#include <ConformalSurfaceFlattening.h>
Public Member Functions | |
| ConformalSurfaceFlattening () | |
| Default constructor. | |
| ConformalSurfaceFlattening (const ConformalSurfaceFlattening &) | |
| Copy constructor. | |
| ConformalSurfaceFlattening & | operator= (const ConformalSurfaceFlattening &) |
| Assignment operator. | |
| virtual | ~ConformalSurfaceFlattening () |
| Destructor. | |
 Public Member Functions inherited from mirtk::SphericalSurfaceMapper | |
| int | NumberOfComponents () const |
| Dimension of map codomain. | |
| virtual | ~SphericalSurfaceMapper () |
| 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 void | ComputeMap () |
| Construct and solve symmetric system of linear equations. | |
| virtual void | Finalize () |
| Finalize filter execution. | |
| virtual void | Initialize () |
| Initialize filter after input and parameters are set. | |
| Protected Member Functions inherited from mirtk::SphericalSurfaceMapper | |
| SphericalSurfaceMapper & | operator= (const SphericalSurfaceMapper &) |
| Assignment operator. | |
| SphericalSurfaceMapper () | |
| Default constructor. | |
| SphericalSurfaceMapper (const SphericalSurfaceMapper &) | |
| Copy constructor. | |
| 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
Computes discrete conformal map of (closed) surface to the complex plane
The conformal map is the solution of a sparse system of linear equations, where the edge weights are identical to those used by Pinkall and Polthier (1993) and later Eck et al. (1995). These cotangent weights are well known in the finite element method (FEM) literature and correspond to a discretization of the Laplace operator. The main difference of the method by Angenent et al. (1999-2000) and Haker et al. (2000) compared to the discrete conformal mapping of Eck et al. (1995) and Desbrun et al. (2002) are the boundary constraints. While all these methods minimize the discrete Dirichlet energy, the latter methods fix the boundary values of a non-closed surface, whereas the method by Angenent and Haker is designed for closed genus-0 surface meshes with a subsequent inverse stereographic projection to the sphere. The intermediate parametric domain is a triangular subdomain of the complex plane.
- Note
- This implementation is based on the corresponding ITK implementation originally contributed to by Gao et al. https://hdl.handle.net/1926/225 which was later extended and integrated into ITK version 4 as https://itk.org/Doxygen/html/classitk_1_1ConformalFlatteningMeshFilter.html.
- 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.
- Angenent et al. (1999). Conformal geometry and brain flattening. MICCAI, 271–278.
- Angenent et al. (n.d.). On the Laplace-Beltrami Operator and Brain Surface Flattening.
- Angenent et al. (2000). On Area Preserving Mappings of Minimal Distortion. In System Theory: Modeling, Analysis and Control, pp. 275–286.
- Haker et al. (2000). Conformal surface parameterization for texture mapping. IEEE Trans. Vis. Comput. Graphics, 6(2), 181–189.
- Desbrun, Meyer, and Alliez (2002). Intrinsic parameterizations of surface meshes. Computer Graphics Forum, 21(3), 209–218.
Definition at line 63 of file ConformalSurfaceFlattening.h.
The documentation for this class was generated from the following file: