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I Session 2638

THE FEATURE POINT TRIANGULATION METHOD FOR SPATIAL SUBDIVISION

Josann Duane, Amgad Saleh Department of Civil and Environmental Engineering and Engineering Graphics The Ohio State University

Abstract

In this paper we describe the geometric and topological requirements of the triangulation scheme used to model the earth’s surface by spatial subdivision. The triangulation scheme that we developed is called the fea- ture point triangulation method and it used Earth Modeler to represent the Earth’s surface. The feature point triangulation has markedly better resolution of features than other triangulation methods. The feature point method represents the terrain within each subdivision with four triangles oriented in three-dimensional space so as to approximate the surface contour of the section being modeled. Features of the earth’s surface are represented by a total of sixteen different triangulation patterns. The triangulation patterns are described and examples are given of their use in representing a variety of cultural and natural features on the earth’s surface, such as, roads, lakes, erosion cuts, and building. We describe the enumeration of spatial subdivision and triangles representing the Earth’s surface and show how the method is used to represent a single surface or multiple subterranean surfaces. We demonstrate the capabilities of the feature point method in representing multiple levels-of-detail and finite element mesh generation.

Introduction

The feature point triangulation is a method that has been developed’ for representation of surfaces in 3D- space by spatial subdivision. The method was developed to be used by Earth Modeler z, a modeler that is based on the spatial subdivision using a quadtree data structure’” and is capable of generating and displaying a three-dimensional model of the earth’s surface at multiple levels of detail. The earth’s surface is modeled in one degree square sections. Each section is successively subdivided into quadrants and sub-quadrants. This process is continued until the smallest subdivi sion is about ten feet square. The terrain within each subdivision is modeled by four triangles oriented in three-dimensional space so as to approximate the surface contour of the section being modeled. 2 Domaratz reviewed the various data input methods that represent a surface terrain. The methods he described using the concepts of discrete point surface sampling methods, and the theory of cartographic objects, attributes and relationships, are the irregular point methods, the linear methods, regular grids methods and irregular grid methods. Irregular point structures suffer from the lack of implicit or explicit descriptions of the spatial relationship between the sample points. Linear structures, such as contour and profile, implicitly define the spatial relationships between the points on the same line but fail to define them for points on different lines. Regular grids implicitly define the spatial relationships between neighboring points and are easy to use but they have a large number of redundant points in smooth regions. Although irregular grids

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Duane, J., & Saleh, A. (1996, June), The Feature Point Triangulation Method For Spatial Subdivision Paper presented at 1996 Annual Conference, Washington, District of Columbia. 10.18260/1-2--6056