Almost completed the Sampling Classes now all the classical methods are in. Added a TrivialSampler class to better illustrate the interface of the sampler object.

This commit is contained in:
Paolo Cignoni 2008-06-20 15:11:30 +00:00
parent 26e1c14de8
commit 79786de3cc
1 changed files with 263 additions and 345 deletions

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@ -39,6 +39,32 @@ namespace vcg
{ {
namespace tri namespace tri
{ {
/// Trivial Sampler, an example sampler object that show the required interface used by the sampling class.
/// Most of the sampling classes call the AddFace method with the face containing the sample and its baricentric coord.
template <class MeshType>
class TrivialSampler
{
public:
typedef typename MeshType::CoordType CoordType;
typedef typename MeshType::VertexType VertexType;
typedef typename MeshType::FaceType FaceType;
TrivialSampler(){};
std::vector<CoordType> sampleVec;
void AddVert(const VertexType &p)
{
sampleVec.push_back(p.cP());
}
void AddFace(const CMeshO::FaceType &f, CMeshO::CoordType p)
{
sampleVec.push_back(f.P(0)*p[0] + f.P(1)*p[1] +f.P(2)*p[2] );
}
}; // end class TrivialSampler
template <class MetroMesh, class VertexSampler> template <class MetroMesh, class VertexSampler>
class SurfaceSampling class SurfaceSampling
{ {
@ -47,6 +73,7 @@ class SurfaceSampling
typedef typename MetroMesh::VertexType VertexType; typedef typename MetroMesh::VertexType VertexType;
typedef typename MetroMesh::VertexPointer VertexPointer; typedef typename MetroMesh::VertexPointer VertexPointer;
typedef typename MetroMesh::VertexIterator VertexIterator; typedef typename MetroMesh::VertexIterator VertexIterator;
typedef typename MetroMesh::FacePointer FacePointer;
typedef typename MetroMesh::FaceIterator FaceIterator; typedef typename MetroMesh::FaceIterator FaceIterator;
typedef typename MetroMesh::FaceType FaceType; typedef typename MetroMesh::FaceType FaceType;
typedef typename MetroMesh::FaceContainer FaceContainer; typedef typename MetroMesh::FaceContainer FaceContainer;
@ -129,13 +156,13 @@ static void VertexAreaUniform(MetroMesh & m, VertexSampler &ps, int sampleNum)
VertexWeighted(m,ps,sampleNum); VertexWeighted(m,ps,sampleNum);
} }
static void FillAndShuffleVertexPointVector(MetroMesh & m, std::vector<VertexPointer> vertVec) static void FillAndShuffleVertexPointVector(MetroMesh & m, std::vector<VertexPointer> &vertVec)
{ {
VertexIterator vi; VertexIterator vi;
for(vi=m.vert.begin();vi!=m.vert.end();++vi) for(vi=m.vert.begin();vi!=m.vert.end();++vi)
if(!(*vi).IsD()) vertVec.push_back(&*vi); if(!(*vi).IsD()) vertVec.push_back(&*vi);
assert(vertVec.size()=m.vn); assert(vertVec.size()==m.vn);
std::random_shuffle(vertVec.begin(),vertVec.end()); std::random_shuffle(vertVec.begin(),vertVec.end());
} }
@ -208,7 +235,8 @@ static void AllEdge(MetroMesh & m, VertexSampler &ps)
} }
*/ */
// Get the baricentric coords of a random point over a single face. // Generate the baricentric coords of a random point over a single face, with a uniform distribution over the triangle.
// It uses the parallelgoram folding trick.
static CoordType RandomBaricentric() static CoordType RandomBaricentric()
{ {
@ -289,305 +317,21 @@ static void WeightedMontecarlo(MetroMesh & m, VertexSampler &ps, int sampleNum)
} }
} }
};
} // end namespace tri // Subdivision sampling of a single face.
