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added arap distortion + class template for UV paramertization

This commit is contained in:
Luigi Malomo 2017-03-24 13:17:37 +01:00
parent 48092ff9b9
commit 9eb6610f34
2 changed files with 188 additions and 57 deletions
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233
vcg/complex/algorithms/parametrization/distortion.h
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@ -25,12 +25,38 @@
#define VCG_PARAM_DISTORTION #define VCG_PARAM_DISTORTION
#include <vcg/complex/algorithms/parametrization/uv_utils.h> #include <vcg/complex/algorithms/parametrization/uv_utils.h>
#include <vcg/complex/algorithms/parametrization/tangent_field_operators.h> #include <vcg/complex/algorithms/parametrization/tangent_field_operators.h>
#include <Eigen/Dense>
namespace vcg { namespace vcg {
namespace tri{ namespace tri {
template <class MeshType, bool PerWedgeFlag>
template <class MeshType, bool PerWedge>
struct UVHelper {};
template <class MeshType>
struct UVHelper<MeshType, true>
{
typedef typename MeshType::FaceType FaceType;
typedef typename FaceType::TexCoordType::PointType TexCoordType;
static TexCoordType Coord(const FaceType *f, int i)
{
return f->cWT(i).P();
}
};
template <class MeshType>
struct UVHelper<MeshType, false>
{
typedef typename MeshType::FaceType FaceType;
typedef typename MeshType::VertexType VertexType;
typedef typename VertexType::TexCoordType::PointType TexCoordType;
static TexCoordType Coord(const FaceType *f, int i)
{
return f->cV(i)->T().P();
}
};
/* /*
* Energy types: * Energy types:
* *
@ -44,12 +70,19 @@ template <class MeshType, bool PerWedgeFlag>
* LInfStretch : as above, but WORST case * LInfStretch : as above, but WORST case
* (returns the worst stretch on any position and direction) * (returns the worst stretch on any position and direction)
* Described in [1] * Described in [1]
* ARAPEnergy : 0 for isometric mappings
* Described in [2]
* *
* [1] Sander, P. V., Snyder, J., Gortler, S. J., & Hoppe, H. * [1] Sander, P. V., Snyder, J., Gortler, S. J., & Hoppe, H.
* "Texture mapping progressive meshes." * "Texture mapping progressive meshes."
* In Proc. ACM SIGGRAPH (pp. 409-416). 2001 * In Proc. ACM SIGGRAPH (pp. 409-416). 2001
*
* [2] Liu, L., Zhang, L., Xu, Y., Gotsman, C., & Gortler, S. J. (2008, July).
* A local/global approach to mesh parameterization.
* Computer Graphics Forum (Vol. 27, No. 5, pp. 1495-1504). Blackwell Publishing Ltd.
*/ */
template <class MeshType, bool PerWedgeFlag>
class Distortion class Distortion
{ {
public: public:
@ -58,8 +91,15 @@ public:
typedef typename MeshType::CoordType CoordType; typedef typename MeshType::CoordType CoordType;
typedef typename MeshType::ScalarType ScalarType; typedef typename MeshType::ScalarType ScalarType;
typedef typename MeshType::FaceType::CurVecType CurVecType; typedef typename MeshType::FaceType::CurVecType CurVecType;
typedef typename MeshType::FaceType::TexCoordType::ScalarType TexScalarType; // typedef typename std::conditional<PerWedgeFlag, FaceType, VertexType>::type BaseTexType;
typedef Point2<TexScalarType> TexCoordType; typedef UVHelper<MeshType, PerWedgeFlag> UV;
