Geometric Modeling

We study the problem of computing a planar curve, restricted to lie between two given polygonal chains, such that the integral of the square of arc-length derivative of curvature along the curve is minimized. We introduce the minimum variation B-spline problem, which is a linearly constrained optimization problem over curves, defined by B-spline functions only. An empirical investigation indicates that this problem has one unique solution among all uniform quartic B-spline functions. Furthermore, we prove that, for any B-spline function, the convexity properties of the problem are preserved subject to a scaling and translation of the knot sequence defining the B-spline.

Evaluation of planar algebraic curves arises in the context of intersections of algebraic surfaces with piecewise continuous rational polynomial parametric surface patches useful in geometric modeling. We address a method of evaluating these curves of intersection that combines the advantageous features of analytic representation of the governing equation of the algebraic curve in the Bernstein basis within a rectangular domain, adaptive subdivision and polyhedral faceting techniques, and the computation of turning and singular points, to provide the basis for a reliable and efficient solution procedure. Using turning and singular points, the intersection problem can be partitioned into subdomains that can be processed independently and which involve intersection segments that can be traced with faceting methods. This partitioning and the tracing of individual segments is carried out using an adaptive subdivision algorithm for Bezier/B-spline surfaces followed by Newton correction o...

International Journal on Foundations of Computer Science & Technology (IJFCST) is a Bi-monthly peer-reviewed and refereed open access journal that publishes articles which contribute new results in all areas of the Foundations of Computer Science & Technology. Over the last decade, there has been an explosion in the field of computer science to solve various problems from mathematics to engineering. This journal aims to provide a platform for exchanging ideas in new emerging trends that needs more focus and exposure and will attempt to publish proposals that strengthen our goals. Topics of interest include, but are not limited to the following:

The intersection between 3D objects plays a prominent role in spatial reasoning, geometric modeling and computer vision. Detection of possible intersection between objects can be based on the objects’ triangulated boundaries, leading to computing triangle-triangle intersection. Traditionally there are separate algorithms for cross intersection and coplanar intersection. There is no single algorithm that can intersect both types of triangles without resorting to special cases. Herein we present a complete design and implementation of a single algorithm independent of the type of intersection. Additionally, this algorithm first detects, then intersects
and classifies the intersections using barycentric coordinates. This work is directly applicable to (1) Mobile Network Computing and Spatial Reasoning, and (2) CAD/CAM geometric modeling where curves of intersection between a pair of surfaces is required for numerical control (NC) machines. Three experiments of the algorithm implementation are presented as a proof this feasibility.

International Journal on Foundations of Computer Science & Technology (IJFCST) is a Bi-monthly peer-reviewed and refereed open access journal that publishes articles which contribute new results in all areas of the Foundations of Computer Science & Technology. Over the last decade, there has been an explosion in the field of computer science to solve various problems from mathematics to engineering. This journal aims to provide a platform for exchanging ideas in new emerging trends that needs more focus and exposure and will attempt to publish proposals that strengthen our goals. Topics of interest include, but are not limited to the following

This paper describes development of a storage, archival, and sketch-based query and retrieval system for 3D objects. The process and results provide a model for a Digital Library of 3D data for further study and analysis. The initial focus has been Native American ceramic vessels, scanned and defined as a set of three-dimensional triangulated meshes composed of points and triangles. The process involves modeling the data with parametric surfaces, and extracting relevant features to raise the level of abstraction of data. The project uses a class based XML schema to catalog and organize vessel data. A visual query process was developed to permit users to interact with the data using sketches or by selecting sample vessel shapes to augment text and metric search criteria to retrieve original and modeled data, and interactive 2D and 3D models. Keywords:

1 Introduction In this paper, we present a new representation for piecewise smooth surfaces of arbitrary topological type, 1 and a method for fitting such surface models to scattered range data, where neither the topolog- ical type of the surface, its geometry, nor the location of ...

