#include <IntrinsicSurfaceMapper.h>
Inheritance diagram for mirtk::IntrinsicSurfaceMapper:
Collaboration diagram for mirtk::IntrinsicSurfaceMapper:
Public Member Functions | |
| IntrinsicSurfaceMapper (double lambda=.5) | |
| IntrinsicSurfaceMapper (const IntrinsicSurfaceMapper &) | |
| Copy constructor. | |
| IntrinsicSurfaceMapper & | operator= (const IntrinsicSurfaceMapper &) |
| Assignment operator. | |
| virtual | ~IntrinsicSurfaceMapper () |
| Destructor. | |
 Public Member Functions inherited from mirtk::NonSymmetricWeightsSurfaceMapper | |
| virtual void | ComputeMap () |
| Construct and solve (non-symmetric) system of linear equations. | |
| NonSymmetricWeightsSurfaceMapper () | |
| Default constructor. | |
| NonSymmetricWeightsSurfaceMapper (const NonSymmetricWeightsSurfaceMapper &) | |
| Copy constructor. | |
| NonSymmetricWeightsSurfaceMapper & | operator= (const NonSymmetricWeightsSurfaceMapper &) |
| Assignment operator. | |
| virtual | ~NonSymmetricWeightsSurfaceMapper () |
| Destructor. | |
| Public Member Functions inherited from mirtk::LinearFixedBoundarySurfaceMapper | |
| virtual void | Finalize () |
| Assemble output surface map. | |
| int | FixedPointId (int i) const |
| int | FixedPointIndex (int i) const |
| int | FreePointId (int i) const |
| int | FreePointIndex (int i) const |
| double | GetFixedValue (int i, int j=0) const |
| double | GetFreeValue (int i, int j=0) const |
| double | GetValue (int i, int j=0) const |
| virtual void | Initialize () |
| Initialize filter after input and parameters are set. | |
| bool | IsFixedPoint (int i) const |
| Whether the map value of the specified surface point is fixed. | |
| bool | IsFreePoint (int i) const |
| Whether the map value of the specified surface point is free. | |
| int | NumberOfFixedPoints () const |
| Number of surface points with fixed map value. | |
| int | NumberOfFreePoints () const |
| Number of surface points with free map value. | |
| virtual | ~LinearFixedBoundarySurfaceMapper () |
| Destructor. | |
| Public Member Functions inherited from mirtk::FixedBoundarySurfaceMapper | |
| virtual | ~FixedBoundarySurfaceMapper () |
| Destructor. | |
| Public Member Functions inherited from mirtk::SurfaceMapper | |
| void | Run () |
| Compute surface map. | |
| virtual | ~SurfaceMapper () |
| Destructor. | |
| Public Member Functions inherited from mirtk::Object | |
| virtual const char * | NameOfClass () const =0 |
| Get name of class, which this object is an instance of. | |
| virtual ParameterList | Parameter () const |
| Get parameter name/value pairs. | |
| bool | Parameter (const ParameterList &) |
| Set parameters from name/value pairs. | |
| virtual bool | Set (const char *name, const char *value) |
| virtual | ~Object () |
| Destructor. | |
Protected Member Functions | |
| virtual double | Weight (int i, int j) const |
| Protected Member Functions inherited from mirtk::NonSymmetricWeightsSurfaceMapper | |
| virtual void | Weights (int i, const int *j, double *w, int d) const |
| Protected Member Functions inherited from mirtk::LinearFixedBoundarySurfaceMapper | |
| LinearFixedBoundarySurfaceMapper () | |
| Default constructor. | |
| LinearFixedBoundarySurfaceMapper (const LinearFixedBoundarySurfaceMapper &) | |
| Copy constructor. | |
| LinearFixedBoundarySurfaceMapper & | operator= (const LinearFixedBoundarySurfaceMapper &) |
| Assignment operator. | |
| void | SetFreeValue (int i, double v) |
| void | SetFreeValue (int i, int j, double v) |
| void | SetValue (int i, double v) |
| void | SetValue (int i, int j, double v) |
| Protected Member Functions inherited from mirtk::FixedBoundarySurfaceMapper | |
| FixedBoundarySurfaceMapper () | |
| Default constructor. | |
