On determining the genus of a graph in O(v O(g)) steps(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
A hierarchical boundary model for solid object representation
ACM Transactions on Graphics (TOG)
Designing solid objects using interactive sketch interpretation
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
A model for n-dimensional boundary topology
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
A shortest path approach to wireframe to solid model conversion
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Geometric modeling of solid objects by using a face adjacency graph representation
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Identifying Faces in a 2D Line Drawing Representing a Manifold Object
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph based topological analysis of tessellated surfaces
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Interpreting a 3D object from a rough 2D line drawing
VIS '90 Proceedings of the 1st conference on Visualization '90
Evolutionary Search for Faces from Line Drawings
IEEE Transactions on Pattern Analysis and Machine Intelligence
nD object representation and detection from Single 2D line drawing
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
nD polyhedral scene reconstruction from single 2D line drawing by local propagation
ADG'04 Proceedings of the 5th international conference on Automated Deduction in Geometry
A general and efficient method for finding cycles in 3D curve networks
ACM Transactions on Graphics (TOG)
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The design of complex geometric models has been and will continue to be one of the limiting factors in computer graphics. A careful enumeration of the properties of topologically correct models, so that they may be automatically enforced, can greatly speed this process. An example of the problems inherent in these methods is the “wire frame” problem, the automatic generation of a volume model from an edge-vertex graph. The solution to this problem has many useful applications in geometric modelling and scene recognition. This paper shows that the “wire frame” problem is equivalent to finding the embedding of a graph on a closed orientable surface. Such an embedding satisfies all the topological properties of physical volumes. Unfortunately graphical embeddings are not necessarily unique. But when we restrict the embedding surface so that it is equivalent to a sphere, and require that the input graph be three-connected, the resulting object is unique. Given these restrictions there exists a linear time algorithm to automatically convert the “wire frame” to the winged edge representation, a very powerful data structure. Applications of this algorithm are discussed and several examples shown.