599 lines
20 KiB
C++
599 lines
20 KiB
C++
/****************************************************************************
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* VCGLib o o *
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* Visual and Computer Graphics Library o o *
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* _ O _ *
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* Copyright(C) 2004-2016 \/)\/ *
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* Visual Computing Lab /\/| *
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* ISTI - Italian National Research Council | *
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* \ *
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* All rights reserved. *
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* *
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* This program is free software; you can redistribute it and/or modify *
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* it under the terms of the GNU General Public License as published by *
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* the Free Software Foundation; either version 2 of the License, or *
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* (at your option) any later version. *
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* *
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* This program is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
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* for more details. *
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* *
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****************************************************************************/
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#ifndef VCG_PARAM_DISTORTION
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#define VCG_PARAM_DISTORTION
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#include <vcg/complex/algorithms/parametrization/uv_utils.h>
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#include <vcg/complex/algorithms/parametrization/tangent_field_operators.h>
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#include <Eigen/Dense>
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namespace vcg {
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namespace tri {
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template <class MeshType, bool PerWedge>
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struct UVHelper {};
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template <class MeshType>
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struct UVHelper<MeshType, true>
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{
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typedef typename MeshType::FaceType FaceType;
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typedef typename FaceType::TexCoordType::PointType TexCoordType;
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static TexCoordType Coord(const FaceType *f, int i)
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{
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return f->cWT(i).P();
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}
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};
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template <class MeshType>
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struct UVHelper<MeshType, false>
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{
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typedef typename MeshType::FaceType FaceType;
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typedef typename MeshType::VertexType VertexType;
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typedef typename VertexType::TexCoordType::PointType TexCoordType;
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static TexCoordType Coord(const FaceType *f, int i)
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{
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return f->cV(i)->T().P();
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}
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};
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/*
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* Energy types:
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*
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* AreaDist : 0 for equiareal (equipotent) mappings
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* EdgeDist (hack): 0 for isometric mappings (computed on edges only)
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* AngleDist (hack): 0 for conformal mappings
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* CrossDist : as above, but computed on tangent directions (not UVs)
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* L2Stretch : 1 for isometric mappings (averaged case on the mesh),
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* +inf on degenerate / folded cases
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* Described in [1]
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* LInfStretch : as above, but WORST case
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* (returns the worst stretch on any position and direction)
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* Described in [1]
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* ARAPEnergy : 0 for isometric mappings
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* Described in [2]
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*
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* [1] Sander, P. V., Snyder, J., Gortler, S. J., & Hoppe, H.
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* "Texture mapping progressive meshes."
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* In Proc. ACM SIGGRAPH (pp. 409-416). 2001
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*
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* [2] Liu, L., Zhang, L., Xu, Y., Gotsman, C., & Gortler, S. J. (2008, July).
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* A local/global approach to mesh parameterization.
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* Computer Graphics Forum (Vol. 27, No. 5, pp. 1495-1504). Blackwell Publishing Ltd.
