Adler and Monteiro (1992) developed a parametric analysis approach that is naturally related to the geometry of the linear pro~am. This approach is based on the availability of primal and dual optimal solutions satisfying strong complementarity. In this paper, we develop an altemative geometric approach for parametric analysis which does not require the strong complementarity condition. This pa...

Parametric optics and second harmonic generation in pure plasmonic particle chains are studied. By a proper design of the plasmonic particle geometry, the modes supported by the chain can achieve phase-matching conditions. Then the magnetic-field dependence of the plasmon electric susceptibility can provide the nonlinearity and the coupling mechanism leading to parametric processes, sum frequen...

In this paper, alternative approaches to structure the parametric geometry in relation to information on various performances are described and exemplified. They relate to different levels of knowledge that concern the performances considered in the process and which are available to the designer while the parametric model is being set. A theoretic framework embeds the different approaches, for...

In this paper, we introduce and study a new implicit representation of parametric curves and parametric surfaces . We show how these representations which we will call the matrix implied, establish a bridge between geometry and linear algebra, thus opening the possibility of a more robust digital processing. The contribution of this approach is discussed and illustrated on important issues of g...

Parameterization of 3D manifold mesh data involves embedding the mesh in some natural parametric domain, such as the plane or the sphere. Parameterization is important for many applications in geometry processing, including texture mapping, remeshing and morphing. The main objective is to generate a bijective mapping between the mesh surface and the parametric domain, which minimizes the distor...

This paper describes one method of constructing a parametric human model for use in evolving humanoid character geometry. Interactive aesthetic selection is employed as a fitness function for producing successive populations of human models from an initial parametric human model constructed from a hierarchy of implicit surfaces. The parameters controlling the size, position, and orientation of ...

We appreciate the comments of Fabius et al. (2013) regarding our general parametric geometric model of native aortic valves (AVs) (Haj-Ali et al., 2012). In their letter, concerns were raised that the use of our geometric model of tricuspid aortic valves (TAVs) might not be suitable when applied for bicuspid valves (BAVs) since it may predict a stenotic configuration. We are glad that Fabius et...

Freeform rational parametric curves and surfaces have been playing a major role in computer aided design for several decades. The ability to analyze local (differential) properties of parametric curves is well established and extensively exploited. In this work, we explore a different lifting approach to global analysis of freeform geometry, mostly curves, in IR and IR. In this lifting scheme, ...

Spatial structures often embody generative systems. Both analog (physical modeling) as well as computational methods have been uses to explore the range of design possibilities. Whereas many of the favored physical modeling techniques, such as soap films or catenary nets, inherently generate forms based on certain performative properties, many of the parametric form generating computational met...

CAD model quality in parametric design scenarios largely determines the level of flexibility and adaptability of a 3D model (how easy it is to alter the geometry) as well as its reusability (the ability to use existing geometry in other contexts and applications). In the context of mechanical CAD systems, the nature of the feature-based parametric modeling paradigm, which is based on parent-chi...