Geometric Visualization

Abstract

While visualization is applicable to any type of data, examining and interacting with geometric data require specialized approaches. Geometric data visualization produces images from a collection of mathematical models, which can be defined interactively or through a set of stored textual commands. Fundamentally, geometric visualization transforms mathematical models into images. Massive model visualization offers interactive performance for visualizing an essentially unlimited amount of geometry. Interactive manipulation assists a person in understanding the nature of an entire 3D model, and allows users to develop models for concept, design, engineering, assembly, and support. The vast majority of devices rely on 2D projections that users must mentally map back into 3D, so a productive interface to the display and the image is a prerequisite for successful design and implementation. Color maps can be used to represent value ranges in order to assist comprehension. Guidelines have been developed from the areas of art and design and applied productively to seeing, drawing, and communicating through geometric and non-geometric images. The earliest solid modeling systems were based on canonical forms that could be assembled through combinatorial solid geometry. Surface representation is important to many application domains because shape can be significant for aerodynamics and aesthetics. Defining and manipulating complex surfaces and shapes have been an area of significant interest throughout the history of Computer-Aided Design and Manufacturing (CAD/CAM). One objective of CAD/CAM is to reap the benefits and cost reductions through design process efficiency. This is particularly important for the automotive and aerospace industries because of the large scale of the products and services that are involved. These industries have pushed the CAD/CAM boundaries in many areas of representation, modeling, and display. Other industry sectors (e.g., shipbuilding, buildings, arts, and entertainment) have benefited from the pioneering work in these areas. This is an illustration of how significant developments in geometric visualization apply across industry domains and the cost/benefits and advantages that accrue to national and international industry. It is also an example of technology transfer, where state-of-the-art research and development has been effectively moved into advanced products and services.