In this paper, the continuous adjoint methodology to compute shape sensitivities in free-surface hydrodynamic design problems (RANS governing systems) has been developed. This technique will allow the specific design of the free-surface interface (typically air/water), which has a great potential in problems where the target is to reduce the wave energy, e.g. ship hull design. A detailed descri...

We present a robust algorithm to construct an “inner” simplicial hull Σ as a single step of subdivision of an input polyhedron P in three dimensional space. Similar to traditional subdivision schemes P becomes the ‘control net’ for free-form modeling while an inner surface triangulation T of Σ is a second level mesh. Free-Form C1 cubic A-patches and C2 quintic A-patches can then be constructed ...

A linear-time algorithm that computes the envelope of the offset of a monotone chain is presented. The scallop hull, an extended notion of the convex hull, of the monotone chain is first computed by using an approach similar to that of the convexhull construction algorithm. The offset of the scallop hull, which yields the desired envelope, can then be computed in linear time from the scallop hu...

In this paper, we present lower bounds on the rank of the split closure, the multi-branch closure and the lattice-free closure for packing sets as a function of the integrality gap. We also provide a similar lower bound on the split rank of covering polyhedra. These results indicate that whenever the integrality gap is high, these classes of cutting planes must necessarily be applied for many r...

If X is a vector space and E is a subset of X, the convex hull of E is defined to be the intersection of all convex sets containing E, and is denoted by co(E). One checks that the convex hull of E is equal to the set of all finite convex combinations of elements of E. If X is a topological vector space, the closed convex hull of E is the intersection of all closed convex sets containing E, and ...

We apply a generalization of Crapo’s β invariant to finite subsets of <n . For a finite subset C of the plane, we prove β(C) = |int(C)|, where |int(C)| is the number of interior points of C , i.e., the number of points of C which are not on the boundary of the convex hull of C . This gives the following formula: ∑ K free(−1) |−1|K | = |int(C)|.

A test coupon coated with light calcareous tubeworm fouling was scanned, scaled and reproduced for wind-tunnel testing to determine the equivalent sand grain roughness ks. It was found that this surface had a ks = 0.325 mm, substantially less than the previously reported values for light calcareous fouling. This result was used to predict the drag on a fouled full scale ship. To achieve this, a...

A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and the problem of its determination in the plane is equivalent to find the shortest curve among all Jordan curves lying in the difference set of B and A and en...

Of late, researchers appear to be intrigued with the question; Given a set of points, what is the region occupied by them? The answer appears to be neither straight forward nor unique. Convex hull, which gives a convex enclosure of the given set, concave hull, which generates nonconvex polygons and other variants such as α-hull, poly hull, r-shape and s-shape etc. have been proposed. In this pa...

We describe a new method for estimating the area of home ranges and constructing utilization distributions (UDs) from spatial data. We compare our method with bivariate kernel and a-hull methods, using both randomly distributed and highly aggregated data to test the accuracy of area estimates and UD isopleth construction. The data variously contain holes, corners, and corridors linking high use...