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*/
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template <class MeshType, bool PerWedgeFlag>
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class Distortion
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{
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public:
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typedef typename MeshType::FaceType FaceType;
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typedef typename MeshType::VertexType VertexType;
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typedef typename MeshType::CoordType CoordType;
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typedef typename MeshType::ScalarType ScalarType;
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typedef typename MeshType::FaceType::CurVecType CurVecType;
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// typedef typename std::conditional<PerWedgeFlag, FaceType, VertexType>::type BaseTexType;
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typedef UVHelper<MeshType, PerWedgeFlag> UV;
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typedef typename UV::TexCoordType TexCoordType;
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typedef typename TexCoordType::ScalarType TexScalarType;
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static TexCoordType UVCoord(const FaceType *f, int i)
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{
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return UV::Coord(f, i);
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}
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static ScalarType Area3D(const FaceType *f)
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{
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return DoubleArea(*f)*(0.5);
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}
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static ScalarType AreaUV(const FaceType *f)
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{
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// TexCoordType uv0,uv1,uv2;
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// if(PerWedgeFlag) {
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// uv0=f->cWT(0).P();
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// uv1=f->cWT(1).P();
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// uv2=f->cWT(2).P();
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// } else {
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// uv0=f->cV(0)->T().P();
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// uv1=f->cV(1)->T().P();
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// uv2=f->cV(2)->T().P();
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// }
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TexCoordType uv0 = UVCoord(f, 0);
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TexCoordType uv1 = UVCoord(f, 1);
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TexCoordType uv2 = UVCoord(f, 2);
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ScalarType AreaUV=((uv1-uv0)^(uv2-uv0))/2.0;
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return AreaUV;
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}
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static ScalarType EdgeLenght3D(const FaceType *f,int e)
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{
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assert((e>=0)&&(e<3));
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ScalarType length=(f->cP0(e)-f->cP1(e)).Norm();
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return (length);
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}
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static ScalarType EdgeLenghtUV(const FaceType *f,int e)
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{
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assert((e>=0)&&(e<3));
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TexCoordType uv0 = UVCoord(f, e+0);
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TexCoordType uv1 = UVCoord(f, (e+1)%3);
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// Point2<TexScalarType> uv0,uv1;
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// if(PerWedgeFlag) {
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// uv0=f->cWT(e+0).P();
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// uv1=f->cWT((e+1)%3).P();
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// } else {
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// uv0=f->cV0(e)->T().P();
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// uv1=f->cV1(e)->T().P();
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// }
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ScalarType UVlength=Distance(uv0,uv1);
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return UVlength;
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}
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static ScalarType AngleCos3D(const FaceType *f,int e)
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{
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assert((e>=0)&&(e<3));
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CoordType p0=f->P((e+2)%3);
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CoordType p1=f->P(e);
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CoordType p2=f->P((e+1)%3);
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CoordType dir0=p2-p1;
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CoordType dir1=p0-p1;
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dir0.Normalize();
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dir1.Normalize();
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ScalarType angle=dir0*dir1;
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return angle;
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}
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static ScalarType AngleCosUV(const FaceType *f,int e)
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{