typedef typename UV::TexCoordType TexCoordType;
typedef typename TexCoordType::ScalarType TexScalarType;
static TexCoordType UVCoord(const FaceType *f, int i)
{
return UV::Coord(f, i);
}
static ScalarType Area3D(const FaceType *f) static ScalarType Area3D(const FaceType *f)
{ {
@ -68,16 +108,19 @@ public:
static ScalarType AreaUV(const FaceType *f) static ScalarType AreaUV(const FaceType *f)
{ {
TexCoordType uv0,uv1,uv2; // TexCoordType uv0,uv1,uv2;
if(PerWedgeFlag) { // if(PerWedgeFlag) {
uv0=f->cWT(0).P(); // uv0=f->cWT(0).P();
uv1=f->cWT(1).P(); // uv1=f->cWT(1).P();
uv2=f->cWT(2).P(); // uv2=f->cWT(2).P();
} else { // } else {
uv0=f->cV(0)->T().P(); // uv0=f->cV(0)->T().P();
uv1=f->cV(1)->T().P(); // uv1=f->cV(1)->T().P();
uv2=f->cV(2)->T().P(); // uv2=f->cV(2)->T().P();
} // }
TexCoordType uv0 = UVCoord(f, 0);
TexCoordType uv1 = UVCoord(f, 1);
TexCoordType uv2 = UVCoord(f, 2);
ScalarType AreaUV=((uv1-uv0)^(uv2-uv0))/2.0; ScalarType AreaUV=((uv1-uv0)^(uv2-uv0))/2.0;
return AreaUV; return AreaUV;
} }
@ -92,14 +135,16 @@ public:
static ScalarType EdgeLenghtUV(const FaceType *f,int e) static ScalarType EdgeLenghtUV(const FaceType *f,int e)
{ {
assert((e>=0)&&(e<3)); assert((e>=0)&&(e<3));
Point2<TexScalarType> uv0,uv1; TexCoordType uv0 = UVCoord(f, e+0);
if(PerWedgeFlag) { TexCoordType uv1 = UVCoord(f, (e+1)%3);
uv0=f->cWT(e+0).P(); // Point2<TexScalarType> uv0,uv1;
uv1=f->cWT((e+1)%3).P(); // if(PerWedgeFlag) {
} else { // uv0=f->cWT(e+0).P();
uv0=f->cV0(e)->T().P(); // uv1=f->cWT((e+1)%3).P();
uv1=f->cV1(e)->T().P(); // } else {
} // uv0=f->cV0(e)->T().P();
// uv1=f->cV1(e)->T().P();
// }
ScalarType UVlength=Distance(uv0,uv1); ScalarType UVlength=Distance(uv0,uv1);
return UVlength; return UVlength;
} }
@ -120,16 +165,19 @@ public:
static ScalarType AngleCosUV(const FaceType *f,int e) static ScalarType AngleCosUV(const FaceType *f,int e)
{ {
Point2<ScalarType> uv0,uv1,uv2; TexCoordType uv0 = UVCoord(f, (e+2)%3);
if(PerWedgeFlag) { TexCoordType uv1 = UVCoord(f, e);
uv0=f->cWT((e+2)%3).P(); TexCoordType uv2 = UVCoord(f, (e+1)%3);
uv1=f->cWT((e+0)%3).P(); // Point2<ScalarType> uv0,uv1,uv2;
uv2=f->cWT((e+1)%3).P(); // if(PerWedgeFlag) {
} else { // uv0=f->cWT((e+2)%3).P();
uv0=f->V2(e)->T().P(); // uv1=f->cWT((e+0)%3).P();
uv1=f->V0(e)->T().P(); // uv2=f->cWT((e+1)%3).P();
uv2=f->V1(e)->T().P(); // } else {
} // uv0=f->V2(e)->T().P();
// uv1=f->V0(e)->T().P();
// uv2=f->V1(e)->T().P();
// }
vcg::Point2<ScalarType> dir0=uv2-uv1; vcg::Point2<ScalarType> dir0=uv2-uv1;
vcg::Point2<ScalarType> dir1=uv0-uv1; vcg::Point2<ScalarType> dir1=uv0-uv1;
dir0.Normalize(); dir0.Normalize();
@ -151,16 +199,19 @@ public:
static ScalarType AngleRadUV(const FaceType *f,int e) static ScalarType AngleRadUV(const FaceType *f,int e)
{ {
Point2<TexScalarType> uv0,uv1,uv2; TexCoordType uv0 = UVCoord(f, (e+2)%3);
if(PerWedgeFlag) { TexCoordType uv1 = UVCoord(f, e);
uv0=f->cWT((e+2)%3).P(); TexCoordType uv2 = UVCoord(f, (e+1)%3);
uv1=f->cWT((e+0)%3).P(); // Point2<TexScalarType> uv0,uv1,uv2;
uv2=f->cWT((e+1)%3).P(); // if(PerWedgeFlag) {
} else { // uv0=f->cWT((e+2)%3).P();
uv0=f->cV2(e)->T().P(); // uv1=f->cWT((e+0)%3).P();
uv1=f->cV0(e)->T().P(); // uv2=f->cWT((e+1)%3).P();
