In design applications, an important problem is to construct surface patches, which fill specific holes, while assembling complex models. Given a set of (parameterized) (semi)-algebraic curves, the problem consists in finding an (algebraic) surface, which passes through these curves and which satisfies other constraints, e.g., minimal curvature. The boundary of a patch of the surface is defined by N of these curves. Auxiliary interpolation curves inside the domain defined by these boundary curves are also given. Tools developed from techniques based on multi-sided toric parameterization will be studied as well as the use of specific families of surfaces such as canal surfaces of low degree. Another approach is to investigate the use of approximate implicitization constrained by interpolation conditions. Applications of these methods to CAGD problems will be developed in interaction with the industrial partner Missler.

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