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vcglib/vcg/complex/algorithms/refine_loop.h

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/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004-2016 \/)\/ *
* Visual Computing Lab /\/| *
* ISTI - Italian National Research Council | *
* \ *
* All rights reserved. *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
* for more details. *
* *
****************************************************************************/
/*! \file refine_loop.h
*
* \brief This file contain code for Loop's subdivision scheme for triangular
* mesh and some similar method.
*
*/
#ifndef __VCGLIB_REFINE_LOOP
#define __VCGLIB_REFINE_LOOP
#include <cmath>
#include <vcg/space/point3.h>
#include <vcg/complex/complex.h>
#include <vcg/complex/algorithms/refine.h>
#include <vcg/complex/algorithms/update/color.h>
namespace vcg{
namespace tri{
/*
Metodo di Loop dalla documentazione "Siggraph 2000 course on subdivision"
d4------d3 d4------d3
/ \ / \ / \ / \ u
/ \ / \ / e4--e3 \ / \
/ \/ \ / / \/ \ \ / \
d5------d1------d2 -> d5--e5--d1--e2--d2 l--M--r
\ /\ / \ \ /\ / / \ /
\ / \ / \ e6--e7 / \ /
\ / \ / \ / \ / d
d6------d7 d6------d7
*******************************************************
*/
/*!
* \brief Weight class for classical Loop's scheme.
*
* See Zorin, D. & Schröeder, P.: Subdivision for modeling and animation. Proc. ACM SIGGRAPH [Courses], 2000
*/
template<class SCALAR_TYPE>
struct LoopWeight {
inline SCALAR_TYPE beta(int k) {
return (k>3)?(5.0/8.0 - std::pow((3.0/8.0 + std::cos(2.0*M_PI/SCALAR_TYPE(k))/4.0),2))/SCALAR_TYPE(k):3.0/16.0;
}
inline SCALAR_TYPE incidentRegular(int) {
return 3.0/8.0;
}
inline SCALAR_TYPE incidentIrregular(int) {
return 3.0/8.0;
}
inline SCALAR_TYPE opposite(int) {
return 1.0/8.0;
}
};
/*!
* \brief Modified Loop's weight to optimise continuity.
*
* See Barthe, L. & Kobbelt, L.: Subdivision scheme tuning around extraordinary vertices. Computer Aided Geometric Design, 2004, 21, 561-583
*/
template<class SCALAR_TYPE>
struct RegularLoopWeight {
inline SCALAR_TYPE beta(int k) {
static SCALAR_TYPE bkPolar[] = {
.32517,
.49954,
.59549,
.625,
.63873,
.64643,
.65127,
.67358,
.68678,
.69908
};
return (k<=12 && k>=3)?(1.0-bkPolar[k-3])/k:LoopWeight<SCALAR_TYPE>().beta(k);
}
inline SCALAR_TYPE incidentRegular(int k) {
return 1.0 - incidentIrregular(k) - opposite(k)*2;
}
inline SCALAR_TYPE incidentIrregular(int k) {
static SCALAR_TYPE bkPolar[] = {
.15658,
.25029,
.34547,
.375,
.38877,
.39644,
.40132,
.42198,
.43423,
.44579
};
return (k<=12 && k>=3)?bkPolar[k-3]:LoopWeight<SCALAR_TYPE>().incidentIrregular(k);
}
inline SCALAR_TYPE opposite(int k) {
static SCALAR_TYPE bkPolar[] = {
.14427,
.12524,
.11182,
.125,
.14771,
.1768,
.21092,
.20354,
.20505,
.19828
};
return (k<=12 && k >= 3)?bkPolar[k-3]:LoopWeight<SCALAR_TYPE>().opposite(k);
}
};
template<class SCALAR_TYPE>
struct ContinuityLoopWeight {
inline SCALAR_TYPE beta(int k) {
static SCALAR_TYPE bkPolar[] = {
.32517,
.50033,
.59464,
.625,
.63903,
.67821,
.6866,
.69248,
.69678,
.70014
};
return (k<=12 && k>= 3)?(1.0-bkPolar[k-3])/k:LoopWeight<SCALAR_TYPE>().beta(k);
}
inline SCALAR_TYPE incidentRegular(int k) {
return 1.0 - incidentIrregular(k) - opposite(k)*2;
}
inline SCALAR_TYPE incidentIrregular(int k) {
static SCALAR_TYPE bkPolar[] = {
.15658,
.26721,
.33539,
.375,
.36909,
.25579,
.2521,
.24926,
.24706,
.2452
};
return (k<=12 && k>=3)?bkPolar[k-3]:LoopWeight<SCALAR_TYPE>().incidentIrregular(k);
}
inline SCALAR_TYPE opposite(int k) {
static SCALAR_TYPE bkPolar[] = {
.14427,
.12495,
.11252,
.125,
.14673,
.16074,
.18939,
.2222,
.25894,
.29934
};
return (k<=12 && k >= 3)?bkPolar[k-3]:LoopWeight<SCALAR_TYPE>().opposite(k);
}
};
// Centroid and LS3Projection classes may be pettre placed in an other file. (which one ?)