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TexCoordType uv0 = UVCoord(f, (e+2)%3);
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TexCoordType uv1 = UVCoord(f, e);
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TexCoordType uv2 = UVCoord(f, (e+1)%3);
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// Point2<ScalarType> uv0,uv1,uv2;
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// if(PerWedgeFlag) {
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// uv0=f->cWT((e+2)%3).P();
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// uv1=f->cWT((e+0)%3).P();
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// uv2=f->cWT((e+1)%3).P();
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// } else {
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// uv0=f->V2(e)->T().P();
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// uv1=f->V0(e)->T().P();
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// uv2=f->V1(e)->T().P();
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// }
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vcg::Point2<ScalarType> dir0=uv2-uv1;
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vcg::Point2<ScalarType> dir1=uv0-uv1;
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dir0.Normalize();
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dir1.Normalize();
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ScalarType angle=dir0*dir1;
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return angle;
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}
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static ScalarType AngleRad3D(const FaceType *f,int e)
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{
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assert((e>=0)&&(e<3));
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CoordType p0=f->cP((e+2)%3);
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CoordType p1=f->cP(e);
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CoordType p2=f->cP((e+1)%3);
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CoordType dir0=p2-p1;
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CoordType dir1=p0-p1;
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return Angle(dir0,dir1);
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}
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static ScalarType AngleRadUV(const FaceType *f,int e)
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{
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TexCoordType uv0 = UVCoord(f, (e+2)%3);
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TexCoordType uv1 = UVCoord(f, e);
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TexCoordType uv2 = UVCoord(f, (e+1)%3);
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// Point2<TexScalarType> uv0,uv1,uv2;
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// if(PerWedgeFlag) {
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// uv0=f->cWT((e+2)%3).P();
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// uv1=f->cWT((e+0)%3).P();
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// uv2=f->cWT((e+1)%3).P();
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// } else {
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// uv0=f->cV2(e)->T().P();
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// uv1=f->cV0(e)->T().P();
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// uv2=f->cV1(e)->T().P();
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// }
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vcg::Point2<TexScalarType> dir0=uv2-uv1;
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vcg::Point2<TexScalarType> dir1=uv0-uv1;
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dir0.Normalize();
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dir1.Normalize();
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ScalarType t=dir0*dir1;
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if(t>1) t = 1;
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else if(t<-1) t = -1;
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return acos(t);
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}
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public:
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enum DistType{AreaDist,EdgeDist,AngleDist,CrossDist,L2Stretch,LInfStretch,ARAPDist};
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///return the absolute difference between angle in 3D space and texture space
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///Actually the difference in cos space
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static ScalarType AngleCosDistortion(const FaceType *f,int e)
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{
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ScalarType Angle_3D=AngleCos3D(f,e);
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ScalarType Angle_UV=AngleCosUV(f,e);
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ScalarType diff=fabs(Angle_3D-Angle_UV);///Angle_3D;
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return diff;
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}
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///return the absolute difference between angle in 3D space and texture space
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///Actually the difference in cos space
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static ScalarType AngleRadDistortion(const FaceType *f,int e)
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{
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ScalarType Angle_3D=AngleRad3D(f,e);
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ScalarType Angle_UV=AngleRadUV(f,e);
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ScalarType diff=fabs(Angle_3D-Angle_UV)/Angle_3D;///Angle_3D;
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return diff;
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}
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///return the variance of angle, normalized
