A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Rapid evaluation of Catmull-Clark subdivision surfaces
Proceedings of the seventh international conference on 3D Web technology
An interpolating 4-point C 2 ternary stationary subdivision scheme
Computer Aided Geometric Design
Exact Evaluation of Non-Polynomial Subdivision Schemes at Rational Parameter Values
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
Interpolatory ternary subdivision surfaces
Computer Aided Geometric Design
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
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This paper presents a new method for exact evaluation of a limit surface generated by stationary interpolatory subdivision schemes and its associated tangent vectors at arbitrary rational points. The algorithm is designed on the basis of the parametric m-ary expansion and construction of the associated matrix sequence. The evaluation stencil of the control points on the initial mesh is obtained, through computation, by multiplying the finite matrices in a sequence corresponding to the expansion sequence and eigendecomposition of the contractive matrix related to the period of rational numbers. The method proposed in this paper works for other non-polynomial subdivision schemes as well.