/*!
* \brief Allow to compute classical Loop subdivision surface with the same code than LS3.
*/
template<class MESH_TYPE, class LSCALAR_TYPE = typename MESH_TYPE::ScalarType>
struct Centroid {
typedef typename MESH_TYPE::ScalarType Scalar;
typedef typename MESH_TYPE::CoordType CoordType;
typedef LSCALAR_TYPE LScalar;
typedef vcg::Point3<LScalar> LVector;
LVector sumP;
LScalar sumW;
Centroid() { reset(); }
inline void reset() {
sumP.SetZero();
sumW = 0.;
}
inline void addVertex(const typename MESH_TYPE::VertexType &v, LScalar w) {
LVector p(v.cP().X(), v.cP().Y(), v.cP().Z());
sumP += p * w;
sumW += w;
}
inline void project(std::pair<CoordType,CoordType> &nv) const {
LVector position = sumP / sumW;
nv.first = CoordType(position.X(), position.Y(), position.Z());
}
};
/*! Implementation of the APSS projection for the LS3 scheme.
*
* See Gael Guennebaud and Marcel Germann and Markus Gross
* Dynamic sampling and rendering of algebraic point set surfaces.
* Computer Graphics Forum (Proceedings of Eurographics 2008), 2008, 27, 653-662
* and Simon Boye and Gael Guennebaud and Christophe Schlick
* Least squares subdivision surfaces
* Computer Graphics Forum, 2010
*/
template<class MESH_TYPE, class LSCALAR_TYPE = typename MESH_TYPE::ScalarType>
struct LS3Projection {
typedef typename MESH_TYPE::ScalarType Scalar;
typedef typename MESH_TYPE::CoordType CoordType;
typedef LSCALAR_TYPE LScalar;
typedef vcg::Point3<LScalar> LVector;
Scalar beta;
LVector sumP;
LVector sumN;
LScalar sumDotPN;
LScalar sumDotPP;
LScalar sumW;
inline LS3Projection(Scalar beta = 1.0) : beta(beta) { reset(); }
inline void reset() {
sumP.SetZero();
sumN.SetZero();
sumDotPN = 0.;
sumDotPP = 0.;
sumW = 0.;
}
inline void addVertex(const typename MESH_TYPE::VertexType &v, LScalar w) {
LVector p(v.cP().X(), v.cP().Y(), v.cP().Z());
LVector n(v.cN().X(), v.cN().Y(), v.cN().Z());
sumP += p * w;
sumN += n * w;
sumDotPN += w * n.dot(p);
sumDotPP += w * vcg::SquaredNorm(p);
sumW += w;
}
void project(std::pair<CoordType,CoordType> &nv) const {
LScalar invSumW = Scalar(1)/sumW;
LScalar aux4 = beta * LScalar(0.5) *
(sumDotPN - invSumW*sumP.dot(sumN))
/(sumDotPP - invSumW*vcg::SquaredNorm(sumP));
LVector uLinear = (sumN-sumP*(Scalar(2)*aux4))*invSumW;
LScalar uConstant = -invSumW*(uLinear.dot(sumP) + sumDotPP*aux4);
LScalar uQuad = aux4;
LVector orig = sumP*invSumW;
// finalize
LVector position;
LVector normal;
if (fabs(uQuad)>1e-7)
{
LScalar b = 1./uQuad;
LVector center = uLinear*(-0.5*b);
LScalar radius = sqrt( vcg::SquaredNorm(center) - b*uConstant );
normal = orig - center;
normal.Normalize();
position = center + normal * radius;
normal = uLinear + position * (LScalar(2) * uQuad);
normal.Normalize();
}
else if (uQuad==0.)