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///in absolute value
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static ScalarType AngleDistortion(const FaceType *f)
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{
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return (AngleRadDistortion(f,0) +
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AngleRadDistortion(f,1) +
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AngleRadDistortion(f,2))/3.0;
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}
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///return the global scaling factors from 3D to UV
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static void MeshScalingFactor(const MeshType &m,
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ScalarType &AreaScale,
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ScalarType &EdgeScale)
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{
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ScalarType SumArea3D=0;
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ScalarType SumArea2D=0;
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ScalarType SumEdge3D=0;
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ScalarType SumEdge2D=0;
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for (size_t i=0;i<m.face.size();i++)
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{
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SumArea3D+=Area3D(&m.face[i]);
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SumArea2D+=AreaUV(&m.face[i]);
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for (int j=0;j<3;j++)
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{
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SumEdge3D+=EdgeLenght3D(&m.face[i],j);
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SumEdge2D+=EdgeLenghtUV(&m.face[i],j);
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}
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}
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AreaScale=SumArea3D/SumArea2D;
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EdgeScale=SumEdge3D/SumEdge2D;
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}
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///return the variance of edge length, normalized in absolute value,
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///the needed scaling factor EdgeScaleVal may be calculated
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///by using the ScalingFactor function
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static ScalarType EdgeDistortion(const FaceType *f,int e,
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ScalarType EdgeScaleVal)
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{
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ScalarType edgeUV=EdgeLenghtUV(f,e)*EdgeScaleVal;
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ScalarType edge3D=EdgeLenght3D(f,e);
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assert(edge3D > 0);
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ScalarType diff=fabs(edge3D-edgeUV)/edge3D;
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assert(!math::IsNAN(diff));
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return diff;
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}
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///return the variance of area, normalized
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///in absolute value, the scalar AreaScaleVal may be calculated
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///by using the ScalingFactor function
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static ScalarType AreaDistortion(const FaceType *f,
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ScalarType AreaScaleVal)
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{
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ScalarType areaUV=AreaUV(f)*AreaScaleVal;
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ScalarType area3D=Area3D(f);
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assert(area3D > 0);
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ScalarType diff=fabs(areaUV-area3D)/area3D;
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assert(!math::IsNAN(diff));
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return diff;
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}
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static ScalarType L2StretchEnergySquared(const FaceType *f,
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ScalarType AreaScaleVal)
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{
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TexCoordType p0 = UVCoord(f, 0);
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TexCoordType p1 = UVCoord(f, 1);
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TexCoordType p2 = UVCoord(f, 2);
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// TexCoordType p0 = (PerWedgeFlag)? f->cWT(0).P() : f->cV(0)->T().P() ;
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// TexCoordType p1 = (PerWedgeFlag)? f->cWT(1).P() : f->cV(1)->T().P() ;
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// TexCoordType p2 = (PerWedgeFlag)? f->cWT(2).P() : f->cV(2)->T().P() ;
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CoordType q0 = f->cP(0);
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CoordType q1 = f->cP(1);
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CoordType q2 = f->cP(2);
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TexScalarType A2 = ((p1-p0)^(p2-p0));
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if (A2<0) A2 = 0; // will be NAN, +infinity
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CoordType Ss = ( q0 * ( p1[1]-p2[1] ) + q1 * (p2[1]-p0[1]) + q2 * (p0[1]-p1[1]) ) / A2;
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CoordType St = ( q0 * ( p2[0]-p1[0] ) + q1 * (p0[0]-p2[0]) + q2 * (p1[0]-p0[0]) ) / A2;
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ScalarType a = Ss.SquaredNorm() / AreaScaleVal;
