A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Non-uniform recursive subdivision surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A multiresolution framework for variational subdivision
ACM Transactions on Graphics (TOG)
Optimal triangulation and quadric-based surface simplification
Computational Geometry: Theory and Applications - Special issue on multi-resolution modelling and 3D geometry compression
Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Polynomial Surfaces Interpolating Arbitrary Triangulations
IEEE Transactions on Visualization and Computer Graphics
A cascadic geometric filtering approach to subdivision
Computer Aided Geometric Design
Normal based subdivision scheme for curve design
Computer Aided Geometric Design
On surface reconstruction: A priority driven approach
Computer-Aided Design
Normal based subdivision scheme for curve design
Computer Aided Geometric Design
Weighted progressive interpolation of Loop subdivision surfaces
Computer-Aided Design
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
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Subdivision surfaces are generated by repeated approximation or interpolation from initial control meshes. In this paper, two new non-linear subdivision schemes, face based subdivision scheme and normal based subdivision scheme, are introduced for surface interpolation of triangular meshes. With a given coarse mesh more and more details will be added to the surface when the triangles have been split and refined. Because every intermediate mesh is a piecewise linear approximation to the final surface, the first type of subdivision scheme computes each new vertex as the solution to a least square fitting problem of selected old vertices and their neighboring triangles. Consequently, sharp features as well as smooth regions are generated automatically. For the second type of subdivision, the displacement for every new vertex is computed as a combination of normals at old vertices. By computing the vertex normals adaptively, the limit surface is G^1 smooth. The fairness of the interpolating surface can be improved further by using the neighboring faces. Because the new vertices by either of these two schemes depend on the local geometry, but not the vertex valences, the interpolating surface inherits the shape of the initial control mesh more fairly and naturally. Several examples are also presented to show the efficiency of the new algorithms.