Phase Unwrapping using Chebyshev Polynomials

Phase unwrapping is an intermediate step for interferogram analysis. The phase associated with an interferogram can be estimated using a curve mesh of functions. Each of these functions can be approximated by a linear combination of basis functions. Chebyshev polynomials in addition to being a family of orthogonal polynomials can be defined recursively. In this work a method for phase unwrapping using Chebyshev polynomials is proposed. Results show good performance when applied to synthetic images without noise and also to synthetic images with noise

Geometric continuity and compatibility conditions for 4-patch surfaces

When considering regularity of surfaces, it is its geometry that is of interest. Thus, the concept of geometric regularity or geometric continuity of a specific order is a relevant concept. In this paper we discuss necessary and sufficient conditions for a 4-patch surface to be geometrically continuous of order one and two or, in other words, being tangent plane continuous and curvature continuous respectively. The focus is on the regularity at the point where the four patches meet and the compatibility conditions that must appear in this case. In this article the compatibility conditions are proved to be independent of the patch parametrization, i.e., the compatibility conditions are universal. In the end of the paper these results are applied to a specific parametrization such as Bezier representation in order to generalize a 4-patch surface result by Sarraga.Comment: 25 pages, 6 figure

Fairing wireframes in industrial surface design

Wireframe is a modeling tool widely used in industrial geometric design. The term wireframe refers to two sets of curves, with the property that each curve from one set intersects with each curve from the other set. Akin to the mu-, v-isocurves in a tensor-product surface, the two sets of curves in a wireframe span an underlying surface. In many industrial design activities, wireframes are usually set up and adjusted by the designers before the whole surfaces are reconstructed. For adjustment, the fairness of wireframe has a direct influence on the quality of the underlying surface. Wireframe fairing is significantly different from fairing individual curves in that intersections should be preserved and kept in the same order. In this paper, we first present a technique for wireframe fairing by fixing the parameters during fairing. The limitation of fixed parameters is further released by an iterative gradient descent optimization method with step-size control. Experimental results show that our solution is efficient, and produces reasonably fairing results of the wireframes