uv2=f->cV1(e)->T().P(); // } else {
} // uv0=f->cV2(e)->T().P();
// uv1=f->cV0(e)->T().P();
// uv2=f->cV1(e)->T().P();
// }
vcg::Point2<TexScalarType> dir0=uv2-uv1; vcg::Point2<TexScalarType> dir0=uv2-uv1;
vcg::Point2<TexScalarType> dir1=uv0-uv1; vcg::Point2<TexScalarType> dir1=uv0-uv1;
dir0.Normalize(); dir0.Normalize();
@ -173,7 +224,7 @@ public:
public: public:
enum DistType{AreaDist,EdgeDist,AngleDist,CrossDist,L2Stretch,LInfStretch}; enum DistType{AreaDist,EdgeDist,AngleDist,CrossDist,L2Stretch,LInfStretch,ARAPDist};
///return the absolute difference between angle in 3D space and texture space ///return the absolute difference between angle in 3D space and texture space
///Actually the difference in cos space ///Actually the difference in cos space
@ -257,9 +308,12 @@ public:
static ScalarType L2StretchEnergySquared(const FaceType *f, static ScalarType L2StretchEnergySquared(const FaceType *f,
ScalarType AreaScaleVal) ScalarType AreaScaleVal)
{ {
TexCoordType p0 = (PerWedgeFlag)? f->cWT(0).P() : f->cV(0)->T().P() ; TexCoordType p0 = UVCoord(f, 0);
TexCoordType p1 = (PerWedgeFlag)? f->cWT(1).P() : f->cV(1)->T().P() ; TexCoordType p1 = UVCoord(f, 1);
TexCoordType p2 = (PerWedgeFlag)? f->cWT(2).P() : f->cV(2)->T().P() ; TexCoordType p2 = UVCoord(f, 2);
// TexCoordType p0 = (PerWedgeFlag)? f->cWT(0).P() : f->cV(0)->T().P() ;
// TexCoordType p1 = (PerWedgeFlag)? f->cWT(1).P() : f->cV(1)->T().P() ;
// TexCoordType p2 = (PerWedgeFlag)? f->cWT(2).P() : f->cV(2)->T().P() ;
CoordType q0 = f->cP(0); CoordType q0 = f->cP(0);
CoordType q1 = f->cP(1); CoordType q1 = f->cP(1);
@ -282,9 +336,12 @@ public:
static ScalarType LInfStretchEnergy(const FaceType *f, ScalarType AreaScaleVal) static ScalarType LInfStretchEnergy(const FaceType *f, ScalarType AreaScaleVal)
{ {
TexCoordType p0 = (PerWedgeFlag)? f->cWT(0).P() : f->cV(0)->T().P() ; TexCoordType p0 = UVCoord(f, 0);
TexCoordType p1 = (PerWedgeFlag)? f->cWT(1).P() : f->cV(1)->T().P() ; TexCoordType p1 = UVCoord(f, 1);
TexCoordType p2 = (PerWedgeFlag)? f->cWT(2).P() : f->cV(2)->T().P() ; TexCoordType p2 = UVCoord(f, 2);
// TexCoordType p0 = (PerWedgeFlag)? f->cWT(0).P() : f->cV(0)->T().P() ;
// TexCoordType p1 = (PerWedgeFlag)? f->cWT(1).P() : f->cV(1)->T().P() ;
// TexCoordType p2 = (PerWedgeFlag)? f->cWT(2).P() : f->cV(2)->T().P() ;
CoordType q0 = f->cP(0); CoordType q0 = f->cP(0);
CoordType q1 = f->cP(1); CoordType q1 = f->cP(1);
@ -307,6 +364,71 @@ public:
return G; return G;
} }
static ScalarType ARAPEnergy(const FaceType *f)
{
if (f == NULL)
{
return std::numeric_limits<ScalarType>::infinity();
}
const Eigen::Matrix2d F = mappingTransform2D(*f);
const Eigen::Vector2d singular = svd2x2(F);
const double a = singular(0) - 1;
const double b = singular(1) - 1;
// std::cout << "Singular" << std::endl << singular << std::endl;
return ScalarType(0.5 * (a*a + b*b));
}
static Eigen::Matrix2d mappingTransform2D(const FaceType & triangle)
{
typedef Eigen::Matrix<double, 3, 2> Matrix32;
typedef Eigen::Matrix2d Matrix22;
Matrix22 param3d, param2d;
// 3D
{
Matrix32 edges3D, P3D;
Eigen::Vector3d e0, e1;
(triangle.cP(1) - triangle.cP(0)).ToEigenVector(e0); // 0->1