In this paper, a model for aerodynamic behaviour of particulates (pollutants) that diffuses into the airway in the human lower respiratory track (LRT) containing mixture of pollutants, water droplets and mucus is considered. The velocity of the airflow is computed using the Nervier Stokes equation with fractal morphologic boundaries and the population of bacteria in the mixture studied using the Lauffeger-Aris-Keller model. The series solutions to the models are obtained using eigenvalue and eigenfunction techniques. The concentration of the pollutants in the LRT and the airflow velocity profile are obtained. It is found that as the thickness of the irreversible structures formed on the walls of LRT increases then the airflow into the airway decreases. The population of bacteria is found to be stable if the if sustenance function is very small compared to the death rate of the bacteria. Therefore, for good throughput of airflow, the muscles of the walls of breathing ducts need to be dilated with drugs or through surgery by constructing Nano pipes to allow passages of air into the air sacs by bypassing the pulmonary obstacles to enhance free flow of air into the lungs. Cite This Article: Oyelami Benjamin Oyediran, " Models for Computing Effect of Pollutants on the Lower Respiratory Tract.

The aim of this research is to formulate a procedure for determining the four copies of conics tangents to three established conics, both homothetic and generic, and to illustrate and justify in space the elements that originated the geometric constructions carried out in the plan. In the process of modeling a tangential connection between two (or three) conic surfaces, we often feel disoriented when we face the problem of tangency between non-homothetic conics. To solve the problem, topics such as involution between coincident conics were treated; the inversion of a quadric cone; the pole line and the corresponding polar plane; the cyclic transformations defined by three coplanar conics; and the polar cone as the locus of the pole lines of three conjugated cones.

Given a smooth surface, a blue (red) ridge is a curve such that at each of its point, the maximum (minimum) principal curvature has an extremum along its curvature line. As curves of extremal curvature, ridges are relevant in a number of applications including surface segmentation, analysis, registration, matching. In spite of these interests, given a smooth surface, no algorithm reporting a certified approximation of its ridges was known so far, even for restricted classes of generic surfaces. This paper partly fills this gap by developing the first algorithm for polynomial parametric surfaces — a class of surfaces ubiquitous in CAGD. The algorithm consists of two stages. First, a polynomial bivariate implicit characterization of ridges P = 0 is computed using an implicitization theorem for ridges of a parametric surface. Second, the singular structure of P = 0 is exploited, and the approximation problem is reduced to solving zero dimensional systems using Rational Univariate Representations. An experimental section illustrates the efficiency of the algorithm on Bézier patches.

We propose a new modeling and rendering system that enables users to construct 3D models with an interface that seems no different from sketching by hand, and that displays models in a sketch-like style, preserving the features of the user's strokes. We call this system 3D SKETCH. To reconstruct 3D objects from sketches, we limit the domain of renderable sketches

As the name imply prolonged surfaces to extract most amount of heat via out the surfaces. There are such a lot of researcher check out the heat transfer from the C I engine by using the use of fins, however nobody can calculate the top temperature of fin and to formulate the result by way of using Finite Element approach. It's far very vital to transfer warmness from the C I engine .The warmth transfer coefficient may be decided the usage of superior FEA codes which include fluid mechanics .Those simplified terms constitute a aggregate of several elements ,which include powerful floor vicinity ,lateral fin conduction ,boundary layer formation and cloth conductivity. It's miles very difficult to modeled a hoop form fin .Each pin should be individually discredited ,increasing the modeling time significantly .On this studies we have to used simulation application will be advanced for predicting and optimizing thermal performance of different sorts of fin component like round fin, axial fin and we compare ring form fin with triangular profile .The end result of the ring form fin can be additionally in comparison with the ones axial fins and ring shape fin with triangular profile the use of finite detail evaluation software advanced on Ansys software. Apart from this we additionally look into the temperature size and thermal pressure distribution.

Superspirals include a very broad family of monotonic curvature curves, whose radius of curvature is defined by a completely monotonic Gauss hypergeometric function. They are generalizations of log-aesthetic curves, and other curves whose radius of curvature is a particular case of a completely monotonic Gauss hypergeometric function. In this work, we study superspirals of confluent type via similarity geometry. Through a detailed investigation of the similarity curvatures of superspirals of confluent type, we find a new class of planar curves with monotone curvature in terms of Tricomi confluent hypergeometric function. Moreover, the proposed ideas will be our guide to expanding superspirals.