//-----------------------------------------------------------------------
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
}
