Digital elevation models can represent many types of geographic data. One of the common digital elevation models is the triangulated irregular network (also called TIN, or polyhedral terrain, or triangulated terrain). We discuss ways to represent a TIN in a data structure, and give some of the basic algorithms that work on TINs. These include retrieving contour lines, computing perspective view...

A 1.5-dimensional terrain T with n vertices is an xmonotone polygonal chain in the plane. A point guard p on T guards a point q of T if the line segment connecting p to q lies on or above T ; p is a vertex guard if it is a vertex of T . In the Optimal Terrain Guarding (OTG) problem on T , the objective is to guard the vertices of T by the minimum number of vertex guards. King and Krohn [9] show...

It is shown that every orthogonal terrain, i.e., an orthogonal (rightangled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single non-overlapping piece by cutting along grid edges defined by coordinate planes through every vertex.

We prove that [n/2J vertex guards are always sufficient and sometimes necessary to guard the surface of an n-vertex polyhedral terrain. We also show that l(4n 4)/13J edge guards are sometimes necessary to guard the surface of an n-vertex polyhedral terrain. The upper bound on the number of edge guards is ln/3J (Everett and Rivera-Campo, 1994). Since both upper bounds are based on the four color...

Abstract Mobile robots usually need to minimize energy when they are traversing uneven terrains. To reach a location of interest, one strategy consists making the robot follow path that demands least possible amount energy. Yet, its calculation is not trivial with irregular surfaces. Gravity makes consumption change according heading. Such variation subject terramechanic characteristics surface...

We introduce the first solution for simulating formation and evolution of glaciers, together with their attendant erosive effects, periods covering combination glacial inter-glacial cycles. Our efficient includes both a fast yet accurate deep learning-based estimation highorder ice flows new, multi-scale advection scheme enabling us to account distinct time scales at which glaciers reach equili...

Approximate scale-invariance and local regularity properties of natural terrains suggest that they can be a accurately modeled with random processes which are locally fractal. Current models for terrain modeling include fractional and multifractional Brownian motion. Though these processes have proved useful, they miss an important feature of real terrains: typically, the local regularity of a ...

Diverse methods have been developed to generate terrains under constraints to control terrain features, but most of them use strict restrictions. However, there are situations were more flexible restrictions are sufficient, such as ensuring that terrains have enough accessible area, which is an important trait for video games. The Genetic Terrain Program technique, based on genetic programming,...

High-speed navigation of autonomous Unmanned Ground Vehicles (UGVs) in rough unknown terrains requires the detection and identification of the terrain in order to make effective navigation decisions. This paper investigates a geometrical approach to identifying terrain based on its roughness using the terrain elevations from a point cloud generated using a 3D camera. This roughness, called the ...