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ACM Transactions on Graphics (TOG), Volume 9 Issue 3, July 1990

Efficient ray tracing of volume data
Marc Levoy
Pages: 245-261
DOI: 10.1145/78964.78965
Volume rendering is a technique for visualizing sampled scalar or vector fields of three spatial dimensions without fitting geometric primitives to the data. A subset of these techniques generates images by computing 2-D...

Rasterization of nonparametric curves
John D. Hobby
Pages: 262-277
DOI: 10.1145/78964.78966
We examine a class of algorithms for rasterizing algebraic curves based on an implicit form that can be evaluated cheaply in integer arithmetic using finite differences. These algorithms run fast and produce “optimal” digital output,...

Computation of the axial view of a set of isothetic parallelepipeds
Franco P. Preparata, Jeffrey S. Vitter, Mariette Yvinec
Pages: 278-300
DOI: 10.1145/78964.78967
We present a new technique to display a scene of three-dimensional isothetic parallelepipeds (3D-rectangles), viewed from infinity along one of the coordinate axes (axial view). In this situation, there always exists a topological sorting of the...

Quartic Beta-splines
Barry Joe
Pages: 301-337
DOI: 10.1145/78964.78968
Quartic Beta-splines have third-degree arc-length or geometric continuity at simple knots and are determined by three &bgr; or shape parameters. We present a general explicit formula for quartic Beta-splines, and determine and illustrate the...