ÐIn this paper, we develop integrated techniques that unify physics-based modeling with geometric subdivision methodology and present a scheme for dynamic manipulation of the smooth limit surface generated by the (modified) butterfly scheme using physics-based aforceo tools. This procedure-based surface model obtained through butterfly subdivision does not have a closed-form analytic formulatio...

Gerald Farin was born on March 20, 1953, and passed away on January 14, 2016. The authors of this note feel that his contributions to CAD and CAGD are so extensive andmultifaceted that they deserve this special ‘‘tribute’’. Correctly, R. Sarraga emphasizes (in Section 1) Gerald Farin’s great contribution to the development of the new scientific field of Computer Aided Geometric Design (CAGD), w...

A monoid hypersurface is an irreducible hypersurface of degree d which has a singular point of multiplicity d−1. Any monoid hypersurface admits a rational parameterization, hence is of potential interest in computer aided geometric design. We study properties of monoids in general and of monoid surfaces in particular. The main results include a description of the possible real forms of the sing...

Free-form curves and surfaces represented by control points together with well-defined basis functions are widely used in computer aided geometric design. Efficient evaluation of points and derivatives of free-form curves and surfaces plays an important role in interactive rendering or CNC machining. In this paper we show that free-form curves with properly defined basis functions are the solut...

The best parameters defining the geometry of a visual sensor generally depend on the particular visual task the sensor is intended to be used in. However, translating task requirements directly into low-level geometric parameters may be difficult, since deep knowledge of the sensor design is usually required, but end users of a sensor need not necessarily be its designers. A framework is sugges...

Desertification refers to land degradation phenomenon in arid, semi-arid and dry sub-humid areas, resulting from various factors including climate variation and human activities. For evaluation and mapping of desertification many research have been conducted leading to regional and local models. In this research, among different existing methods IMDPA‌ was selected and desertification intensity...

Developable strip is commonly used in product design due to its ease of manufacture. This paper proposes an algorithm for geometric design of strip using developable Bézier patches. It computes an aggregate of triangular and quadrilateral patches interpolate two given space curves defining a strip. The computation process selects optimal solutions in terms of surface assessment criteria specifi...

In this paper we present a novel, interactive shape modeling technique: Dynamic Implicit Solid Modeling, which unifies volumetric implicit functions and powerful physics-based modeling. Although implicit functions are extremely powerful in graphics, geometric design, and shape modeling, the full potential of implicit functions is yet to be fully realized due to the lack of flexible and interact...

The main results of this article are small time heat comparison results for two points in two manifolds with characteristic functions as initial temperature distributions (Theorems 1 and 2). These results are based on the geometric concepts of (essential) distance from the complement and spherical area function. We also discuss some other geometric results about the heat development and illustr...