Name
Abstract | ||
|---|---|---|
In this paper, we study the construction of a B-spline surface satisfying prescribed angle distribution (with respect to a chosen vector) of tangent planes along its boundary curve. This problem arises e.g. in a creation of a parametric geometric model of a Pelton turbine bucket, where specific angle distributions along a splitter and an outlet curve have to be fulfilled in order to control the flow of water into and out of the bucket. We prove that for a given B-spline curve c ( t ) , t 0 , 1 ] , the exact solution exists only in very special cases (for a special form of an angle function f ( t ) ). Further, we formulate an algorithm for finding an approximate solution. We also derive a bound on its approximation error and give a numerical evidence that the approximation order of the proposed algorithm is four. Finally, the method is demonstrated on several examples. We study the construction of a B-spline surface satisfying prescribed angle distribution of tangent planes along its boundary curve.We prove that for a given B-spline curve, the exact solution exists only in very special cases (for a special form of an angle function).We propose an algorithm for finding an approximate solution, derive a bound on its approximation error and study the approximation order of the proposed algorithm. Display Omitted |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.cad.2014.10.002 | Computer-Aided Design |
Keywords | Field | DocType |
nurbs surface | B-spline,Exact solutions in general relativity,Boundary value problem,Mathematical optimization,Flow (psychology),Geometric modeling,Tangent,Parametric statistics,Mathematics,Approximation error | Journal |
Volume | Issue | ISSN |
62 | C | 0010-4485 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kristýna Michálková | 1 | 2 | 1.74 |
| Bohumír Bastl | 2 | 136 | 10.49 |