} // end namespace vcg // return number of added samples
#endif static int SingleFaceSubdivision(const CoordType & v0, const CoordType & v1, const CoordType & v2, int maxdepth, VertexSampler &ps, FacePointer fp)
#if 0
struct SamplingFlags{
enum{
VERTEX_SAMPLING = 0x0002,
EDGE_SAMPLING = 0x0004,
FACE_SAMPLING = 0x0008,
MONTECARLO_SAMPLING = 0x0010,
SUBDIVISION_SAMPLING = 0x0020,
SIMILAR_SAMPLING = 0x0040,
INCLUDE_UNREFERENCED_VERTICES = 0x0200,
};
};
// -----------------------------------------------------------------------------------------------
template <class MetroMesh>
class Sampling
{
public:
unsigned int n_samples_per_face ;
float n_samples_edge_to_face_ratio ;
float bbox_factor ;
float inflate_percentage ;
unsigned int min_size ;
int n_hist_bins ;
int print_every_n_elements ;
int referredBit ;
// parameters
double dist_upper_bound;
double n_samples_per_area_unit;
unsigned long n_samples_target;
int Flags;
// results
unsigned long n_total_samples;
unsigned long n_total_area_samples;
unsigned long n_total_edge_samples;
unsigned long n_total_vertex_samples;
double max_dist;
double mean_dist;
double RMS_dist;
double volume;
double area_S1;
// globals
int n_samples;
// private methods
inline double ComputeMeshArea(MetroMesh & mesh);
float AddSample(const Point3x &p);
inline void AddRandomSample(FaceIterator &T);
inline void SampleEdge(const Point3x & v0, const Point3x & v1, int n_samples_per_edge);
void VertexSampling();
void EdgeSampling();
void FaceSubdiv(const Point3x & v0, const Point3x &v1, const Point3x & v2, int maxdepth);
void SimilarTriangles(const Point3x &v0, const Point3x &v1, const Point3x &v2, int n_samples_per_edge);
void MontecarloFaceSampling();
void SubdivFaceSampling();
void SimilarFaceSampling();
public :
// public methods
Sampling(MetroMesh &_s1, MetroMesh &_s2);
~Sampling();
double GetDistVolume() {return volume;}
unsigned long GetNSamples() {return n_total_samples;}
unsigned long GetNAreaSamples() {return n_total_area_samples;}
unsigned long GetNEdgeSamples() {return n_total_edge_samples;}
unsigned long GetNVertexSamples() {return n_total_vertex_samples;}
double GetNSamplesPerAreaUnit() {return n_samples_per_area_unit;}
unsigned long GetNSamplesTarget() {return n_samples_target;}
void SetFlags(int flags) {Flags = flags;}
void ClearFlag(int flag) {Flags &= (flag ^ -1);}
void SetParam(double _n_samp) {n_samples_target = _n_samp;}
void SetSamplesTarget(unsigned long _n_samp);
void SetSamplesPerAreaUnit(double _n_samp);
};
// -----------------------------------------------------------------------------------------------
// constructor
template <class MetroMesh>
Sampling<MetroMesh>::Sampling(MetroMesh &_s1, MetroMesh &_s2):S1(_s1),S2(_s2)
{
Flags = 0;
area_S1 = ComputeMeshArea(_s1);
// set default numbers
n_samples_per_face = 10;
n_samples_edge_to_face_ratio = 0.1f;
bbox_factor = 0.1f;
inflate_percentage = 0.02f;
min_size = 125; /* 125 = 5^3 */
n_hist_bins = 256;
print_every_n_elements = S1.fn/100;
if(print_every_n_elements <= 1)
print_every_n_elements = 2;
referredBit = VertexType::NewBitFlag();
// store the unreferred vertices
FaceIterator fi; VertexIterator vi; int i;
for(fi = _s1.face.begin(); fi!= _s1.face.end(); ++fi)
for(i=0;i<3;++i) (*fi).V(i)->SetUserBit(referredBit);
}
template <class MetroMesh>
Sampling<MetroMesh>::~Sampling()
{
VertexType::DeleteBitFlag(referredBit);
}
// set sampling parameters
template <class MetroMesh>
void Sampling<MetroMesh>::SetSamplesTarget(unsigned long _n_samp)
{
n_samples_target = _n_samp;
n_samples_per_area_unit = n_samples_target / (double)area_S1;
}
template <class MetroMesh>
