Elliptiliste

Elliptiliste is a term used in computational geometry to describe a finite, ordered collection of ellipses that together approximate a two-dimensional region or its boundary. Each element e_i in the list is an ellipse characterized by a center c_i = (x_i,y_i), semi-major axis a_i, semi-minor axis b_i, and orientation θ_i. The union U = ∪_{i=1}^n e_i provides an approximation of a target region R with a prescribed tolerance ε, and the boundary ∂U closely tracks ∂R as n increases or the fitting improves.

Construction methods include point-set fitting, where a sample of points from R is partitioned into clusters and an ellipse is fitted to each cluster; greedy algorithms that iteratively add ellipses to cover uncovered points; and optimization-based approaches that minimize a cost function (e.g., total area, number of ellipses) subject to coverage constraints. Hierarchical strategies use multi-resolution representations to refine the elliptiliste progressively.

Key properties include flexibility in approximating irregular boundaries, smoothness of constituent shapes, and the potential for overlap between ellipses. The choice of parameters affects accuracy, runtime, and robustness to noise. In practice, elliptiliste balances precision against computational cost.

Applications span computer graphics and rendering, where elliptiliste provide efficient collision detection and level-of-detail representations; robotics and autonomous navigation for map simplification and obstacle approximation; and pattern recognition, where shapes are described by a compact set of ellipses to facilitate matching and classification.

Relation to related concepts includes the single-ellipse case of a minimum bounding ellipse and the broader area of shape decomposition into primitive geometric primitives. See also: ellipse, minimum enclosing ellipse, shape approximation.