Generating blend surfaces using partial differential equations
Computer-Aided Design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Multiresolution analysis for surfaces of arbitrary topological type
Multiresolution analysis for surfaces of arbitrary topological type
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Approximating weighted shortest paths on polyhedral surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Efficient computation of geodesic shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Computer Aided Geometric Design
Geodesic Paths on Triangular Meshes
SIBGRAPI '04 Proceedings of the Computer Graphics and Image Processing, XVII Brazilian Symposium
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Calculating Shortest Path on Edge-Based Data Structure of Graph
DMAMH '07 Proceedings of the Second Workshop on Digital Media and its Application in Museum & Heritage
Partial Differential Equations for Function Based Geometry Modelling within Visual Cyberworlds
CW '08 Proceedings of the 2008 International Conference on Cyberworlds
Towards a Definition of Virtual Objects Using Partial Differential Equations
CW '09 Proceedings of the 2009 International Conference on CyberWorlds
Visual immersive haptic mathematics
Virtual Reality - Themed Issue on Virtual Reality in Scientific Application
A PDE method for patchwise approximation of large polygon meshes
The Visual Computer: International Journal of Computer Graphics
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Various Partial Differential Equations (PDEs) have been used in computer graphics for approximating surfaces of geometric shapes by finding solutions to PDEs, subject to suitable boundary conditions. The PDE boundary conditions are defined as 3D curves on surfaces of the shapes. We propose how to automatically derive these curves from the surface of the original polygon mesh. Analytic solutions to the PDEs used throughout this work are fully determined by finding a set of coefficients associated with parametric functions according to the particular set of boundary conditions. When large polygon meshes are used, the PDE coefficients require an order of magnitude smaller space compared to the original polygon data and can be interactively rendered with different levels of detail. It allows for an efficient exchange of the PDE shapes in 3D Cyberworlds and their web visualization. In this paper we analyze and formulate the requirements for extracting suitable boundary conditions, describe the algorithm for the automatic deriving of the boundary curves, and present its implementation as a part of the function-based extension of VRML and X3D.