{
LScalar s = LScalar(1)/vcg::Norm(uLinear);
assert(!vcg::math::IsNAN(s) && "normal should not have zero len!");
uLinear *= s;
uConstant *= s;
normal = uLinear;
position = orig - uLinear * (orig.dot(uLinear) + uConstant);
}
else
{
// normalize the gradient
LScalar f = 1./sqrt(vcg::SquaredNorm(uLinear) - Scalar(4)*uConstant*uQuad);
uConstant *= f;
uLinear *= f;
uQuad *= f;
// Newton iterations
LVector grad;
LVector dir = uLinear+orig*(2.*uQuad);
LScalar ilg = 1./vcg::Norm(dir);
dir *= ilg;
LScalar ad = uConstant + uLinear.dot(orig) + uQuad * vcg::SquaredNorm(orig);
LScalar delta = -ad*std::min<Scalar>(ilg,1.);
LVector p = orig + dir*delta;
for (int i=0 ; i<2 ; ++i)
{
grad = uLinear+p*(2.*uQuad);
ilg = 1./vcg::Norm(grad);
delta = -(uConstant + uLinear.dot(p) + uQuad * vcg::SquaredNorm(p))*std::min<Scalar>(ilg,1.);
p += dir*delta;
}
position = p;
normal = uLinear + position * (Scalar(2) * uQuad);
normal.Normalize();
}
nv.first = CoordType(position.X(), position.Y(), position.Z());
nv.second = CoordType(normal.X(), normal.Y(), normal.Z());
}
};
template<class MESH_TYPE, class METHOD_TYPE=Centroid<MESH_TYPE>, class WEIGHT_TYPE=LoopWeight<typename MESH_TYPE::ScalarType> >
struct OddPointLoopGeneric : public std::unary_function<face::Pos<typename MESH_TYPE::FaceType> , typename MESH_TYPE::VertexType>
{
typedef METHOD_TYPE Projection;
typedef WEIGHT_TYPE Weight;
typedef typename MESH_TYPE::template PerVertexAttributeHandle<int> ValenceAttr;
typedef typename MESH_TYPE::CoordType CoordType;
MESH_TYPE &m;
Projection proj;
Weight weight;
ValenceAttr *valence;
inline OddPointLoopGeneric(MESH_TYPE &_m, Projection proj = Projection(), Weight weight = Weight()) :
m(_m), proj(proj), weight(weight), valence(0) {}
void operator()(typename MESH_TYPE::VertexType &nv, face::Pos<typename MESH_TYPE::FaceType> ep) {
proj.reset();
face::Pos<typename MESH_TYPE::FaceType> he(ep.f,ep.z,ep.f->V(ep.z));
typename MESH_TYPE::VertexType *l,*r,*u,*d;
l = he.v;
he.FlipV();
r = he.v;
if( tri::HasPerVertexColor(m))
nv.C().lerp(ep.f->V(ep.z)->C(),ep.f->V1(ep.z)->C(),.5f);
if (he.IsBorder()) {
proj.addVertex(*l, 0.5);
proj.addVertex(*r, 0.5);
std::pair<CoordType,CoordType>pp;
proj.project(pp);
nv.P()=pp.first;
nv.N()=pp.second;
}
else {
he.FlipE(); he.FlipV();
u = he.v;
he.FlipV(); he.FlipE();
assert(he.v == r); // back to r
he.FlipF(); he.FlipE(); he.FlipV();
d = he.v;
if(valence && ((*valence)[l]==6 || (*valence)[r]==6)) {
int extra = ((*valence)[l]==6)?(*valence)[r]:(*valence)[l];
proj.addVertex(*l, ((*valence)[l]==6)?weight.incidentRegular(extra):weight.incidentIrregular(extra));
proj.addVertex(*r, ((*valence)[r]==6)?weight.incidentRegular(extra):weight.incidentIrregular(extra));
proj.addVertex(*u, weight.opposite(extra));
proj.addVertex(*d, weight.opposite(extra));
}
// unhandled case that append only at first subdivision step: use Loop's weights
else {
proj.addVertex(*l, 3.0/8.0);
proj.addVertex(*r, 3.0/8.0);
proj.addVertex(*u, 1.0/8.0);
proj.addVertex(*d, 1.0/8.0);
}
std::pair<CoordType,CoordType>pp;
proj.project(pp);
nv.P()=pp.first;
nv.N()=pp.second;
// proj.project(nv);
}
}
Color4<typename MESH_TYPE::ScalarType> WedgeInterp(Color4<typename MESH_TYPE::ScalarType> &c0, Color4<typename MESH_TYPE::ScalarType> &c1)
{
Color4<typename MESH_TYPE::ScalarType> cc;
return cc.lerp(c0,c1,0.5f);
}
template<class FL_TYPE>
TexCoord2<FL_TYPE,1> WedgeInterp(TexCoord2<FL_TYPE,1> &t0, TexCoord2<FL_TYPE,1> &t1)
