Variational modeling methods for Visualization

• Publisher Summary Variational modeling techniques are powerful tools for free-form modeling in CAD/CAM applications. Some of the basic principles are carrying over to scientific visualization. Others have to be modified and some totally new methods have been developed over the past couple of years. This chapter gives an extended survey of this area. Surfaces and solids designed in a computer graphics environment have many applications in modeling, animation, and visualization. The chapter concentrates on the visualization part. The chapter starts with the basics from differential geometry, which are essential for any variational method. Then, it surveys on variational surface modeling. The last step is the visualization part of geometric modeling. In this context, surface curves like geodesies and curvature lines play an important role. The corresponding differential equations are nonlinear, and in most cases numerical algorithms must be used. To be sure to visualize features at a high quality, algorithms with an inherent quality control are needed. The chapter presents the geometric algorithms, which satisfy this demand.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Annan teknik -- Mediateknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Other Engineering and Technologies -- Media Engineering (hsv//eng)

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