Interactive display of 2D and 3D discrete quadrics with controlled topology

In this demonstration, we are going to propose an interactive animation of analytically defined discrete conics (quadrics in 2D) and discrete quadrics in 3D. The digitization is performed on the 2D quadratic equation: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 and the 3D quadric equation Ax2 + By2 + Cz2 + Dxy + Exz + F yz + Gx + Hy + Iz + J = 0.We propose 4 and 8-connected discrete 2D conics (naive and standard discrete conics) defined analytically where the user can see the resulting discrete conic while interacting with the parameters A, B, C, D, E and F. In the same way, we propose 6-separating and tunnel free 3D quadrics (naive and standard 3D quadrics) defined analytically where the user can can interactively modify the parameters A, B, C, D, E, F, G, H, I and J

Approximation of Discs by Octagons on Pixel-Plane via Jaccards Proximity Criterion: Theoretical Approach and Experimental Results Analysis

In the present paper we study approximation of discs by octagons on the pixel plane. To decide which octagon approximates better the given disc we use Jaccard's distance. The table of Jaccard's distances (calculated by a software created for these purposes) are presented at the end of the paper. The results for proximity are given in the form of a graph. Some properties of considered octagons are also studie

Digital Analytical Geometry: How do I define a digital analytical object?

International audienceThis paper is meant as a short survey on analytically de-ned digital geometric objects. We will start by giving some elements on digitizations and its relations to continuous geometry. We will then explain how, from simple assumptions about properties a digital object should have, one can build mathematical sound digital objects. We will end with open problems and challenges for the future

Analytical Description of Digital Circles

In this paper we propose an analytical description of different kinds of digital circles that appear in the literature and especially in digital circle recognition algorithms