An algebraic approach to curves and surfaces on the sphere and on other quadrics
Selected papers of the international symposium on Free-form curves and free-form surfaces
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multiresolution analysis for surfaces of arbitrary topological type
ACM Transactions on Graphics (TOG)
Subdivision surfaces in character animation
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Wavelets for computer graphics: theory and applications
Wavelets for computer graphics: theory and applications
Multiresolution signal processing for meshes
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Displaced subdivision surfaces
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Hybrid meshes: multiresolution using regular and irregular refinement
Proceedings of the eighteenth annual symposium on Computational geometry
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Stationary Subdivision
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Computational Line Geometry
Computing Distances between Surfaces Using Line Geometry
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
A Corner-Cutting Scheme for Hexagonal Subdivision Surfaces
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Stationary subdivision and multiresolution surface representations
Stationary subdivision and multiresolution surface representations
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This paper proposes a new subdivision scheme based on line geometry. We name the scheme ‘line subdivision'. Line subdivision scheme acts on the line space, and generates two-dimensional manifolds contained in the Klein quadric. The two-dimensional manifolds are the Klein images of line congruences in P3. So, this new subdivision scheme generates line congruences at the limit. Here, we define the line subdivision surface as an envelope surface which is made by the line congruence. Then, this paper derives basic properties of the surface. Moreover, we show that line subdivision contains ordinary subdivision and dual subdivision.