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ScalarType c = St.SquaredNorm() / AreaScaleVal;
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return ((a+c)/2);
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}
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static ScalarType LInfStretchEnergy(const FaceType *f, ScalarType AreaScaleVal)
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{
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TexCoordType p0 = UVCoord(f, 0);
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TexCoordType p1 = UVCoord(f, 1);
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TexCoordType p2 = UVCoord(f, 2);
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// TexCoordType p0 = (PerWedgeFlag)? f->cWT(0).P() : f->cV(0)->T().P() ;
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// TexCoordType p1 = (PerWedgeFlag)? f->cWT(1).P() : f->cV(1)->T().P() ;
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// TexCoordType p2 = (PerWedgeFlag)? f->cWT(2).P() : f->cV(2)->T().P() ;
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CoordType q0 = f->cP(0);
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CoordType q1 = f->cP(1);
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CoordType q2 = f->cP(2);
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TexScalarType A2 = ((p1-p0)^(p2-p0));
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if (A2<0) A2 = 0; // will be NAN, +infinity
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CoordType Ss = ( q0 * ( p1[1]-p2[1] ) + q1 * (p2[1]-p0[1]) + q2 * (p0[1]-p1[1]) ) / A2;
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CoordType St = ( q0 * ( p2[0]-p1[0] ) + q1 * (p0[0]-p2[0]) + q2 * (p1[0]-p0[0]) ) / A2;
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ScalarType a = Ss.SquaredNorm() / AreaScaleVal;
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ScalarType b = Ss*St / AreaScaleVal;
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ScalarType c = St.SquaredNorm() / AreaScaleVal;
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ScalarType delta = sqrt((a-c)*(a-c)+4*b*b);
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ScalarType G = sqrt( (a+c+delta)/2 );
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//ScalarType g = sqrt( (a+c-delta)/2 ); // not needed
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return G;
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}
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static ScalarType ARAPEnergy(const FaceType *f)
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{
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if (f == NULL)
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{
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return std::numeric_limits<ScalarType>::infinity();
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}
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const Eigen::Matrix2d F = mappingTransform2D(*f);
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const Eigen::Vector2d singular = svd2x2(F);
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const double a = singular(0) - 1;
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const double b = singular(1) - 1;
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// std::cout << "Singular" << std::endl << singular << std::endl;
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return ScalarType(0.5 * (a*a + b*b));
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}
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static Eigen::Matrix2d mappingTransform2D(const FaceType & triangle)
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{
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typedef Eigen::Matrix<double, 3, 2> Matrix32;
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typedef Eigen::Matrix2d Matrix22;
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Matrix22 param3d, param2d;
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// 3D
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{
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Matrix32 edges3D, P3D;
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Eigen::Vector3d e0, e1;
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(triangle.cP(1) - triangle.cP(0)).ToEigenVector(e0); // 0->1
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(triangle.cP(2) - triangle.cP(0)).ToEigenVector(e1); // 0->2
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edges3D.col(0) = e0;
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edges3D.col(1) = e1;
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// Projection/frame change matrix
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P3D.col(0) = edges3D.col(0).normalized(); // 0->1 normalized e0 basis
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P3D.col(1) = (edges3D.col(1) - edges3D.col(1).dot(P3D.col(0)) * P3D.col(0)).normalized(); // e1 basis orthogonal to e0
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param3d = (P3D.transpose() * edges3D);
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}
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// 2D
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{
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Matrix22 edges2D, P2D;
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TexCoordType uv0 = UVCoord(&triangle, 0);
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TexCoordType uv1 = UVCoord(&triangle, 1);
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TexCoordType uv2 = UVCoord(&triangle, 2);
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const TexCoordType e0 = (uv1 - uv0); // 0->1
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const TexCoordType e1 = (uv2 - uv0); // 0->2
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param2d << e0.X(), e1.X(),
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e0.Y(), e1.Y();
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}
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return param2d * param3d.inverse(); // transf mapping
