Fitting of Analytic Surfaces to Noisy Point Clouds (2013)
Fitting -continuous or superior surfaces to a set of points sampled on a 2-manifold is central to reverse engi- neering, computer aided geometric modeling, entertaining, modeling of art heritage, etc -- This article addresses the fit- ting of analytic (ellipsoid, cones, cylinders) surfaces in general position in -- Currently, the state of the art presents limitations in 1) automatically finding an initial guess for the analytic surface F sought, and 2) economically estimat- ing the geometric distance between a point of and the analytic surface SF -- These issues are central in estimating an analytic surface which minimizes its accumulated distances to the point set -- In response to this situation, this article presents and tests novel user-independent strategies for addressing aspects 1) and 2) above, for cylinders, cones and ellipsoids -- A conjecture for the calculation of the distance point-ellipsoid is also proposed -- Our strategies produce good initial guesses for F and fast fitting error estimation for F, leading to an agile and robust optimization algorithm -- Ongoing work addresses the fitting of free-form parametric surfaces to S