B\'ezier curves that are close to elastica

We study the problem of identifying those cubic B\'ezier curves that are close in the L2 norm to planar elastic curves. The problem arises in design situations where the manufacturing process produces elastic curves; these are difficult to work with in a digital environment. We seek a sub-class of special B\'ezier curves as a proxy. We identify an easily computable quantity, which we call the lambda-residual, that accurately predicts a small L2 distance. We then identify geometric criteria on the control polygon that guarantee that a B\'ezier curve has lambda-residual below 0.4, which effectively implies that the curve is within 1 percent of its arc-length to an elastic curve in the L2 norm. Finally we give two projection algorithms that take an input B\'ezier curve and adjust its length and shape, whilst keeping the end-points and end-tangent angles fixed, until it is close to an elastic curve.Comment: 13 pages, 15 figure

Repairing triangle meshes built from scanned point cloud

The Reverse Engineering process consists of a succession of operations that aim at creating a digital representation of a physical model. The reconstructed geometric model is often a triangle mesh built from a point cloud acquired with a scanner. Depending on both the object complexity and the scanning process, some areas of the object outer surface may never be accessible, thus inducing some deficiencies in the point cloud and, as a consequence, some holes in the resulting mesh. This is simply not acceptable in an integrated design process where the geometric models are often shared between the various applications (e.g. design, simulation, manufacturing). In this paper, we propose a complete toolbox to fill in these undesirable holes. The hole contour is first cleaned to remove badly-shaped triangles that are due to the scanner noise. A topological grid is then inserted and deformed to satisfy blending conditions with the surrounding mesh. In our approach, the shape of the inserted mesh results from the minimization of a quadratic function based on a linear mechanical model that is used to approximate the curvature variation between the inner and surrounding meshes. Additional geometric constraints can also be specified to further shape the inserted mesh. The proposed approach is illustrated with some examples coming from our prototype software

Integration between Creativity and Engineering in Industrial Design

The objective of the paper is to illustrate which are the key issues today in the industrial design workflow, paying particular attention to the most creative part of the workflow, highlighting those nodes which still make hard the styling activities and giving a brief survey of the researches aimed at smoothing the transfer of the design intent along the whole design cycle and at providing tools even more adhering at the mentality of creative people. Based on the experience gained working in two different European projects, through the collaboration with industrial designers in the automotive and the household supplies fields, a general industrial design workflow will be depicted, highlighting the main differences between the automotive and non-automotive sectors; the problems still present in the design activity will be also illustrated. The paper includes short surveys, in relation to the aesthetic design, in matter of research activities aimed at - identifying the links between shape characteristics of a product and the transmitted emotions - better supporting, in a digital way, the 2D sketching phase and the automatic interpretation and transfer of the 2D sketches into a 3D surface model - improving the 3D Modeling phase