This paper introduces a new neutral hybrid discrete (in the limit continuous) solid CAD model for meshing applications within the Integrated Computational Environments, based on subdivision surfaces. The model uses the Boundary Representation for the CAD model topology and the Butterfly Interpolating subdivision scheme for definition of underlying curves and surfaces. It is automatically derive...

The process of developing architectural forms has greatly been changed by advances in digital technology, especially in design tools and applications. In recent years, the advent of graphical scripting languages in the design process has profoundly affected 3D modeling. Scripting languages help develop algorithms and geometrical grammar of shapes based on their constituent parameters. This stud...

Computational models offer an excellent tool for the study and analysis of scientific discovery processes. The study of failures provides an insight into the history and philosophy of science as valuable as the study of successful discoveries. Using a computational model I analyzed Kepler’s approach in formulating a quantitative law for refraction. Although Kepler ultimately failed in discoveri...

Accurate geometrical models of the head are necessary for solving the forward and inverse problems of magneto- and electro-encephalography (MEG/EEG). Boundary element methods (BEMs) require a geometrical model describing the interfaces between different tissue types. Classically, head models with a nested volume topology have been used. In this paper, we demonstrate how this constraint can be r...

A new geometrical model for the fundamental mode of a Gaussian beam is presented in the oblate spheroidal coordinate system. The model is an interpretation of a Gaussian amplitude wave function, which is an exact solution of the scalar Helmholtz equation. The model uses the skew-line generator of a hyperboloid of one sheet as a raylike element on a contour of constant amplitude. The geometrical...

We give a new geometrical interpretation of the well-known algebraic trilinear constraints used in motion analysis from three views observation. We show that those algebraic equations correspond to depth errors appropriately weighted by a function of the relative reliability of the corresponding measurements. Therefore directly minimizing the algebraic trilinear equations, in the least squares ...

In order to accommodate solutions with multiple phases, corresponding to crossing rays, we formulate geometrical opties for the scalar wave équation as a kinetic transport équation set in phase space. If the maximum number of phases is finite and known a priori we can recover the exact multiphase solution from an associated System of moment équations, closed by an assumption on the form of the ...