6533b855fe1ef96bd12b0014
RESEARCH PRODUCT
Explicit Bézier control net of a PDE surface
Ana ArnalJuan Monterdesubject
Bézier surfaceSurface GenerationPartial differential equationPDE surfaceScalar (mathematics)Mathematical analysis020207 software engineeringBézier curve010103 numerical & computational mathematics02 engineering and technologyBiharmonic Bézier surfaceBiharmonic surface01 natural sciencesComputational MathematicsPDE surfacePartial Differential EquationComputational Theory and MathematicsElliptic partial differential equationExplicit solutionModeling and Simulation0202 electrical engineering electronic engineering information engineering0101 mathematicsLinear combinationTensor product Bézier surfaceMathematicsdescription
The PDE under study here is a general fourth-order linear elliptic Partial Differential Equation. Having prescribed the boundary control points, we provide the explicit expression of the whole control net of the associated PDE Bézier surface. In other words, we obtain the explicit expressions of the interior control points as linear combinations of free boundary control points. The set of scalar coefficients of these combinations works like a mould for PDE surfaces. Thus, once this mould has been computed for a given degree, real-time manipulation of the resulting surfaces becomes possible by modifying the prescribed information. The work was partially supported by Spanish Ministry of Economy and Competitiveness DGICYT grant MTM2015-64013.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-02-01 | Computers & Mathematics with Applications |