This paper presents a systematic approach to the problem of photorealistic 3-D model acquisition from the combination of range and image sensing. The input is a sequence of unregistered range scans of the scene and a sequence of unregistered 2-D photographs of the same scene. The output is a true texture-mapped geometric model of the scene. We believe that the developed modules are of vital imp...

Many situations in real world cannot be described by a single variable. Simul taneous occurrence of multiple events warrants multivariate distributions. For instance, univariate geometric distribution can represent occurrence of failure of one component of a system. However, to study systems with several com ponents that may have different types of failures, such as twin engines of an airplane ...

The effects of computer-assisted and distance learning of geometric modeling and computer aided geometric design are studied. It was shown that computer algebra systems and dynamic geometric environments can be considered as excellent tools for teaching mathematical concepts of mentioned areas, and distance education technologies would be indispensable for consolidation of successfully passed t...

Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known in 19th century invariant theory. Using a generalized version of this inner product, we derive in a straightforward way some of the recent results in CAGD, like Marsden’s identity, the expression fo...

The process of modeling geometric objects often entails modifica­ tion of a portion of a surface--a subsurface-which is part of a larger geometric shape. Most geometric modeling applications do not pro­ vide an interface that allows for user specification of arbitrarily shaped subsurfaces. We have developed two polygonal modeling applications which overcome this limitation. They employ an inter...

Geometric modeling is of signi cance to a wide variety of elds such as graphics computer aided design CAD visualization medicine and virtual environment This paper presents a novel modeling methodology physics based geometric modeling paradigm which can combine geometric objects with physical and material properties thus allowing intuitive interaction with geometric objects by means of force Co...

The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which is commonly used in algebraic geometry. Not all algebraic developable surfaces have rational parametrizations. In this paper, we focus on the rational developable surfaces. For a ...

We give a characterization of vertex-monotone properties with sharp thresholds in a Poisson random geometric graph or hypergraph. As an application we show that a geometric model of random k-SAT exhibits a sharp threshold for satisfiability.

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...