygon::EdgeMap ConvexBody::getSingleEdges() const { Polygon::EdgeMap edgeMap; // put all edges of all polygons into a list every edge has to be // walked in each direction once for ( size_t i = 0; i < getPolygonCount(); ++i ) { const Polygon& p = getPolygon( i ); for ( size_t j = 0; j < p.getVertexCount(); ++j ) { const Vector3& a = p.getVertex( j ); const Vector3& b = p.getVertex( ( j + 1 ) % p.getVertexCount() ); edgeMap.insert( Polygon::Edge( a, b ) ); } } // search corresponding parts Polygon::EdgeMap::iterator it; Polygon::EdgeMap::iterator itStart; Polygon::EdgeMap::const_iterator itEnd; while( !edgeMap.empty() ) { it = edgeMap.begin(); ++it; // start one element after itStart itStart = edgeMap.begin(); // the element to be compared with the others itEnd = edgeMap.end(); // beyond the last element bool bFound = false; for ( ; it != itEnd; ++it ) { if (itStart->first.positionEquals(it->second) && itStart->second.positionEquals(it->first)) { // erase itStart and it edgeMap.erase( it ); edgeMap.erase( itStart ); bFound = true; break; // found } } if ( bFound == false ) { break; // not all edges could be matched // body is not closed } } return edgeMap; }
//----------------------------------------------------------------------- void ConvexBody::clip( const Plane& pl, bool keepNegative ) { if ( getPolygonCount() == 0 ) return; // current will be used as the reference body ConvexBody current; current.moveDataFromBody(*this); OgreAssert( this->getPolygonCount() == 0, "Body not empty!" ); OgreAssert( current.getPolygonCount() != 0, "Body empty!" ); // holds all intersection edges for the different polygons Polygon::EdgeMap intersectionEdges; // clip all polygons by the intersection plane // add only valid or intersected polygons to *this for ( size_t iPoly = 0; iPoly < current.getPolygonCount(); ++iPoly ) { // fetch vertex count and ignore polygons with less than three vertices // the polygon is not valid and won't be added const size_t vertexCount = current.getVertexCount( iPoly ); if ( vertexCount < 3 ) continue; // current polygon const Polygon& p = current.getPolygon( iPoly ); // the polygon to assemble Polygon *pNew = allocatePolygon(); // the intersection polygon (indeed it's an edge or it's empty) Polygon *pIntersect = allocatePolygon(); // check if polygons lie inside or outside (or on the plane) // for each vertex check where it is situated in regard to the plane // three possibilities appear: Plane::Side clipSide = keepNegative ? Plane::POSITIVE_SIDE : Plane::NEGATIVE_SIDE; // - side is clipSide: vertex will be clipped // - side is !clipSide: vertex will be untouched // - side is NOSIDE: vertex will be untouched Plane::Side *side = OGRE_ALLOC_T(Plane::Side, vertexCount, MEMCATEGORY_SCENE_CONTROL); for ( size_t iVertex = 0; iVertex < vertexCount; ++iVertex ) { side[ iVertex ] = pl.getSide( p.getVertex( iVertex ) ); } // now we check the side combinations for the current and the next vertex // four different combinations exist: // - both points inside (or on the plane): keep the second (add it to the body) // - both points outside: discard both (don't add them to the body) // - first vertex is inside, second is outside: add the intersection point // - first vertex is outside, second is inside: add the intersection point, then the second for ( size_t iVertex = 0; iVertex < vertexCount; ++iVertex ) { // determine the next vertex size_t iNextVertex = ( iVertex + 1 ) % vertexCount; const Vector3& vCurrent = p.getVertex( iVertex ); const Vector3& vNext = p.getVertex( iNextVertex ); // case 1: both points inside (store next) if ( side[ iVertex ] != clipSide && // NEGATIVE or NONE side[ iNextVertex ] != clipSide ) // NEGATIVE or NONE { // keep the second pNew->insertVertex( vNext ); } // case 3: inside -> outside (store intersection) else if ( side[ iVertex ] != clipSide && side[ iNextVertex ] == clipSide ) { // Do an intersection with