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
A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
Journal of the ACM (JACM)
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
An interpolating 4-point C 2 ternary stationary subdivision scheme
Computer Aided Geometric Design
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
Deducing interpolating subdivision schemes from approximating subdivision schemes
ACM SIGGRAPH Asia 2008 papers
Exact evaluation of limits and tangents for non-polynomial subdivision schemes
Computer Aided Geometric Design
ACM Transactions on Graphics (TOG)
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
Non-uniform non-tensor product local interpolatory subdivision surfaces
Computer Aided Geometric Design
| Hi-index | 0.00 |
A method to construct arbitrary order continuous curves, which pass through a given set of data points, is introduced. The method can derive a new family of symmetric interpolating splines with various nice properties, such as partition of unity, interpolation property, local support and second order precision etc. Applying these new splines to construct curves and surfaces, one can adjust the shape of the constructed curve and surface locally by moving some interpolating points or by inserting new interpolating points. Constructing closed smooth curves and surfaces and smooth joining curves and surfaces also become very simple, in particular, for constructing C^r(r=1) continuous closed surfaces by using the repeating technique. These operations mentioned do not require one to solve a system of equations. The resulting curves or surfaces are directly expressed by the basis spline functions. Furthermore, the method can also directly produce control points of the interpolating piecewise Bezier curves or tensor product Bezier surfaces by using matrix formulas. Some examples are given to support the conclusions.