Rational-spline approximation with automatic tension adjustment

An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline

Computer program to prepare airfoil characteristic data for use in helicopter performance calculations

A computer program developed to prepare wind tunnel generated airfoil data for input into helicopter performance prediction programs is described. The program provides for numerically cross plotting the data, plotting the data, and tabulating and punching the tabulated result into computer cards for use in the rotorcraft flight simulation model

On a class of polynomial triangular macro-elements

AbstractIn this paper we present a new class of polynomial triangular macro-elements of arbitrary degree which are an extension of the classical Clough-Tocher cubic scheme. Their most important property is that the degree plays the role of a tension parameter, since these macro elements tend to the plane interpolating the vertices data. Graphical examples showing their use in scattered data interpolation are reported

Understanding the need of the compression branch to characterize hyperelastic materials

[EN] Soft biological tissues are frequently modeled as hyperelastic materials. Hyperelastic behavior is typically ensured by the assumption of a stored energy function with a pre-determined shape. This function depends on some material parameters which are obtained through an optimization algorithm in order to fit experimental data from different tests. For example, when obtaining the material parameters of isotropic, incompressible models, only the extension part of a uniaxial test is frequently taken into consideration. In contrast, spline-based models do not require material parameters to exactly fit the experimental data, but need the compression branch of the curve. This is not a disadvantage because as we explain herein, to properly characterize hyperelastic materials, the compression branch of the uniaxial tests (or valid alternative tests) is also needed, in general. Then, unless we know beforehand the tendency of the compression branch, a material model should not be characterized only with tensile tests. For simplicity, here we address isotropic, incompressible materials which use the Valanis-Landel decomposition. However, the concepts are also applicable to compressible isotropic materials and are specially relevant to compressible and incompressible anisotropic materials, because in biomechanics, materials are frequently characterized only by tensile tests.Partial financial support for this work has been given by grants DPI2011-26635 and DPI2015-69801-R from the Direccion General de Proyectos de Investigacion of the Ministerio de Economia y Competitividad of Spain. Erica De Rosa acknowledges the funding for a stay at the UPM, Progetto di internazionalizzazione dei corsi di studio from COINOR-Universita Degli Studi di Napoli Federico II. F.J. Montans also acknowledges the support of the Department of Mechanical and Aerospace Engineering of University of Florida during the sabbatical period in which this paper was finished and that of Ministerio de Educacion, Cultura y Deporte of Spain for the financial support for that stay under grant PRX15/00065Latorre, M.; De Rosa, E.; Montáns, FJ. (2017). Understanding the need of the compression branch to characterize hyperelastic materials. International Journal of Non-Linear Mechanics. 89:14-24. https://doi.org/10.1016/j.ijnonlinmec.2016.11.00514248

Tools for computer graphics applications

Extensive research in computer graphics has produced a collection of basic algorithms and procedures whose utility spans many disciplines. These tools are described in terms of their fundamental aspects, implementations, applications, and availability. Programs which are discussed include basic data plotting, curve smoothing, and depiction of three dimensional surfaces. As an aid to potential users of these tools, particular attention is given to discussing their availability and, where applicable, their cost

Generating anatomical substructures for physically-based facial animation.

Physically-based facial animation techniques are capable of producing realistic facial deformations, but have failed to find meaningful use outside the academic community because they are notoriously difficult to create, reuse, and art-direct, in comparison to other methods of facial animation. This thesis addresses these shortcomings and presents a series of methods for automatically generating a skull, the superficial musculoaponeurotic system (SMAS – a layer of fascia investing and interlinking the mimic muscle system), and mimic muscles for any given 3D face model. This is done toward (the goal of) a production-viable framework or rig-builder for physically-based facial animation. This workflow consists of three major steps. First, a generic skull is fitted to a given head model using thin-plate splines computed from the correspondence between landmarks placed on both models. Second, the SMAS is constructed as a variational implicit or radial basis function surface in the interface between the head model and the generic skull fitted to it. Lastly, muscle fibres are generated as boundary-value straightest geodesics, connecting muscle attachment regions defined on the surface of the SMAS. Each step of this workflow is developed with speed, realism and reusability in mind