void Sampling<MetroMesh>::SetSamplesPerAreaUnit(double _n_samp)
{
n_samples_per_area_unit = _n_samp;
n_samples_target = (unsigned long)((double) n_samples_per_area_unit * area_S1);
}
// auxiliary functions
template <class MetroMesh>
inline double Sampling<MetroMesh>::ComputeMeshArea(MetroMesh & mesh)
{
FaceIterator face;
double area = 0.0;
for(face=mesh.face.begin(); face != mesh.face.end(); face++)
if(!(*face).IsD())
area += DoubleArea(*face);
return area/2.0;
}
template <class MetroMesh>
float Sampling<MetroMesh>::AddSample(const Point3x &p )
{
SampleVec.push_back(p);
}
// -----------------------------------------------------------------------------------------------
// --- Vertex Sampling ---------------------------------------------------------------------------
template <class MetroMesh>
void Sampling<MetroMesh>::VertexSampling()
{
VertexIterator vi;
for(vi=S1.vert.begin();vi!=S1.vert.end();++vi)
if( (*vi).IsUserBit(referredBit) || // it is referred
((Flags&SamplingFlags::INCLUDE_UNREFERENCED_VERTICES) != 0) ) //include also unreferred
{
AddSample((*vi).cP());
}
}
// -----------------------------------------------------------------------------------------------
// --- Edge Sampling -----------------------------------------------------------------------------
template <class MetroMesh>
inline void Sampling<MetroMesh>::SampleEdge(const Point3x & v0, const Point3x & v1, int n_samples_per_edge)
{
// uniform sampling of the segment v0v1.
Point3x e((v1-v0)/(double)(n_samples_per_edge+1));
for(int i=1; i <= n_samples_per_edge; i++)
{
AddSample(v0 + e*i);
n_total_edge_samples++;
}
}
template <class MetroMesh>
void Sampling<MetroMesh>::EdgeSampling()
{
// Edge sampling.
typedef std::pair<VertexPointer, VertexPointer> pvv;
std::vector< pvv > Edges;
printf("Edge sampling\n");
// compute edge list.
FaceIterator fi;
for(fi=S1.face.begin(); fi != S1.face.end(); fi++)
for(int i=0; i<3; ++i)
{
Edges.push_back(make_pair((*fi).V0(i),(*fi).V1(i)));
if(Edges.back().first > Edges.back().second)
swap(Edges.back().first, Edges.back().second);
}
sort(Edges.begin(), Edges.end());
typename std::vector< pvv>::iterator edgeend = unique(Edges.begin(), Edges.end());
Edges.resize(edgeend-Edges.begin());
// sample edges.
typename std::vector<pvv>::iterator ei;
double n_samples_per_length_unit;
double n_samples_decimal = 0.0;
int cnt=0;
if(Flags & SamplingFlags::FACE_SAMPLING) n_samples_per_length_unit = sqrt((double)n_samples_per_area_unit);
else n_samples_per_length_unit = n_samples_per_area_unit;
for(ei=Edges.begin(); ei!=Edges.end(); ++ei)
{
n_samples_decimal += Distance((*ei).first->cP(),(*ei).second->cP()) * n_samples_per_length_unit;
n_samples = (int) n_samples_decimal;
SampleEdge((*ei).first->cP(), (*ei).second->cP(), (int) n_samples);
n_samples_decimal -= (double) n_samples;
}
}
// -----------------------------------------------------------------------------------------------
// --- Face Sampling -----------------------------------------------------------------------------
// Montecarlo sampling.
template <class MetroMesh>
inline void Sampling<MetroMesh>::AddRandomSample(FaceIterator &T)
{
// random sampling over the input face.
double rnd_1, rnd_2;
// vertices of the face T.
Point3x p0(T->V(0)->cP());
Point3x p1(T->V(1)->cP());
Point3x p2(T->V(2)->cP());
// calculate two edges of T.
Point3x v1(p1 - p0);
Point3x v2(p2 - p0);
// choose two random numbers.
rnd_1 = (double)rand() / (double)RAND_MAX;
rnd_2 = (double)rand() / (double)RAND_MAX;
if(rnd_1 + rnd_2 > 1.0)
{
rnd_1 = 1.0 - rnd_1;
rnd_2 = 1.0 - rnd_2;
}
// add a random point on the face T.
