Interval Assignment for Volumes with Holes Page: 6 of 24
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Because the linking surfaces within the hole are not connected through any shared edges to the
linking surfaces on the boundary of the volume, the constraints imposed on the edges of these two
sets of surfaces are independent, ignoring volume constraints for the moment. Without the ability
to match these two sets of intervals, the sweeping algorithm may fail. Previously, this matching
had to be done explicitly by the user through a tedious manual process.
This paper presents a new graphing algorithm to formulate additional volume interval
constraints which couple the intervals within a hole, to intervals on the outer surfaces of a swept
volume. The volume and surface constraints are solved with a linear program.8 Thus, swept
volumes may be meshed more automatically.
Interval Assignment Background
The process of interval assignment and control is fundamental to obtaining automatic
mapped and submapped meshes on surfaces. In this section, a brief introduction to linear programs
is given followed by a brief discussion on their use in interval assignment and control.3
Introduction to Linear Programs
A linear program is an optimization problem in which the objective function and design
constraints are linear functions of the design variables.9 For interval assignment, the design
constraints are derived from the surface geometry and meshing scheme, and the design variables
are the intervals on the curves of the surfaces.
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BENZLEY, STEVEN; MITCHELL, SCOTT A. & SHEPHERD, JASON F. Interval Assignment for Volumes with Holes, article, September 7, 1999; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc627482/m1/6/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.