Topological graph theory
Introduction to Solid Modeling
Introduction to Solid Modeling
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
On the representation and manipulation of rigid solids
On the representation and manipulation of rigid solids
Topological design of sculptured surfaces
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Maximum genus and connectivity
Discrete Mathematics
Consistent solid and boundary representations from arbitrary polygonal data
Proceedings of the 1997 symposium on Interactive 3D graphics
Theoretical Computer Science - Special issue on computing and combinatorics
VIS '97 Proceedings of the 8th conference on Visualization '97
A non-photorealistic lighting model for automatic technical illustration
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Handle and Hole Improvement by Using New Corner Cutting Subdivision Scheme with Tension
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Winged edge polyhedron representation.
Winged edge polyhedron representation.
Set operations on polyhedra using decomposition methods
Set operations on polyhedra using decomposition methods
Computer aided sculpting: a multidisciplinary course in shape modeling
ACM SIGGRAPH 2006 Educators program
Connected & manifold Sierpinsky polyhedra
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Interactive face-replacements for modeling detailed shapes
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
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In this paper, we identify a minimal and complete set of fundamental operators, which is necessary and sufficient for performing all homeomorphic and topological operations on 2- manifold mesh structures. Efficient algorithms are developed for the implementation of these operators. We also developed a set of powerful, user-friendly, and effective operators at the level of user-interface. Using these operators, we have developed a prototype system for robust, interactive, and user-friendly modeling of orientable 2-manifold meshes. Users of our system can perform a large set of homeomorphic and topological changes with these user-interface level operators. Our system is topologically robust in the sense that users will never create invalid 2-manifold mesh structure with these operators. In our system, the homeomorphic and topological surgery operations can be applied alternatively on 2-manifold meshes. With our system, users can blend surfaces, construct rinds, and open holes on these rind shapes. With our system, the shapes that look like solid, non-manifold, or 2-manifold with boundary can be manipulated. The system also provides automatic texture mapping during topology changes.