AddSample (p0 + (v1 * rnd_1 + v2 * rnd_2));
n_total_area_samples++;
}
template <class MetroMesh>
void Sampling<MetroMesh>::MontecarloFaceSampling()
{
// Montecarlo sampling.
int cnt = 0;
double n_samples_decimal = 0.0;
FaceIterator fi;
for(fi=S1.face.begin(); fi != S1.face.end(); fi++)
if(!(*fi).IsD())
{
// compute # samples in the current face.
n_samples_decimal += 0.5*DoubleArea(*fi) * n_samples_per_area_unit;
n_samples = (int) n_samples_decimal;
// for every sample p_i in T...
for(int i=0; i < n_samples; i++)
AddRandomSample(fi);
n_samples_decimal -= (double) n_samples;
}
}
// Subdivision sampling.
template <class MetroMesh>
void Sampling<MetroMesh>::FaceSubdiv(const Point3x & v0, const Point3x & v1, const Point3x & v2, int maxdepth)
{ {
// recursive face subdivision. // recursive face subdivision.
if(maxdepth == 0) if(maxdepth == 0)
{ {
// ground case. // ground case.
AddSample((v0+v1+v2)/3.0f); CoordType SamplePoint((v0+v1+v2)/3.0f);
n_total_area_samples++; CoordType SampleBary;
return; InterpolationParameters(*fp,SamplePoint,SampleBary[0],SampleBary[1],SampleBary[2]);
ps.AddFace(*fp,SampleBary);
return 1;
} }
// compute the longest edge. // compute the longest edge.
@ -601,104 +345,278 @@ void Sampling<MetroMesh>::FaceSubdiv(const Point3x & v0, const Point3x & v1, con
else else
if(maxd12 > maxd20) res = 1; if(maxd12 > maxd20) res = 1;
else res = 2; else res = 2;
// break the input triangle along the median to the the longest edge. int faceSampleNum=0;
Point3x pp; // break the input triangle along the midpoint of the longest edge.
CoordType pp;
switch(res) switch(res)
{ {
case 0 : pp = (v0+v1)/2; case 0 : pp = (v0+v1)/2;
FaceSubdiv(v0,pp,v2,maxdepth-1); faceSampleNum+=SingleFaceSubdivision(v0,pp,v2,maxdepth-1,ps,fp);
FaceSubdiv(pp,v1,v2,maxdepth-1); faceSampleNum+=SingleFaceSubdivision(pp,v1,v2,maxdepth-1,ps,fp);
break; break;
case 1 : pp = (v1+v2)/2; case 1 : pp = (v1+v2)/2;
FaceSubdiv(v0,v1,pp,maxdepth-1); faceSampleNum+=SingleFaceSubdivision(v0,v1,pp,maxdepth-1,ps,fp);
FaceSubdiv(v0,pp,v2,maxdepth-1); faceSampleNum+=SingleFaceSubdivision(v0,pp,v2,maxdepth-1,ps,fp);
break; break;
case 2 : pp = (v2+v0)/2; case 2 : pp = (v2+v0)/2;
FaceSubdiv(v0,v1,pp,maxdepth-1); faceSampleNum+=SingleFaceSubdivision(v0,v1,pp,maxdepth-1,ps,fp);
FaceSubdiv(pp,v1,v2,maxdepth-1); faceSampleNum+=SingleFaceSubdivision(pp,v1,v2,maxdepth-1,ps,fp);
break; break;
} }
return faceSampleNum;
} }
template <class MetroMesh>
void Sampling<MetroMesh>::SubdivFaceSampling()
{
// Subdivision sampling.
int cnt = 0, maxdepth;
double n_samples_decimal = 0.0;
typename MetroMesh::FaceIterator fi;
printf("Subdivision face sampling\n"); /// Compute a sampling of the surface where the points are regularly scattered over the face surface using a recursive longest-edge subdivision rule.
for(fi=S1.face.begin(); fi != S1.face.end(); fi++) static void FaceSubdivision(MetroMesh & m, VertexSampler &ps,int sampleNum)
{
ScalarType area = Stat<MetroMesh>::ComputeMeshArea(m);
ScalarType samplePerAreaUnit = sampleNum/area;
qDebug("samplePerAreaUnit %f",samplePerAreaUnit);
double floatSampleNum = 0.0;
int faceSampleNum;
// Subdivision sampling.