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}
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// svd 2x2 matrix (singular values only)
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static Eigen::Vector2d svd2x2(const Eigen::Matrix2d & M)
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{
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const double a=M(0,0), b=M(0,1), c=M(1,0), d=M(1,1);
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const double tmp1 = a*a + b*b;
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const double tmp2 = c*c + d*d;
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const double s1 = tmp1 + tmp2;
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const double s2 = std::sqrt(std::pow((tmp1 -tmp2), 2.0) + 4 * std::pow(a*c + b*d, 2.0));
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return Eigen::Vector2d(std::sqrt((s1+s2)/2.0), std::sqrt((s1-s2)/2.0));
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}
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///return the number of folded faces
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static bool Folded(const FaceType *f)
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{
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ScalarType areaUV=AreaUV(f);
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/*if (areaUV<0)
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printf("area %5.5f \n",areaUV);*/
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return (areaUV<0);
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}
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static int Folded(const MeshType &m)
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{
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int folded=0;
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for (size_t i=0;i<m.face.size();i++)
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{
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if (m.face[i].IsD())continue;
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if(Folded(&m.face[i]))folded++;
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}
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return folded;
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}
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static bool GloballyUnFolded(const MeshType &m)
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{
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int num=Folded(m);
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return (num>(m.fn)/2);
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}
|
|
|
|
static ScalarType MeshAngleDistortion(const MeshType &m)
|
|
{
|
|
ScalarType UDdist=0;
|
|
for (int i=0;i<m.face.size();i++)
|
|
{
|
|
if (m.face[i].IsD())continue;
|
|
const FaceType *f=&(m.face[i]);
|
|
UDdist+=AngleDistortion(f)*Area3D(f);
|
|
}
|
|
return UDdist;
|
|
}
|
|
|
|
static ScalarType SetFQAsCrossDirDistortion(MeshType &m)
|
|
{
|
|
//first save the old UV dir
|
|
std::vector<CurVecType> Dir1,Dir2;
|
|
for (size_t i=0;i<m.face.size();i++)
|
|
{
|
|
Dir1.push_back(m.face[i].PD1());
|
|
Dir2.push_back(m.face[i].PD2());
|
|
}
|
|
vcg::tri::CrossField<MeshType>::InitDirFromWEdgeUV(m);
|
|
|
|
ScalarType tot = 0, totA = 0;
|
|
|
|
//then compute angle deficit
|
|
for (size_t i=0;i<m.face.size();i++)
|
|
{
|
|
|
|
FaceType &f( m.face[i] );
|
|
CoordType transfPD1=vcg::tri::CrossField<MeshType>::K_PI(CoordType::Construct( Dir1[i] ),
|
|
CoordType::Construct( f.PD1() ),
|
|
f.N());
|
|
transfPD1.Normalize();
|
|
ScalarType AngleDeficit=vcg::Angle(transfPD1,CoordType::Construct( f.PD1() ));
|
|
AngleDeficit=math::ToDeg(AngleDeficit);
|
|
if ((AngleDeficit>45)||(AngleDeficit<0))
|
|
{
|
|
std::cout<<"Warnign A Deficit "<<AngleDeficit<<std::endl;
|
|
}
|
|
// assert(AngleDeficit<45);
|
|
// assert(AngleDeficit>=0);
|
|
|
|
ScalarType doubleArea = vcg::DoubleArea( f );
|
|
ScalarType distortion = (AngleDeficit)/ 45 ;
|
|
|
|
m.face[i].Q()= distortion;
|
|
tot += distortion * doubleArea;
|
|
totA += doubleArea;
|
|
}
|
|
|
|
//finally restore the original directions
|
|
for (size_t i=0;i<m.face.size();i++)
|
|
{
|
|
m.face[i].PD1()=Dir1[i];
|
|
m.face[i].PD2()=Dir2[i];
|
|
}
|
|
|
|
return tot / totA;
|
|
}
|
|
|
|
static ScalarType SetQasDistorsion(MeshType &m, DistType DType=AreaDist)
|
|
{
|
|
if (DType==CrossDist)
|
|
{
|
|
ScalarType res = SetFQAsCrossDirDistortion(m);
|
|
|
|
vcg::tri::UpdateQuality<MeshType>::VertexFromFace(m,true);
|
|
return res;
|
|
}
|
|
|
|
ScalarType edge_scale,area_scale;
|
|
MeshScalingFactor(m,area_scale,edge_scale);
|
|
|
|
ScalarType tot = 0;
|
|
ScalarType totA = 0;
|
|
|
|
for (int i=0;i<m.face.size();i++)
|
|
{
|
|
if (m.face[i].IsD())continue;
|
|
ScalarType q;
|
|
switch (DType) {
|
|
case CrossDist:
|
|
// make compiler happy
|
|
q = 0;
|
|
break;
|
|
case AreaDist:
|
|
q = AreaDistortion(&m.face[i],area_scale);
|
|
break;
|
|
case AngleDist:
|
|
q = AngleDistortion(&m.face[i]);
|
|
break;
|
|
case EdgeDist:
|
|
q =( EdgeDistortion(&m.face[i],0,edge_scale)+
|
|
EdgeDistortion(&m.face[i],1,edge_scale)+
|
|
EdgeDistortion(&m.face[i],2,edge_scale) )/3;
|
|
break;
|
|
case L2Stretch:
|
|
q = L2StretchEnergySquared( &m.face[i],area_scale );
|
|
break;
|
|
case LInfStretch:
|
|
q = LInfStretchEnergy( &m.face[i],area_scale );
|
|
break;
|
|
case ARAPDist:
|
|
q = ARAPEnergy(&m.face[i]);
|
|
break;
|
|
}
|
|
|
|
m.face[i].Q() = q; // note: for L2Stretch, we are puttning E^2 on Q
|
|
|
|
// aggregate:
|
|
if (DType==LInfStretch) {
|
|
tot = std::max( tot, q );
|
|
} else {
|
|
ScalarType a = Area3D(&m.face[i]);
|
|
tot += q*a;
|
|
totA += a;
|
|
}
|
|
|
|
}
|
|
|
|
vcg::tri::UpdateQuality<MeshType>::VertexFromFace(m,true);
|
|
|
|
switch (DType) {
|
|
case L2Stretch: return sqrt(tot/totA);
|
|
case LInfStretch: return tot;
|
|
default: return tot/totA;
|
|
}
|
|
}
|
|
};
|
|
|
|
//template <class MeshType, false>
|
|
//static TexCoordType Distortion::UVCoord<false>(const FaceType *f, int i)
|
|
//{
|
|
// return f->cV(0)->T().P();
|
|
//}
|
|
|
|
}} // namespace end
|
|
|
|
#endif
|