MishMesh

A mishmash of useful mesh functions.

Dependencies

• OpenMESH 8.1

Optional Dependencies

• doxygen: When doxygen is found, a doxygen target is created to generate API documentation.
• OpenMP: When OpenMP is available, some algorithms are parallelized.
• Eigen3: Needed for computing laplace matrices.

Build

Set CMake variables:

• OPENMESH_LIBRARY_DIR: The root folder of an OpenMesh installation.
• Eigen3_DIR: The CMake directory of a installed libeigen, e.g. <EIGEN_PREFIX>/share/eigen3/cmake.

---

Functions

Data Types

• DoublePrecisionTraits allow for meshes using double instead of float
• TriMesh and PolyMesh types allow for consistent mesh types across different projects linking against each other.

Searching

• An implementation of Dijkstra's algorithm (shortest edge path search), that allows to use custom distance functions
• Breadth first search for elements
  • Get faces reachable from a source face
  • Get vertices reachable from a source vertex
  • Get the sets of vertices of the connected components in a mesh.

Minimum Spanning Trees

• Calculate a Minimum Spanning Tree of the Dijkstra paths between a set of vertices
• Calculate one Dijkstra Minimum Spanning Tree per connected connected component
• Calculate all shortest distances for a single source vertex

Splitting

• Build a submesh from a set of faces of a mesh
• Split mesh into its connected components

Refinement

• Create a global refinement using 1-to-4 splits

Sampling

• Uniform sampling inside triangles
• Uniform sampling inside circles
• Uniform sampling inside annuli (rings)
• Poisson disk sampling inside triangles and circles using the algorithm of Bridson (``Bridson, R. (2007). Fast Poisson disk sampling in arbitrary dimensions.
  • In ACM SIGGRAPH 2007 Sketches on - SIGGRAPH ’07, (San Diego, California: ACM Press), pp. 22-es.``) [URL]
• Fibonnaci sphere sampling

Visualization

• Create an "edge mesh", that highlights a set of edges of a mesh
• Create a "vertex mesh", that highlights a set of vertices of a mesh
• Colorize a mesh using a given vertex double property
• Construct a grid
• Construct a grid around an isosurface of a given signed distance function

Simplification & Smoothing

• A simple wrapper around the OpenMesh smoothing function
• Collapse short edges to improve mesh quality

Utilities

• Get an array of the vertex handles of a face
• Compute the triangle area of a face or a set of points or vertex handles
• Get the halfedge opposite to a vertex in a given face
• Compute the euler characteristic of the mesh
• Embed a 3D triangle in the 2D plane

Macros

• Add macros for often used iterator loops

Example:

MishMesh::TriMesh::FaceHandle fh = mesh.face_handle(0);
FOR_CFV(v_it, fh) {
    std::cout << "Vertex Index: " << v_it->idx() << std::endl;
}

Bounding Box

• A templated bounding box implementation with functions for testing if points are inside the box and for clipping points at the bounding box

Mesh Laplace

• Compute a mesh laplacian with support for normalization and vertex area weighting

Geodesics

• Compute geodesic distances using the algorithm of Novotni and Klein (Novotni, M., & Klein, R. (2002). Computing geodesic distances on triangular meshes. In In Proc. of WSCG’2002) [URL].
• Compute geodesic distances using the heat method (Crane, K., Weischedel, C., and Wardetzky, M. (2013). Geodesics in Heat. ACM Trans. Graph. 32, 1–11) [URL].

Cone Singularities

• Compute cone singularities on the mesh using the algorithm of Ben-Chen et. al (Ben-Chen, M., Gotsman, C., & Bunin, G. (2008). Conformal Flattening by Curvature Prescription and Metric Scaling. Computer Graphics Forum, 27(2), 449–458) [URL].