FaceIterator fi;
for(fi=m.face.begin(); fi!=m.face.end(); fi++)
{ {
// compute # samples in the current face. // compute # samples in the current face.
n_samples_decimal += 0.5*DoubleArea(*fi) * n_samples_per_area_unit; floatSampleNum += 0.5*DoubleArea(*fi) * samplePerAreaUnit;
n_samples = (int) n_samples_decimal; faceSampleNum = (int) floatSampleNum;
if(n_samples) if(faceSampleNum>0)
{ {
// face sampling. // face sampling.
maxdepth = ((int)(log((double)n_samples)/log(2.0))); int maxdepth = ((int)(log((double)faceSampleNum)/log(2.0)));
n_samples = 0; faceSampleNum = SingleFaceSubdivision((*fi).V(0)->cP(), (*fi).V(1)->cP(), (*fi).V(2)->cP(), maxdepth,ps,&*fi);
FaceSubdiv((*fi).V(0)->cP(), (*fi).V(1)->cP(), (*fi).V(2)->cP(), maxdepth);
} }
n_samples_decimal -= (double) n_samples; floatSampleNum -= (double) faceSampleNum;
// print progress information
if(!(++cnt % print_every_n_elements))
printf("Sampling face %d%%\r", (100 * cnt/S1.fn));
} }
printf(" \r");
} }
// Similar Triangles sampling. // Similar Triangles sampling.
template <class MetroMesh> // Skip vertex and edges
void Sampling<MetroMesh>::SimilarTriangles(const Point3x & v0, const Point3x & v1, const Point3x & v2, int n_samples_per_edge) // Sample per edges includes vertexes, so here we should expect n_samples_per_edge >=4
{
Point3x V1((v1-v0)/(double)(n_samples_per_edge-1));
Point3x V2((v2-v0)/(double)(n_samples_per_edge-1));
int i, j;
// face sampling. static int SingleFaceSimilar(FacePointer fp, VertexSampler &ps, int n_samples_per_edge)
{
int n_samples=0;
int i, j;
float segmentNum=n_samples_per_edge -1 ;
float segmentLen = 1.0/segmentNum;
// face sampling.
for(i=1; i < n_samples_per_edge-1; i++) for(i=1; i < n_samples_per_edge-1; i++)
for(j=1; j < n_samples_per_edge-1-i; j++) for(j=1; j < n_samples_per_edge-1-i; j++)
{ {
AddSample( v0 + (V1*(double)i + V2*(double)j) ); //AddSample( v0 + (V1*(double)i + V2*(double)j) );
n_total_area_samples++; CoordType sampleBary(i*segmentLen,j*segmentLen, 1.0 - (i*segmentLen+j*segmentLen) ) ;
n_samples++; n_samples++;
ps.AddFace(*fp,sampleBary);
} }
return n_samples;
} }
template <class MetroMesh> /// Similar sampling. Each triangle is subdivided into similar triangles following a generalization of the classical 1-to-4 splitting rule of triangles.
void Sampling<MetroMesh>::SimilarFaceSampling() /// According to the level of subdivision <k> you get 1, 4 , 9, 16 , <k^2> triangles.
/// Of these triangles we consider only internal vertices. (to avoid multiple sampling of edges and vertices).
/// Therefore the number of internal points is ((k-3)*(k-2))/2. where k is the number of point on an edge (vertex included)
// e.g. for a k=4 you get (1*2)/2 == 1 e.g. a single point, etc.
/// So if you want N samples in a triangle i have to solve k^2 -5k +6 - 2N = 0
// 5 + sqrt( 1 + 8N )
// k = -------------------
// 2
//template <class MetroMesh>
//void Sampling<MetroMesh>::SimilarFaceSampling()
static void FaceSimilar(MetroMesh & m, VertexSampler &ps,int sampleNum)
{ {
// Similar Triangles sampling.
