
Terrain trees are a new incore family of spatial indexes for the representation and analysis of Triangulated Irregular Networks (TINs).
Terrain trees combine a minimal encoding of the connectivity of the underlying triangle mesh with a hierarchical spatial index, implicitly representing the other topological relations among vertices, edges and vertices. Topological relations are extracted locally within each leaf block of the hierarchal index at runtime, based on specific application needs. We have developed a tool based on Terrain trees for terrain analysis, which includes stateoftheart estimators for slope and curvature, and for the extraction of critical points. By working on TINs generated from big LiDAR (Light, Detection and Ranging) data sets, we demonstrate the effectiveness and scalability of the Terrain trees against a stateoftheart compact data structures. The source code and additional information can be found on GitHub. For the experimental comparison, we have developed a tool based on the IA data structure that includes stateoftheart estimators like slope and curvature computation, as well as the extraction of critical points. The source code can be found on GitHub. References:

The ICT  Introduction to Computational Topology is a webbased userguide on
computational topology equipped with interactive examples to facilitate the comprehension of the notions at the of such theory.
Currently the guide presents a description of persistent homology. The source code and additional information can be found on GitHub. Moreover, an interactive guide to Persistent Topology can be found on GitHub. 


The Forman Gradient 2D is a comprehensive library for computing a Forman Gradient on triangle meshes. The library provides all the basic functions for encoding a triangle mesh and a scalar function defined on its vertices (both provided in input) and for computing a Forman gradient on it. Two different methods have been implemented. The first one is based on homotopic expansion and the second one uses an input watershed segmentation to avoid spurious critical simplices. Additional functions are furnished for computing the cells of the discrete Morse complex and for producing output files to be visualized in Paraview. The library is composed of two main parts. The first one provides all the basic functions for managing the triangle mesh (LibMesh). The second part provides the functions for computing the Forman gradient and the Morse cells (LibForman). The source code and additional information can be found on GitHub. References:

The Supertetras is a C++ tool for computing an oversegmentation of a tetrahedral mesh. The tool extends the stateoftheart superpixel algorithm to tetrahedral mesh representations with scalar fields defined over their vertices.
The source code and additional information can be found on GitHub. Reference:


The Superfacets2D is a C++ tool for segmenting the boundary of triangulated 3D shapes into patches. The tools computes superfacet segmentations of meshes based on a kmeans style approach using shortestpath distances over the face graph of the mesh. By using a bounded expansion strategy in the reclassification step, our approach obtains a loglinear complexity, enabling the segmentation of large meshes (with several million triangles) where applying normalized cuts or other such cutbased approaches would be intractable.
The source code and additional information can be found on GitHub. Reference:


The Mangrove Topological Data Structure (Mangrove TDS) Library is a C++ tool for the fast prototyping of topological data structures representing cell and simplicial complexes of any dimension, not necessarily embedded in an Euclidean space.
All types of domains are supported efficiently, including nonmanifolds.
The source code and additional information can be found on Sourceforge. Reference:


The TetraMesh is a C++ library for the topological representation of scalar fields defined on tetrahedral meshes. The underlying tetrahedral mesh is encoded as an indexed data structure with explicit adjacencies and the scalar function is associated with its vertices. The library provides all the functionalities for reading a mesh (in TS or RAW format) and for retrieving the topological relations among its simplices such as VertexEdge relation, EdgeFace relation, FaceTetrahedra relation and so on. The source code and additional information can be found on GitHub. 

The MT Package contains a C++ library that allows you to design
interactive applications which exploit the full power of multiresolution
on geometric objects represented by meshes in any dimension.
There are two basic actions in multiresolution modeling:
The source code and additional information can be found on GitHub. 

The MT Delaunay is a set of programs dealing with (constrained) Delaunay triangulations
of terrain data (triangulation in the plane with elevations associated
with vertices). They can be used to build a triangulation with a set of points,
to simplify an existing triangulation by removing a subset of the points,
and they can also be used to build an MT during this process. The source code and additional information can be found on GitHub. 