The Mortonor z-curve is one example for a space filling curve: Given a level of refinement L ∈ N0, it maps the interval [0, 2)∩Z one-to-one to a set of d-dimensional cubes of edge length 2−L that form a subdivision of the unit cube. Similar curves have been proposed for triangular and tetrahedral unit domains. In contrast to the Hilbert curve that is continuous, the Morton-type curves produce j...

a {em roman dominating function} on a graph $g = (v ,e)$ is a function $f : vlongrightarrow {0, 1, 2}$ satisfying the condition that every vertex $v$ for which $f (v) = 0$ is adjacent to at least one vertex $u$ for which $f (u) = 2$. the {em weight} of a roman dominating function is the value $w(f)=sum_{vin v}f(v)$. the roman domination number of a graph $g$, denoted by $gamma_r(g)$, equals the...

Farin proposed a method for designing Bezier curves with monotonic curvature and torsion. Such are relevant in design due to their aesthetic shape. The relies on applying matrix M the first edge of control polygon curve order obtain by iteration remaining edges. With this method, sufficient conditions $M$ provided, which lead definition Class A curves, generalising previous result Mineur et al ...

This paper presents a short, simple, and general proof showing that the control polygons generated by subdivision and degree elevation converge to the underlying splines, box-splines, or multivariate B~zier polynomials, respectively. The proof is based only on a Taylor expansion. Then the results are carried over to rational curves and surfaces. Finally, an even shorter but as simple proof is p...

Interactive Stereoscopic Visualization of Very Large Visible Men on CAVE p. 41 Panoramic Spherical Video The Space Ball p. 51 Human Expressions Interaction Between Avatar and Virtual World p. 59 Progressive Curve Representation Based on Reverse Subdivision p. 67 Concept-Based Image Retrieval Using the New Semantic Similarity Measurement p. 79 Caseand Rule-Based Algorithms for the Contextual Pat...

This paper presents a new approach to rendering triangular algebraic free form surfaces. A hierarchical subdivision of the surface with associated tight bounding volumes provides for quick identification of the surface regions likely to be hit by a ray. For each leaf of the hierarchy an approximation to the corresponding surface region is stored. The approximation is used to compute a good star...

To design and implement a system of simulating the process of charging and discharging awkward length cargo with computer, key task is to construct high precision three-dimensional model of the hull. In view of problems exiting in distance subdivision method, we proposed one adaptive subdivision method for NURBS (Non-Uniform Rational B-Splines) curve based on energy function. In view of problem...

This work explores how three techniques for defining and representing curves and surfaces can be related efficiently. The techniques are subdivision, least-squares data fitting, and wavelets. We show how leastsquares data fitting can be used to “reverse” a subdivision rule, how this reversal is related to wavelets, how this relationship can provide a multilevel representation, and how the decom...

In this paper, we firstly devise a new and general p-ary subdivision scheme based on normal vectors with multi-parameters to generate fractals. Rich and colorful fractals including some known fractals and a lot of unknown ones can be generated directly and conveniently by using it uniformly. The method is easy to use and effective in generating fractals since the values of the parameters and th...