ScalarType area = Stat<MetroMesh>::ComputeMeshArea(m);
ScalarType samplePerAreaUnit = sampleNum/area;
qDebug("samplePerAreaUnit %f",samplePerAreaUnit);
// Similar Triangles sampling.
int cnt = 0, n_samples_per_edge; int cnt = 0, n_samples_per_edge;
double n_samples_decimal = 0.0; double n_samples_decimal = 0.0;
FaceIterator fi; FaceIterator fi;
printf("Similar Triangles face sampling\n"); printf("Similar Triangles face sampling\n");
for(fi=S1.face.begin(); fi != S1.face.end(); fi++) for(fi=m.face.begin(); fi != m.face.end(); fi++)
{ {
// compute # samples in the current face. // compute # samples in the current face.
n_samples_decimal += 0.5*DoubleArea(*fi) * n_samples_per_area_unit; n_samples_decimal += 0.5*DoubleArea(*fi) * samplePerAreaUnit;
n_samples = (int) n_samples_decimal; int n_samples = (int) n_samples_decimal;
if(n_samples) if(n_samples)
{ {
// face sampling. // face sampling.
n_samples_per_edge = (int)((sqrt(1.0+8.0*(double)n_samples) +5.0)/2.0); n_samples_per_edge = (int)((sqrt(1.0+8.0*(double)n_samples) +5.0)/2.0);
n_samples = 0; n_samples = 0;
SimilarTriangles((*fi).V(0)->cP(), (*fi).V(1)->cP(), (*fi).V(2)->cP(), n_samples_per_edge); //SingleFaceSimilar((*fi).V(0)->cP(), (*fi).V(1)->cP(), (*fi).V(2)->cP(), n_samples_per_edge);
SingleFaceSimilar(&*fi,ps, n_samples_per_edge);
} }
n_samples_decimal -= (double) n_samples; n_samples_decimal -= (double) n_samples;
// print progress information
if(!(++cnt % print_every_n_elements))
printf("Sampling face %d%%\r", (100 * cnt/S1.fn));
} }
printf(" \r");
} }
};
#if 0
template<class S>
void BaryCoord( const Point2<S> & p,
const Point2<S> & v0, const Point2<S> & v1, const Point2<S> & v2,
S & a, S & b, S & c )
{
S de = v0[0]*v1[1]-v0[0]*v2[1]-v1[0]*v0[1]+v1[0]*v2[1]-v2[0]*v1[1]+v2[0]*v0[1];
b = -(p[0]*v0[1]-p[0]*v2[1]-v0[0]*p[1]+v0[0]*v2[1]-v2[0]*v0[1]+v2[0]*p[1])/de;
a = (-p[1]*v1[0]+v2[0]*p[1]+v1[1]*p[0]-v2[0]*v1[1]+v1[0]*v2[1]-p[0]*v2[1])/de;
c = 1-a-b;
} }
// Rasterization fuction
// Take a triangle
// T deve essere una classe funzionale che ha l'operatore ()
// con due parametri x,y di tipo S esempio:
// class Foo { public void operator()(int x, int y ) { ??? } };
template<class S,class T>
void Raster( const Point2<S> & v0, const Point2<S> & v1, const Point2<S> & v2,
T & op )
{
// Calcolo bounding box
Box2i bbox;
if(v0[0]<v1[0]) { bbox.min[0]=v0[0]; bbox.max[0]=v1[0]; }
else { bbox.min[0]=v1[0]; bbox.max[0]=v0[0]; }
if(v0[1]<v1[1]) { bbox.min[1]=v0[1]; bbox.max[1]=v1[1]; }
else { bbox.min[1]=v1[1]; bbox.max[1]=v0[1]; }
if(bbox.min[0]>v2[0]) bbox.min[0]=v2[0];
