Progressive Rendering of Transparent Integral Surfaces

Abstract

Integral surfaces are a useful method in illustrative and geometry-based flow visualization, as they convey shading, depth and geometric information better than their line-based counterparts. However, they are not as frequently used as line-based techniques due to the added complexity that arises from their computation. Frontline-based methods, such as stream surfaces and path surfaces require an adaptive subdivision of the frontline, whereas advected surfaces, such as streak surfaces and time surfaces, require refinement and possibly retriangulation of the entire surface after each time step. In this paper, we extend an image-space surface rendering technique to support transparency, which enables the application of illustrative surface rendering techniques without the need to adaptively refine frontlines or entire surfaces. We develop a pixel-based dynamic tree data structure that is progressively filled with integral curves and compactly stores the transparent layers arising in the rendering of the surfaces. We apply the method to the illustrative rendering of path surfaces and streak surfaces in a number of time-dependent vector fields.