(triangle.cP(2) - triangle.cP(0)).ToEigenVector(e1); // 0->2
edges3D.col(0) = e0;
edges3D.col(1) = e1;
// Projection/frame change matrix
P3D.col(0) = edges3D.col(0).normalized(); // 0->1 normalized e0 basis
P3D.col(1) = (edges3D.col(1) - edges3D.col(1).dot(P3D.col(0)) * P3D.col(0)).normalized(); // e1 basis orthogonal to e0
param3d = (P3D.transpose() * edges3D);
}
// 2D
{
Matrix22 edges2D, P2D;
TexCoordType uv0 = UVCoord(&triangle, 0);
TexCoordType uv1 = UVCoord(&triangle, 1);
TexCoordType uv2 = UVCoord(&triangle, 2);
const TexCoordType e0 = (uv1 - uv0); // 0->1
const TexCoordType e1 = (uv2 - uv0); // 0->2
param2d << e0.X(), e1.X(),
e0.Y(), e1.Y();
}
return param2d * param3d.inverse(); // transf mapping
}
// svd 2x2 matrix (singular values only)
static Eigen::Vector2d svd2x2(const Eigen::Matrix2d & M)
{
const double a=M(0,0), b=M(0,1), c=M(1,0), d=M(1,1);
const double tmp1 = a*a + b*b;
const double tmp2 = c*c + d*d;
const double s1 = tmp1 + tmp2;
const double s2 = std::sqrt(std::pow((tmp1 -tmp2), 2.0) + 4 * std::pow(a*c + b*d, 2.0));
return Eigen::Vector2d(std::sqrt((s1+s2)/2.0), std::sqrt((s1-s2)/2.0));
}
///return the number of folded faces ///return the number of folded faces
static bool Folded(const FaceType *f) static bool Folded(const FaceType *f)
@ -408,8 +530,8 @@ public:
ScalarType edge_scale,area_scale; ScalarType edge_scale,area_scale;
MeshScalingFactor(m,area_scale,edge_scale); MeshScalingFactor(m,area_scale,edge_scale);
float tot = 0; ScalarType tot = 0;
float totA = 0; ScalarType totA = 0;
for (int i=0;i<m.face.size();i++) for (int i=0;i<m.face.size();i++)
{ {
@ -437,6 +559,9 @@ public:
case LInfStretch: case LInfStretch:
q = LInfStretchEnergy( &m.face[i],area_scale ); q = LInfStretchEnergy( &m.face[i],area_scale );
break; break;
case ARAPDist:
q = ARAPEnergy(&m.face[i]);
break;
} }
m.face[i].Q() = q; // note: for L2Stretch, we are puttning E^2 on Q m.face[i].Q() = q; // note: for L2Stretch, we are puttning E^2 on Q
@ -462,6 +587,12 @@ public:
} }
}; };
//template <class MeshType, false>
//static TexCoordType Distortion::UVCoord<false>(const FaceType *f, int i)
//{
// return f->cV(0)->T().P();
//}
}} // namespace end }} // namespace end
#endif #endif

12
vcg/complex/algorithms/parametrization/tangent_field_operators.h
View File

@ -1506,12 +1506,12 @@ public:
{ {
for (size_t i=0;i<mesh.face.size();i++) for (size_t i=0;i<mesh.face.size();i++)
{ {
vcg::Point2<ScalarType> UV0=mesh.face[i].WT(0).P(); vcg::Point2<ScalarType> UV0 = vcg::Point2<ScalarType>::Construct(mesh.face[i].WT(0).P());
vcg::Point2<ScalarType> UV1=mesh.face[i].WT(1).P(); vcg::Point2<ScalarType> UV1 = vcg::Point2<ScalarType>::Construct(mesh.face[i].WT(1).P());
vcg::Point2<ScalarType> UV2=mesh.face[i].WT(2).P(); vcg::Point2<ScalarType> UV2 = vcg::Point2<ScalarType>::Construct(mesh.face[i].WT(2).P());
GradientToCross(mesh.face[i],UV0,UV1,UV2, CoordType uDir = CoordType::Construct(mesh.face[i].PD1());
CoordType::Construct(mesh.face[i].PD1()), CoordType vDir = CoordType::Construct(mesh.face[i].PD2());
CoordType::Construct(mesh.face[i].PD2()) ); GradientToCross(mesh.face[i],UV0,UV1,UV2, uDir, vDir);
} }
OrientDirectionFaceCoherently(mesh); OrientDirectionFaceCoherently(mesh);
} }