else if(bbox.max[0]<v2[0]) bbox.max[0]=v2[0];
if(bbox.min[1]>v2[1]) bbox.min[1]=v2[1];
else if(bbox.max[1]<v2[1]) bbox.max[1]=v2[1];
// Compute edge vectors
Point2<S> d10 = v1 - v0;
Point2<S> d21 = v2 - v1;
Point2<S> d02 = v0 - v2;
// Compute cross products
S b0 = (bbox.min[0]-v0[0])*d10[1] - (bbox.min[1]-v0[1])*d10[0];
S b1 = (bbox.min[0]-v1[0])*d21[1] - (bbox.min[1]-v1[1])*d21[0];
S b2 = (bbox.min[0]-v2[0])*d02[1] - (bbox.min[1]-v2[1])*d02[0];
// Compute steps
S db0 = d10[1];
S db1 = d21[1];
S db2 = d02[1];
// Compute Signs
S dn0 = -d10[0];
S dn1 = -d21[0];
S dn2 = -d02[0];
// Rasterizzazione
for(int x=bbox.min[0];x<=bbox.max[0];++x)
{
bool in = false;
S n0 = b0;
S n1 = b1;
S n2 = b2;
for(int y=bbox.min[1];y<=bbox.max[1];++y)
{
if( (n0>=0 && n1>=0 && n2>=0) || (n0<=0 && n1<=0 && n2<=0) )
{
op(x,y);
in = true;
} else if(in) break;
n0 += dn0;
n1 += dn1;
n2 += dn2;
}
b0 += db0;
b1 += db1;
b2 += db2;
}
}
template<class S,class T>
void RasterBary( const Point2<S> & v0, const Point2<S> & v1, const Point2<S> & v2,
T & op )
{
// Calcolo bounding box
Box2i bbox;
if(v0[0]<v1[0]) { bbox.min[0]=v0[0]; bbox.max[0]=v1[0]; }
else { bbox.min[0]=v1[0]; bbox.max[0]=v0[0]; }
if(v0[1]<v1[1]) { bbox.min[1]=v0[1]; bbox.max[1]=v1[1]; }
else { bbox.min[1]=v1[1]; bbox.max[1]=v0[1]; }
if(bbox.min[0]>v2[0]) bbox.min[0]=v2[0];
else if(bbox.max[0]<v2[0]) bbox.max[0]=v2[0];
if(bbox.min[1]>v2[1]) bbox.min[1]=v2[1];
else if(bbox.max[1]<v2[1]) bbox.max[1]=v2[1];
// Calcolo versori degli spigoli
Point2<S> d10 = v1 - v0;
Point2<S> d21 = v2 - v1;
Point2<S> d02 = v0 - v2;
// Preparazione prodotti scalari
S b0 = (bbox.min[0]-v0[0])*d10[1] - (bbox.min[1]-v0[1])*d10[0];
S b1 = (bbox.min[0]-v1[0])*d21[1] - (bbox.min[1]-v1[1])*d21[0];
S b2 = (bbox.min[0]-v2[0])*d02[1] - (bbox.min[1]-v2[1])*d02[0];
// Preparazione degli steps
S db0 = d10[1];
S db1 = d21[1];
S db2 = d02[1];
// Preparazione segni
S dn0 = -d10[0];
S dn1 = -d21[0];
S dn2 = -d02[0];
// Rasterizzazione
double de = v0[0]*v1[1]-v0[0]*v2[1]-v1[0]*v0[1]+v1[0]*v2[1]-v2[0]*v1[1]+v2[0]*v0[1];
for(int x=bbox.min[0];x<=bbox.max[0];++x)
{
bool in = false;
S n0 = b0;
S n1 = b1;
S n2 = b2;
for(int y=bbox.min[1];y<=bbox.max[1];++y)
{
if( (n0>=0 && n1>=0 && n2>=0) || (n0<=0 && n1<=0 && n2<=0) )
{
double b = -double( x*v0[1]-x*v2[1]-v0[0]*y+v0[0]*v2[1]-v2[0]*v0[1]+v2[0]*y)/de;
double a = double(-y*v1[0]+v2[0]*y+v1[1]*x-v2[0]*v1[1]+v1[0]*v2[1]-x*v2[1])/de;
double c = 1-a-b;
op(x,y,a,b,c);
in = true;
} else if(in) break;
n0 += dn0;
n1 += dn1;
n2 += dn2;
}
b0 += db0;
b1 += db1;
b2 += db2;
}
}
#endif
} // end namespace tri
} // end namespace vcg
#endif #endif