Evolved Art with Transparent, Overlapping, and Geometric Shapes

In this work, an evolutionary art project is presented where images are approximated by transparent, overlapping and geometric shapes of different types, e.g., polygons, circles, lines. Genotypes representing features and order of the geometric shapes are evolved with a fitness function that has the corresponding pixels of an input image as a target goal. A genotype-to-phenotype mapping is therefore applied to render images, as the chosen genetic representation is indirect, i.e., genotypes do not include pixels but a combination of shapes with their properties. Different combinations of shapes, quantity of shapes, mutation types and populations are tested. The goal of the work herein is twofold: (1) to approximate images as precisely as possible with evolved indirect encodings, (2) to produce visually appealing results and novel artistic styles.Comment: Proceedings of the Norwegian AI Symposium 2019 (NAIS 2019), Trondheim, Norwa

Approximating Smallest Containers for Packing Three-dimensional Convex Objects

We investigate the problem of computing a minimal-volume container for the non-overlapping packing of a given set of three-dimensional convex objects. Already the simplest versions of the problem are NP-hard so that we cannot expect to find exact polynomial time algorithms. We give constant ratio approximation algorithms for packing axis-parallel (rectangular) cuboids under translation into an axis-parallel (rectangular) cuboid as container, for cuboids under rigid motions into an axis-parallel cuboid or into an arbitrary convex container, and for packing convex polyhedra under rigid motions into an axis-parallel cuboid or arbitrary convex container. This work gives the first approximability results for the computation of minimal volume containers for the objects described

Polygon Exploration with Time-Discrete Vision

With the advent of autonomous robots with two- and three-dimensional scanning capabilities, classical visibility-based exploration methods from computational geometry have gained in practical importance. However, real-life laser scanning of useful accuracy does not allow the robot to scan continuously while in motion; instead, it has to stop each time it surveys its environment. This requirement was studied by Fekete, Klein and Nuechter for the subproblem of looking around a corner, but until now has not been considered in an online setting for whole polygonal regions. We give the first algorithmic results for this important algorithmic problem that combines stationary art gallery-type aspects with watchman-type issues in an online scenario: We demonstrate that even for orthoconvex polygons, a competitive strategy can be achieved only for limited aspect ratio A (the ratio of the maximum and minimum edge length of the polygon), i.e., for a given lower bound on the size of an edge; we give a matching upper bound by providing an O(log A)-competitive strategy for simple rectilinear polygons, using the assumption that each edge of the polygon has to be fully visible from some scan point.Comment: 28 pages, 17 figures, 2 photographs, 3 tables, Latex. Updated some details (title, figures and text) for final journal revision, including explicit assumption of full edge visibilit

3D oceanographic data compression using 3D-ODETLAP

This paper describes a 3D environmental data compression technique for oceanographic datasets. With proper point selection, our method approximates uncompressed marine data using an over-determined system of linear equations based on, but essentially different from, the Laplacian partial differential equation. Then this approximation is refined via an error metric. These two steps work alternatively until a predefined satisfying approximation is found. Using several different datasets and metrics, we demonstrate that our method has an excellent compression ratio. To further evaluate our method, we compare it with 3D-SPIHT. 3D-ODETLAP averages 20% better compression than 3D-SPIHT on our eight test datasets, from World Ocean Atlas 2005. Our method provides up to approximately six times better compression on datasets with relatively small variance. Meanwhile, with the same approximate mean error, we demonstrate a significantly smaller maximum error compared to 3D-SPIHT and provide a feature to keep the maximum error under a user-defined limit

How to Walk Your Dog in the Mountains with No Magic Leash

We describe a $O(\log n )$-approximation algorithm for computing the homotopic \Frechet distance between two polygonal curves that lie on the boundary of a triangulated topological disk. Prior to this work, algorithms were known only for curves on the Euclidean plane with polygonal obstacles. A key technical ingredient in our analysis is a $O(\log n)$-approximation algorithm for computing the minimum height of a homotopy between two curves. No algorithms were previously known for approximating this parameter. Surprisingly, it is not even known if computing either the homotopic \Frechet distance, or the minimum height of a homotopy, is in NP