{
TexCoord2<FL_TYPE,1> tmp;
tmp.n()=t0.n();
tmp.t()=(t0.t()+t1.t())/2.0;
return tmp;
}
inline void setValenceAttr(ValenceAttr *valence) {
this->valence = valence;
}
};
template<class MESH_TYPE, class METHOD_TYPE=Centroid<MESH_TYPE>, class WEIGHT_TYPE=LoopWeight<typename MESH_TYPE::ScalarType> >
struct EvenPointLoopGeneric : public std::unary_function<face::Pos<typename MESH_TYPE::FaceType> , typename MESH_TYPE::VertexType>
{
typedef METHOD_TYPE Projection;
typedef WEIGHT_TYPE Weight;
typedef typename MESH_TYPE::template PerVertexAttributeHandle<int> ValenceAttr;
typedef typename MESH_TYPE::CoordType CoordType;
Projection proj;
Weight weight;
ValenceAttr *valence;
inline EvenPointLoopGeneric(Projection proj = Projection(), Weight weight = Weight()) :
proj(proj), weight(weight), valence(0) {}
void operator()(std::pair<CoordType,CoordType> &nv, face::Pos<typename MESH_TYPE::FaceType> ep) {
proj.reset();
face::Pos<typename MESH_TYPE::FaceType> he(ep.f,ep.z,ep.f->V(ep.z));
typename MESH_TYPE::VertexType *r, *l, *curr;
curr = he.v;
face::Pos<typename MESH_TYPE::FaceType> heStart = he;
// compute valence of this vertex or find a border
int k = 0;
do {
he.NextE();
k++;
} while(!he.IsBorder() && he != heStart);
if (he.IsBorder()) { // Border rule
// consider valence of borders as if they are half+1 of an inner vertex. not perfect, but better than nothing.
if(valence) {
k = 0;
do {
he.NextE();
k++;
} while(!he.IsBorder());
(*valence)[he.V()] = std::max(2*(k-1), 3);
// (*valence)[he.V()] = 6;
}
he.FlipV();
r = he.v;
he.FlipV();
he.NextB();
l = he.v;
proj.addVertex(*curr, 3.0/4.0);
proj.addVertex(*l, 1.0/8.0);
proj.addVertex(*r, 1.0/8.0);
// std::pair<Point3f,Point3f>pp;
proj.project(nv);
// nv.P()=pp.first;
// nv.N()=pp.second;
// proj.project(nv);
}
else { // Inner rule
// assert(!he.v->IsB()); border flag no longer updated (useless)
if(valence)
(*valence)[he.V()] = k;
typename MESH_TYPE::ScalarType beta = weight.beta(k);
proj.addVertex(*curr, 1.0 - (typename MESH_TYPE::ScalarType)(k) * beta);
do {
proj.addVertex(*he.VFlip(), beta);
he.NextE();
} while(he != heStart);
proj.project(nv);
}
} // end of operator()
Color4<typename MESH_TYPE::ScalarType> WedgeInterp(Color4<typename MESH_TYPE::ScalarType> &c0, Color4<typename MESH_TYPE::ScalarType> &c1)
{
Color4<typename MESH_TYPE::ScalarType> cc;
return cc.lerp(c0,c1,0.5f);
}
Color4b WedgeInterp(Color4b &c0, Color4b &c1)
{
Color4b cc;
cc.lerp(c0,c1,0.5f);
return cc;
}
template<class FL_TYPE>
TexCoord2<FL_TYPE,1> WedgeInterp(TexCoord2<FL_TYPE,1> &t0, TexCoord2<FL_TYPE,1> &t1)
{
TexCoord2<FL_TYPE,1> tmp;
// assert(t0.n()== t1.n());
tmp.n()=t0.n();
tmp.t()=(t0.t()+t1.t())/2.0;
return tmp;
}
inline void setValenceAttr(ValenceAttr *valence) {
this->valence = valence;
}
};
template<class MESH_TYPE>
struct OddPointLoop : OddPointLoopGeneric<MESH_TYPE, Centroid<MESH_TYPE> >
{
OddPointLoop(MESH_TYPE &_m):OddPointLoopGeneric<MESH_TYPE, Centroid<MESH_TYPE> >(_m){}
};
template<class MESH_TYPE>
struct EvenPointLoop : EvenPointLoopGeneric<MESH_TYPE, Centroid<MESH_TYPE> >
{
};
template<class MESH_TYPE,class ODD_VERT, class EVEN_VERT>
bool RefineOddEven(MESH_TYPE &m, ODD_VERT odd, EVEN_VERT even,float length,
bool RefineSelected=false, CallBackPos *cbOdd = 0, CallBackPos *cbEven = 0)
{
EdgeLen <MESH_TYPE, typename MESH_TYPE::ScalarType> ep(length);
return RefineOddEvenE(m, odd, even, ep, RefineSelected, cbOdd, cbEven);
}
/*!