the plane. We use a ray with a start point and a direction. // The ray is forced to hit the plane with any option available (eigher current or next // is the starting point) // intersect from the outside vertex towards the inside one Vector3 vDirection = vCurrent - vNext; vDirection.normalise(); Ray ray( vNext, vDirection ); std::pair< bool, Real > intersect = ray.intersects( pl ); // store intersection if ( intersect.first ) { // convert distance to vector Vector3 vIntersect = ray.getPoint( intersect.second ); // store intersection pNew->insertVertex( vIntersect ); pIntersect->insertVertex( vIntersect ); } } // case 4: outside -> inside (store intersection, store next) else if ( side[ iVertex ] == clipSide && side[ iNextVertex ] != clipSide ) { // Do an intersection with the plane. We use a ray with a start point and a direction. // The ray is forced to hit the plane with any option available (eigher current or next // is the starting point) // intersect from the outside vertex towards the inside one Vector3 vDirection = vNext - vCurrent; vDirection.normalise(); Ray ray( vCurrent, vDirection ); std::pair< bool, Real > intersect = ray.intersects( pl ); // store intersection if ( intersect.first ) { // convert distance to vector Vector3 vIntersect = ray.getPoint( intersect.second ); // store intersection pNew->insertVertex( vIntersect ); pIntersect->insertVertex( vIntersect ); } pNew->insertVertex( vNext ); } // else: // case 2: both outside (do nothing) } // insert the polygon only, if at least three vertices are present if ( pNew->getVertexCount() >= 3 ) { // in case there are double vertices, remove them pNew->removeDuplicates(); // in case there are still at least three vertices, insert the polygon if ( pNew->getVertexCount() >= 3 ) { this->insertPolygon( pNew ); } else { // delete pNew because it's empty or invalid freePolygon(pNew); pNew = 0; } } else { // delete pNew because it's empty or invalid freePolygon(pNew); pNew = 0; } // insert intersection polygon only, if there are two vertices present if ( pIntersect->getVertexCount() == 2 ) { intersectionEdges.insert( Polygon::Edge( pIntersect->getVertex( 0 ), pIntersect->getVertex( 1 ) ) ); } // delete intersection polygon // vertices were copied (if there were any) freePolygon(pIntersect); pIntersect = 0; // delete side info OGRE_FREE(side, MEMCATEGORY_SCENE_CONTROL); side = 0; } // if the polygon was partially clipped, close it // at least three edges are needed for a polygon if ( intersectionEdges.size() >= 3 ) { Polygon *pClosing = allocatePolygon(); // Analyze the intersection list and insert the intersection points in ccw order // Each point is twice in the list because of the fact that we have a convex body // with convex polygons. All we have to do is order the edges (an even-odd pair) // in a ccw order. The plane normal shows us the direction. Polygon::EdgeMap::iterator it = intersectionEdges.begin(); // check the cross product of the first two edges Vector3 vFirst = it->first; Vector3 vSecond = it->second; // remove inserted edge intersectionEdges.erase( it ); Vector3 vNext; // find mating edge if (findAndEraseEdgePair(vSecond, intersectionEdges, vNext)) { // detect the orientation // the polygon must have the same normal direction as the plane and then n Vector3 vCross = ( vFirst - vSecond ).crossProduct( vNext - vSecond ); bool frontside = ( pl.normal ).directionEquals( vCross, Degree( 1 ) ); // first inserted vertex Vector3 firstVertex; // currently inserted vertex Vector3 currentVertex; // direction equals -> front side (walk ccw) if ( frontside ) { // start with next as first vertex, then second, then first and continue with first to walk ccw pClosing->insertVertex( vNext ); pClosing->insertVertex( vSecond ); pClosing->insertVertex( vFirst ); firstVertex = vNext; currentVertex = vFirst; #ifdef _DEBUG_INTERSECTION_LIST std::cout << "Plane: n=" << pl.normal << ", d=" << pl.d << std::endl; std::cout << "First inserted vertex: " << *next << std::endl; std::cout << "Second inserted vertex: " << *vSecond << std::endl; std::cout << "Third inserted vertex: " << *vFirst << std::endl; #endif } // direction does not equal -> back side (walk cw) else { // start with first as first vertex, then second, then next and continue with next to walk ccw pClosing->insertVertex( vFirst ); pClosing->insertVertex( vSecond ); pClosing->insertVertex( vNext ); firstVertex = vFirst; currentVertex = vNext; #ifdef _DEBUG_INTERSECTION_LIST std::cout << "Plane: n=" << pl.normal << ", d=" << pl.d << std::endl; std::cout << "First inserted vertex: " << *vFirst << std::endl; std::cout << "Second inserted vertex: " << *vSecond << std::endl; std::cout << "Third inserted vertex: " << *next << std::endl; #endif } // search mating edges that have a point in common // continue this operation as long as edges are present while ( !intersectionEdges.empty() ) { if (findAndEraseEdgePair(currentVertex, intersectionEdges, vNext)) { // insert only if it's not the last (which equals the first) vertex if ( !intersectionEdges.empty() ) { currentVertex = vNext; pClosing->insertVertex( vNext ); } } else { // degenerated... break; } } // while intersectionEdges not empty // insert polygon (may be degenerated!) this->insertPolygon( pClosing ); } // mating intersection edge NOT found! else { freePolygon(pClosing); } } // if intersectionEdges contains more than three elements }
//----------------------------------------------------------------------- void ConvexBody::extend(const Vector3& pt) { // Erase all polygons facing towards the point. For all edges that // are not removed twice (once in AB and once BA direction) build a // convex polygon (triangle) with the point. Polygon::EdgeMap edgeMap; for ( size_t i = 0; i < getPolygonCount(); ++i ) { const Vector3& normal = getNormal( i ); // direction of the point in regard to the polygon // the polygon is planar so we can take an arbitrary vertex Vector3 ptDir = pt - getVertex( i, 0 ); ptDir.normalise(); // remove polygon if dot product is greater or equals null. if ( normal.dotProduct( ptDir ) >= 0 ) { // store edges (copy them because if the polygon is deleted // its vertices are also deleted) storeEdgesOfPolygon( i, &edgeMap ); // remove polygon deletePolygon( i ); // decrement iterator because of deleted polygon --i; } } // point is already a part of the hull (point lies inside) if ( edgeMap.empty() ) return; // remove the edges that are twice in the list (once from each side: AB,BA) Polygon::EdgeMap::iterator it; // iterate from first to the element before the last one for (Polygon::EdgeMap::iterator itStart = edgeMap.begin(); itStart != edgeMap.end(); ) { // compare with iterator + 1 to end // don't need to skip last entry in itStart since omitted in inner loop it = itStart; ++it; bool erased = false; // iterate from itStart+1 to the element before the last one for ( ; it != edgeMap.end(); ++it ) { if (itStart->first.positionEquals(it->second) && itStart->second.positionEquals(it->first)) { edgeMap.erase(it); // increment itStart before deletion (iterator invalidation) Polygon::EdgeMap::iterator delistart = itStart++; edgeMap.erase(delistart); erased = true; break; // found and erased } } // increment itStart if we didn't do it when erasing if (!erased) ++itStart; } // use the remaining edges to build triangles with the point // the vertices of the edges are in ccw order (edgePtA-edgePtB-point // to form a ccw polygon) while ( !edgeMap.empty() ) { Polygon::EdgeMap::iterator mapIt = edgeMap.begin(); // build polygon it.first, it.second, point Polygon *p = allocatePolygon(); p->insertVertex(mapIt->first); p->insertVertex(mapIt->second); p->insertVertex( pt ); // attach polygon to body insertPolygon( p ); // erase the vertices from the list // pointers are now held by the polygon edgeMap.erase( mapIt ); } }