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

Abstract

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.