Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogonal group representations on the other hand. In this way, several known results for spheres in Euclidean spaces, involving cubature formulas for polynomial functions and spherical designs, are shown to generalize to la...

Key concepts and geometrical constraints are discussed that allow the construction of a usable bridge that is topological equivalent to a Möbius band. A multi-year search in publications and on the internet for real-world bridges that meet these requirements has not identified a single clean construction that warrants the designation “Möbius bridge,” but a few promising designs can be found. Se...

A new and complete methodology of monofocal intraocular lens (IOL) design is presented aiming at isoplanatism, i.e. IOLs that provide the eye with optimized optical quality over a wide field of view (typically in a range of ten degrees). The methodology uses a merit function considering dimensional and biomechanical constraints, and a geometrical optical quality metric that is evaluated simulta...

Contaminant transport analysis was performed for four selected solid waste landfill designs using the computer code POLLUTE. The diffusion coefficients were determined for the natural soils (aquitard) and compacted soils from the Urumia landfill site, using the diffusion tests. These coefficients along with the geometrical, physical, and chemical parameters of the natural soil and engineered la...

We build an original synthetic dataset of 2D mechanical designs alongside their and geometric constraints, GMCAD. Such a allows training Deep Learning (DL) models for Design Additive Manufacturing (DfAM) to incorporate control Computer-Aided-Design (CAD) features with performance. Geometric AM constraints are often complex describe, depending on applications, processes, materials. They lack exp...

A literature review of sheet metal forming errors as well as geometrical dimensions and tolerances (GD&T) shows that the theoretical means for the allocation of process tolerances with respect to GD&T are insufficient. In order to judge the influence of geometrical process errors (e.g., angular errors of bends), two typical sheet metal designs with parallelism and a position tolerance are studi...

The role of computers and of computer-aided design tools for the creation of geometrical shapes that will be judged primarily by aesthetic considerations is reviewed. Examples are the procedural generation of abstract geometrical sculpture or the shape optimization of constrained curves and surfaces with some global “cost” functional. Different possibilities for such “beauty functionals” are di...