• Publications
  • Influence
Discrete Analytical Hyperplanes
TLDR
The main result is the links made between the arithmetical thickness of a hyperplane and its topology. Expand
The Discrete Analytical Hyperspheres
TLDR
An analytical definition of a discrete hypersphere with arbitrary center, radius, and thickness in dimension n is introduced and is called a discrete analytical hypersPhere. Expand
Discrete circles, rings and spheres
  • E. Andres
  • Mathematics, Computer Science
  • Comput. Graph.
  • 1 September 1994
TLDR
A new approach to discrete circles, rings, and an immediate extension to spheres is presented, showing that the arithmetical circle extends Bresenham's circle and an efficient incremental generation algorithm is given. Expand
Discrete linear objects in dimension n: the standard model
  • E. Andres
  • Mathematics, Computer Science
  • Graph. Model.
  • 2003
TLDR
A new analytical description model, called the standard model, for the discretization of Euclidean linear objects (point, m-flat, m -simplex) in dimension n is proposed and is well suited for modelling applications. Expand
Discrete analytical Ridgelet transform
TLDR
Experimental results show that the simple thresholding of the DART coefficients is competitive or more effective than the classical denoising techniques. Expand
Implicit Digital Surfaces in Arbitrary Dimensions
TLDR
Under some constraints, the digital implicit surface has some interesting properties, such as k-tunnel freeness, and there exists a very simple analytical characterization. Expand
The Quasi-Shear Rotation
  • E. Andres
  • Mathematics, Computer Science
  • DGCI
  • 13 November 1996
TLDR
The QSR represents so far the “best” choice of an one-to-one discrete rotation for a practical application. Expand
Tunnel‐Free Supercover 3D Polygons and Polyhedra
A new discrete 3D line and 3D polygon, called Supercover 3D line and Supercover 3D polygon, are introduced. Analytical definitions are provided. The Supercover 3D polygon is a tunnel free planeExpand
A First Look into a Formal and Constructive Approach for Discrete Geometry Using Nonstandard Analysis
TLDR
The aim of this paper is to take a first look at a possible formal and constructive approach to discrete geometry that would open the way to better algorithmic definition of discrete differential concepts. Expand
Generalized Perpendicular Bisector and Circumcenter
TLDR
A theoretical generalization of the circumcenter as the intersection of generalized perpendicular bisectors between two regions is presented, which should allow the design of new circle recognition algorithms. Expand
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