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Non-Interpolatory Hermite subdivision schemes (2003)
| Content Provider | CiteSeerX |
|---|---|
| Author | Han, Bin Yu, Thomas P. -Y. Xue, Yonggang |
| Abstract | Bivariate interpolatory Hermite subdivision schemes are recently applied to build free-form subdivision surfaces. It is well-known to geometric modelling practitioners that interpolatory schemes typically lead to “unfair” surfaces – surfaces with unwanted wiggles or undulations – and non-interpolatory (a.k.a. approximating in the CAGD community) schemes are much preferred in geometric modelling applications. In this article, we introduce, analyze and construct non-interpolatory Hermite subdivision schemes, a class of vector subdivision schemes which can be applied to iteratively refine Hermite data in a not necessarily interpolatory fashion. We study also symmetry properties of such subdivision schemes which are crucial for application in free-form subdivision surfaces. A key step in our mathematical analysis of Hermite type subdivision schemes is that we make use of the strong convergence theory of refinement equation to convert a prescribed geometric condition on the subdivision scheme – namely, the subdivision scheme is of Hermite type – to an algebraic condition on the subdivision mask. The latter algebraic condition can then be used in a computational framework to construct specific schemes. |
| File Format | |
| Volume Number | 74 |
| Journal | MATH. COMP |
| Language | English |
| Publisher Date | 2003-01-01 |
| Access Restriction | Open |
| Subject Keyword | Non-interpolatory Hermite Subdivision Scheme Subdivision Scheme Free-form Subdivision Surface Strong Convergence Theory Hermite Type Refinement Equation Latter Algebraic Condition Cagd Community Unfair Surface Surface Subdivision Mask Specific Scheme Unwanted Wiggle Geometric Modelling Application Computational Framework Algebraic Condition Prescribed Geometric Condition Mathematical Analysis Interpolatory Fashion Vector Subdivision Scheme Key Step Hermite Type Subdivision Scheme Hermite Data Construct Non-interpolatory Hermite Subdivision Scheme Symmetry Property Bivariate Interpolatory Hermite Subdivision Scheme |
| Content Type | Text |
| Resource Type | Article |
