Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
A subdivision algorithm for generating rational curves
Journal of Graphics Tools
ACM Transactions on Graphics (TOG)
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
Modeling smooth shape using subdivision on differential coordinates
Computer-Aided Design
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This paper explores a new family of 2D interpolating subdivision schemes that calculate subdivision points from tangent specifications. In this approach each level of subdivision drives the curve toward its specified tangents. The paper describes the underlying algorithmic formulation, and outlines a number of variations, which differ in how subdivision points are computed from tangents or in how tangents are derived. The different characteristics of these variations are shown to provide an interesting range of shapes, giving a high degree of artistic control. Each variation is shown to guarantee C1 continuity except for special identifiable cases, and some of these variations can produce circles. A number of examples are explored that demonstrate the power of the approach as a modeling tool for constructing complex curves, and a comparison is made with curves produced by the Kobbelt subdivision scheme.