* \brief Perform diadic subdivision using given rules for odd and even vertices.
*/
template<class MESH_TYPE, class ODD_VERT, class EVEN_VERT, class PREDICATE>
bool RefineOddEvenE(MESH_TYPE &m, ODD_VERT odd, EVEN_VERT even, PREDICATE edgePred,
bool RefineSelected=false, CallBackPos *cbOdd = 0, CallBackPos *cbEven = 0)
{
typedef typename MESH_TYPE::template PerVertexAttributeHandle<int> ValenceAttr;
// momentaneamente le callback sono identiche, almeno cbOdd deve essere passata
cbEven = cbOdd;
// to mark visited vertices
int evenFlag = MESH_TYPE::VertexType::NewBitFlag();
for (int i = 0; i < m.vn ; i++ ) {
m.vert[i].ClearUserBit(evenFlag);
}
int j = 0;
// di texture per wedge (uno per ogni edge)
ValenceAttr valence = vcg::tri::Allocator<MESH_TYPE>:: template AddPerVertexAttribute<int>(m);
odd.setValenceAttr(&valence);
even.setValenceAttr(&valence);
// store updated vertices
std::vector<bool> updatedList(m.vn, false);
//std::vector<typename MESH_TYPE::VertexType> newEven(m.vn);
std::vector<std::pair<typename MESH_TYPE::CoordType, typename MESH_TYPE::CoordType> > newEven(m.vn);
typename MESH_TYPE::VertexIterator vi;
typename MESH_TYPE::FaceIterator fi;
for (fi = m.face.begin(); fi != m.face.end(); fi++) if(!(*fi).IsD() && (!RefineSelected || (*fi).IsS())){ //itero facce
for (int i = 0; i < 3; i++) { //itero vert
if ( !(*fi).V(i)->IsUserBit(evenFlag) && ! (*fi).V(i)->IsD() ) {
(*fi).V(i)->SetUserBit(evenFlag);
// use face selection, not vertex selection, to be coherent with RefineE
//if (RefineSelected && !(*fi).V(i)->IsS() )
// break;
face::Pos<typename MESH_TYPE::FaceType>aux (&(*fi),i);
if( tri::HasPerVertexColor(m) ) {
(*fi).V(i)->C().lerp((*fi).V0(i)->C() , (*fi).V1(i)->C(),0.5f);
}
if (cbEven) {
(*cbEven)(int(100.0f * (float)j / (float)m.fn),"Refining");
j++;
}
int index = tri::Index(m, (*fi).V(i));
updatedList[index] = true;
even(newEven[index], aux);
}
}
}
MESH_TYPE::VertexType::DeleteBitFlag(evenFlag);
// Now apply the stored normal and position to the initial vertex set (note that newEven is << m.vert)
RefineE< MESH_TYPE, ODD_VERT > (m, odd, edgePred, RefineSelected, cbOdd);
for(size_t i=0;i<newEven.size();++i) {
if(updatedList[i]) {
m.vert[i].P()=newEven[i].first;
m.vert[i].N()=newEven[i].second;
}
}
odd.setValenceAttr(0);
even.setValenceAttr(0);
vcg::tri::Allocator<MESH_TYPE>::DeletePerVertexAttribute(m, valence);
return true;
}
} // namespace tri
} // namespace vcg
#endif
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