Controlled simplification of genus for polygonal models
VIS '97 Proceedings of the 8th conference on Visualization '97
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Seamster: inconspicuous low-distortion texture seam layout
Proceedings of the conference on Visualization '02
GRIN'01 No description on Graphics interface 2001
Removing excess topology from isosurfaces
ACM Transactions on Graphics (TOG)
Loops in Reeb Graphs of 2-Manifolds
Discrete & Computational Geometry
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Tightening non-simple paths and cycles on surfaces
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Topology Repair of Solid Models Using Skeletons
IEEE Transactions on Visualization and Computer Graphics
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
On Computing Handle and Tunnel Loops
CW '07 Proceedings of the 2007 International Conference on Cyberworlds
Reeb graphs for shape analysis and applications
Theoretical Computer Science
Computing geometry-aware handle and tunnel loops in 3D models
ACM SIGGRAPH 2008 papers
Efficient algorithms for computing Reeb graphs
Computational Geometry: Theory and Applications
Minimum cuts and shortest homologous cycles
Proceedings of the twenty-fifth annual symposium on Computational geometry
Loop surgery for volumetric meshes: Reeb graphs reduced to contour trees
IEEE Transactions on Visualization and Computer Graphics
A randomized O(m log m) time algorithm for computing Reeb graphs of arbitrary simplicial complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Minimum cuts and shortest non-separating cycles via homology covers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A deterministic o(m log m) time algorithm for the reeb graph
Proceedings of the twenty-eighth annual symposium on Computational geometry
Finding Cycles with Topological Properties in Embedded Graphs
SIAM Journal on Discrete Mathematics
Annotating simplices with a homology basis and its applications
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Delaunay Mesh Generation
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A special family of non-trivial loops on a surface called handle and tunnel loops associates closely to geometric features of "handles" and "tunnels" respectively in a 3D model. The identification of these handle and tunnel loops can benefit a broad range of applications from topology simplification/repair, and surface parameterization, to feature and shape recognition. Many of the existing efficient algorithms for computing non-trivial loops cannot be used to compute these special type of loops. The two algorithms known for computing handle and tunnel loops provably have a serious drawback that they both require a tessellation of the interior and exterior spaces bounded by the surface. Computing such a tessellation of three dimensional space around the surface is a non-trivial task and can be quite expensive. Furthermore, such a tessellation may need to refine the surface mesh, thus causing the undesirable side-effect of outputting the loops on an altered surface mesh. In this paper, we present an efficient algorithm to compute a basis for handle and tunnel loops without requiring any 3D tessellation. This saves time considerably for large meshes making the algorithm scalable while computing the loops on the original input mesh and not on some refined version of it. We use the concept of the Reeb graph which together with several key theoretical insights on linking number provide an initial set of loops that provably constitute a handle and a tunnel basis. We further develop a novel strategy to tighten these handle and tunnel basis loops to make them geometrically relevant. We demonstrate the efficiency and effectiveness of our algorithm as well as show its robustness against noise, and other anomalies in the input.