G I S   &   C A D   S y s t e m s

GIS and CAD Systems: Excerpt of User List

• CSI International
• Department of Geography, University of Maryland
• Institute for Cartography and Geoinformatics, Hannover
• Mapshots
• Navigon
• Paradigm Geophysical
• Potsdam Institute for Climate Impact Research
• PTV
• SWBB
• Viewscape

 PROBLEM SOLUTIONS: Typical Examples

Area Intersection

LEDA helps you compute area intersection.

This does not mean the area intersection feature as a function of a geometric viewer performed on a display screen. That is easy and can be established by more or less every CAD system. Rather, this refers to the correct computation of intersections of the real underlying data, as it is aspired by for instance modern Geographic Information Systems. That especially means, that the result of such computation can be stored or used for further computation.

Why LEDA :

There is a strong geometric kernel in LEDA. It provides data types such as polygons, polygons with holes, and polygons with circular arcs. Of course, these data types support many other operations beyond area intersection:

... info on polygons
... info on generalized polygons
... info on circular polygons

The correctness of the computations and results can be achieved by using several exact number types that overcome the well-known problem of finite precision arithmetic on computers:

... info on rational numbers
... info on real numbers
... info on big integers
... info on floating point numbers
... info on other algebraic data types

Circular Arcs

Several of our customers have to compute with polygons where at least some edges are circular arcs. Often, approximating such an edge by several straight line segments is not appropriate:

>>> click the picture to see details

The type r_circle_gen_polygon allows to model polygons with holes, where straight line segments as well as circular segments are supported. All the usual polygon operations are provided.

In particular, we offer the following boolean operations:

• intersection,
• union,
• difference, and
• symmetric difference.

It is important to note that all these computations are exact, i.e. no rounding errors can occur.

Documentation:

Read the manual page on r_circle_gen_polygon.
Read the manual page on r_circle_polygon.

Route Planning Module

Storing geometric data is usually space and time critical. Use compression algorithms when storing or distributing your geometric data and get the most out of time and space.

Compress your data in order to...

... save external memory space.
... accelerate storing and loading procedures.
... minimize data traffic via internet or other networks.
... fit your geografic data into memory chips with limited size.

EXAMPLE APPLICATION: PolyGIS

PolyGIS, a Geographic Information System empowered by LEDA, is the fastest GIS available on the German market.

Software-Buero Lothar Bubel GmbH, Kirkel: PolyGIS, Geographic Information System

EXAMPLE APPLICATION: Decomposition-Based Assemby Synthesis

The research project Decomposition-Based Assembly Synthesis aims at developing a method for the automatic synthesis of mechanical assemblies, via the top-down hierachical decomposition of product geometry. It has been successfuly applied to the assembly design of automotive body structures, focusing on several different design aspects: structural stiffness, in-process dimensional adjustability, and component modularity for part sharing. The project received the CAREER Award from the National Science Foundation of the United States.

University of Michigan, Ann Arbor: Decomposition-Based Assembly Synthesis

EXAMPLE APPLICATION: Effective Computational Geometry for Curves and Surfaces (ECG) Project

The ECG project is focused on effectively handling curved objects.

The project wants to take into consideration the multidisciplinary nature of the problem and to develop cooperative research in three main directions: computational geometry, computer algebra and numerical analysis.
Overall goal f the project is to give Effective Computational Geometry for Curves and Surfaces a solid mathematical and algorithmic foundation, and to provide solutions to key problems and to validate their theoretical advances through extensive experimental research, as well as the development of software packages that could serve as steps towards a standard for safe and effective geometric computing.

ECG, European Collaboration: Effective Computational Geometry for Curves and Surfaces

LINKS

LEDA
LEDA extension package: SD Trees