On Intersecting IFS Fractals with Lines

01/08/2013
by   József Vass, et al.
0

IFS fractals - the attractors of Iterated Function Systems - have motivated plenty of research to date, partly due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design of fractal antennas. The statement and resolution of the Fractal-Line Intersection Problem is imperative for a more efficient treatment of certain applications. This paper intends to take further steps towards this resolution, building on the literature. For the broad class of hyperdense fractals, a verifiable condition guaranteeing intersection with any line passing through the convex hull of a planar IFS fractal is shown, in general R^d for hyperplanes. The condition also implies a constructive algorithm for finding the points of intersection. Under certain conditions, an infinite number of approximate intersections are guaranteed, if there is at least one. Quantification of the intersection is done via an explicit formula for the invariant measure of IFS.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/28/2020

On the number of intersection points of lines and circles in ℝ^3

We consider the following question: Given n lines and n circles in ℝ^3, ...
research
08/18/2018

A 2-Norm Condition Number for Bézier Curve Intersection

We present a short note describing a condition number of the intersectio...
research
08/07/2022

A New Approach to Line-Sphere and Line-Quadrics Intersection Detection and Computation

Line intersection with convex and un-convex polygons or polyhedron algor...
research
05/28/2018

On the intersection graph of the disks with diameters the sides of a convex n-gon

Given a convex n-gon, we can draw n disks (called side disks) where each...
research
08/21/2021

From Tutte to Floater and Gotsman: On the Resolution of Planar Straight-line Drawings and Morphs

The algorithm of Tutte for constructing convex planar straight-line draw...
research
01/09/2023

Line-Torus Intersection for Ray Tracing: Alternative Formulations

Intersection algorithms are very important in computation of geometrical...
research
04/04/2019

Embeddings of k-complexes into 2k-manifolds

If K is a simplicial k-complex, the standard van Kampen obstructions tel...

Please sign up or login with your details

Forgot password? Click here to reset