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Multivariate spline algorithms for cagd
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Boehm, W. |
| Copyright Year | 1985 |
| Description | Two special polyhedra present themselves for the definition of B-splines: a simplex S and a box or parallelepiped B, where the edges of S project into an irregular grid, while the edges of B project into the edges of a regular grid. More general splines may be found by forming linear combinations of these B-splines, where the three-dimensional coefficients are called the spline control points. Univariate splines are simplex splines, where s = 1, whereas splines over a regular triangular grid are box splines, where s = 2. Two simple facts render the development of the construction of B-splines: (1) any face of a simplex or a box is again a simplex or box but of lower dimension; and (2) any simplex or box can be easily subdivided into smaller simplices or boxes. The first fact gives a geometric approach to Mansfield-like recursion formulas that express a B-spline in B-splines of lower order, where the coefficients depend on x. By repeated recursion, the B-spline will be expressed as B-splines of order 1; i.e., piecewise constants. In the case of a simplex spline, the second fact gives a so-called insertion algorithm that constructs the new control points if an additional knot is inserted. |
| File Size | 5442403 |
| Page Count | 5 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19850020254 |
| Archival Resource Key | ark:/13960/t8hf2qg1b |
| Language | English |
| Publisher Date | 1985-06-01 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Geometry Algorithms Coordinates Spline Functions Surfaces Shapes Computer Aided Design Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Article |