| FixedBoundarySurfaceMapper (const FixedBoundarySurfaceMapper &) | |
| Copy constructor. | |
| int | NumberOfComponents () const |
| Number of boundary/surface map components. | |
| FixedBoundarySurfaceMapper & | operator= (const FixedBoundarySurfaceMapper &) |
| Assignment operator. | |
| Protected Member Functions inherited from mirtk::SurfaceMapper | |
| int | GetEdgeNeighborPoints (int i, int j, int &k, int &l) const |
| void | GetPoint (int ptId, double p[3]) const |
| int | NumberOfInteriorPoints () const |
| Number of surface points minus the number of boundary points. | |
| int | NumberOfPoints () const |
| Number of surface points. | |
| SurfaceMapper & | operator= (const SurfaceMapper &) |
| Assignment operator. | |
| class Point | Point (int ptId) const |
| SurfaceMapper () | |
| Default constructor. | |
| SurfaceMapper (const SurfaceMapper &) | |
| Copy constructor. | |
| Protected Member Functions inherited from mirtk::Object | |
| template<typename... Args> | |
| void | Throw (ErrorType err, const char *func, Args... args) const |
Additional Inherited Members | |
| Static Public Member Functions inherited from mirtk::Object | |
| static const char * | NameOfType () |
| Get name of this class type. | |
| Static Protected Member Functions inherited from mirtk::Object | |
| template<typename... Args> | |
| static void | ThrowStatic (ErrorType err, const char *cls, const char *func, Args... args) |
Detailed Description
Surface maps based on a class of intrinsic surface parameterizations
Surface mapping methods based on this class use a linear combination of edge weights which result from the discrete formulations of Dirichlet (angle preserving) and Chi (Euler characteristic, area preserving) energy functionals (Desbrun et al., 2002) obtaind using the finite element method (FEM). A discrete harmonic map, also referred to as Discrete Conformal Parameterization (DCP), is obtained by minimizing the Dirichlet energy functional. A convex combination map referred to as Discrete Authalic Parameterization (DAP) is obtained by minimizing only the Chi energy. The normalized weights are a generalization of Barycentric coordinates (Meyer, 2002). The discrete Dirichlet energy functional used by this mapper is the piecewise linear finite element approximation of the Laplace equation (Eck et al., 1995; Wardetzky et al., 2007). These cotangent weights were previously used by Pinkall and Polthier (1993) to compute a conformal surface map.
- Wachspress (1975). A Rational Finite Element Basis.
- Pinkall and Polthier (1993). Computing Discrete Minimal Surfaces and Their Conjugates. Experiment. Math., 2(1), 15–36.
- Eck et al. (1995). Multiresolution analysis of arbitrary meshes. SIGGRAPH.
- Desbrun, Meyer, and Alliez (2002). Intrinsic parameterizations of surface meshes. Computer Graphics Forum, 21(3), 209–218.
- Meyer et al. (2002). Generalized Barycentric Coordinates on Irregular Polygons. Journal of Graphics Tools, 7(1), 13–22.
- Wardetzky et al. (2007). Discrete quadratic curvature energies. Computer Aided Geometric Design, 24(8–9), 499–518.
Definition at line 56 of file IntrinsicSurfaceMapper.h.
Constructor & Destructor Documentation
§ IntrinsicSurfaceMapper()
| mirtk::IntrinsicSurfaceMapper::IntrinsicSurfaceMapper | ( | double | lambda = .5 | ) |
Constructor
- Parameters
-
[in] lambda Weight of conformal energy in [0, 1]. The weight of the authalic energy is 1 - lambda.
Member Function Documentation
§ Weight()
|
protectedvirtual |
Weight of directed edge (i, j)
- Parameters
-
[in] i Index of start point. [in] j Index of end point.
- Returns
- Weight of directed edge (i, j).
Reimplemented from mirtk::NonSymmetricWeightsSurfaceMapper.
The documentation for this class was generated from the following file: