//----------------------------------------------------------------------- void FocusedShadowCameraSetup::calculateLVS(const SceneManager& sm, const Camera& cam, const Light& light, const AxisAlignedBox& sceneBB, PointListBody *out_LVS) const { ConvexBody bodyLVS; // init body with view frustum bodyLVS.define(cam); // clip the body with the light frustum (point + spot) // for a directional light the space of the intersected // view frustum and sceneBB is always lighted and in front // of the viewer. if (light.getType() != Light::LT_DIRECTIONAL) { // clip with the light frustum // set up light camera to clip the resulting frustum if (!mLightFrustumCameraCalculated) { calculateShadowMappingMatrix(sm, cam, light, NULL, NULL, mLightFrustumCamera); mLightFrustumCameraCalculated = true; } bodyLVS.clip(*mLightFrustumCamera); } // clip the body with the scene bounding box bodyLVS.clip(sceneBB); // extract bodyLVS vertices out_LVS->build(bodyLVS); }
int main() { int i; while (scanf("%d",&hull.n), hull.n) { for (i = 0; i < hull.n; i++) scanf("%lf%lf%lf", &hull.P[i].x, &hull.P[i].y, &hull.P[i].z); hull.convex_hull(); printf("%.2lf\n", hull.volume()); } }
//----------------------------------------------------------------------- ConvexBody::ConvexBody( const ConvexBody& cpy ) { for ( size_t i = 0; i < cpy.getPolygonCount(); ++i ) { Polygon *p = allocatePolygon(); *p = cpy.getPolygon( i ); mPolygons.push_back( p ); } }
//----------------------------------------------------------------------- bool ConvexBody::operator == ( const ConvexBody& rhs ) const { if ( getPolygonCount() != rhs.getPolygonCount() ) return false; // Compare the polygons. They may not be in correct order. // A correct convex body does not have identical polygons in its body. bool *bChecked = OGRE_ALLOC_T(bool, getPolygonCount(), MEMCATEGORY_SCENE_CONTROL); for ( size_t i=0; i<getPolygonCount(); ++i ) { bChecked[ i ] = false; } for ( size_t i=0; i<getPolygonCount(); ++i ) { bool bFound = false; for ( size_t j=0; j<getPolygonCount(); ++j ) { const Polygon& pA = getPolygon( i ); const Polygon& pB = rhs.getPolygon( j ); if ( pA == pB ) { bFound = true; bChecked[ i ] = true; break; } } if ( bFound == false ) { OGRE_FREE(bChecked, MEMCATEGORY_SCENE_CONTROL); bChecked = 0; return false; } } for ( size_t i=0; i<getPolygonCount(); ++i ) { if ( bChecked[ i ] != true ) { OGRE_FREE(bChecked, MEMCATEGORY_SCENE_CONTROL); bChecked = 0; return false; } } OGRE_FREE(bChecked, MEMCATEGORY_SCENE_CONTROL); bChecked = 0; return true; }
//----------------------------------------------------------------------- bool ConvexBody::operator == ( const ConvexBody& rhs ) const { if ( getPolygonCount() != rhs.getPolygonCount() ) return false; // Compare the polygons. They may not be in correct order. // A correct convex body does not have identical polygons in its body. bool *bChecked = new bool[ getPolygonCount() ]; for ( size_t i=0; i<getPolygonCount(); ++i ) { bChecked[ i ] = false; } for ( size_t i=0; i<getPolygonCount(); ++i ) { bool bFound = false; for ( size_t j=0; j<getPolygonCount(); ++j ) { const Polygon& pA = getPolygon( i ); const Polygon& pB = rhs.getPolygon( j ); if ( pA == pB ) { bFound = true; bChecked[ i ] = true; break; } } if ( bFound == false ) { OGRE_DELETE_ARRAY( bChecked ); return false; } } for ( size_t i=0; i<getPolygonCount(); ++i ) { if ( bChecked[ i ] != true ) { OGRE_DELETE_ARRAY( bChecked ); return false; } } OGRE_DELETE_ARRAY( bChecked ); return true; }
//----------------------------------------------------------------------- void FocusedShadowCameraSetup::PointListBody::buildAndIncludeDirection( const ConvexBody& body, Real extrudeDist, const Vector3& dir) { // reset point list this->reset(); // intersect the rays formed by the points in the list with the given direction and // insert them into the list const size_t polyCount = body.getPolygonCount(); for (size_t iPoly = 0; iPoly < polyCount; ++iPoly) { // store the old inserted point and plane info // if the currently processed point hits a different plane than the previous point an // intersection point is calculated that lies on the two planes' intersection edge // fetch current polygon const Polygon& p = body.getPolygon(iPoly); size_t pointCount = p.getVertexCount(); for (size_t iPoint = 0; iPoint < pointCount ; ++iPoint) { // base point const Vector3& pt = p.getVertex(iPoint); // add the base point this->addPoint(pt); // intersection ray Ray ray(pt, dir); const Vector3 ptIntersect = ray.getPoint(extrudeDist); this->addPoint(ptIntersect); } // for: polygon point iteration } // for: polygon iteration }
//----------------------------------------------------------------------- void ConvexBody::clip(const ConvexBody& body) { if ( this == &body ) return; // for each polygon; clip 'this' with each plane of 'body' // front vertex representation is ccw Plane pl; for ( size_t iPoly = 0; iPoly < body.getPolygonCount(); ++iPoly ) { const Polygon& p = body.getPolygon( iPoly ); OgreAssert( p.getVertexCount() >= 3, "A valid polygon must contain at least three vertices." ); // set up plane with first three vertices of the polygon (a polygon is always planar) pl.redefine( p.getVertex( 0 ), p.getVertex( 1 ), p.getVertex( 2 ) ); clip(pl); } }
//----------------------------------------------------------------------- void FocusedShadowCameraSetup::PointListBody::build(const ConvexBody& body, bool filterDuplicates) { // erase list mBodyPoints.clear(); // Try to reserve a representative amount of memory mBodyPoints.reserve(body.getPolygonCount() * 6); // build new list for (size_t i = 0; i < body.getPolygonCount(); ++i) { for (size_t j = 0; j < body.getVertexCount(i); ++j) { const Vector3 &vInsert = body.getVertex(i, j); // duplicates allowed? if (filterDuplicates) { bool bPresent = false; for(Polygon::VertexList::iterator vit = mBodyPoints.begin(); vit != mBodyPoints.end(); ++vit) { const Vector3& v = *vit; if (vInsert.positionEquals(v)) { bPresent = true; break; } } if (bPresent == false) { mBodyPoints.push_back(body.getVertex(i, j)); } } // else insert directly else { mBodyPoints.push_back(body.getVertex(i, j)); } } } // update AAB // no points altered, so take body AAB mAAB = body.getAABB(); }
//----------------------------------------------------------------------- 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 }