Fast and Easy Reach-Cone Joint Limits

Jane Wilhelms and Allen Van Gelder
University of California

This paper appears in issue Volume 6, Number 2.
Purchase this issue from the akpeters.com web site.

Abstract

We describe a simple and fast method of creating and using joint sinus reach cones to limit the range of motion on universal and ball-and-socket joints. Reach cones can be created interactively or based on results from biomechanics. A reach cone is specified as a spherical polygon on the surface of a reach sphere that defines all positions the longitudinal segment axis beyond the joint can take. Reach polygons can be concave or convex, and cover more than one hemisphere. Longitudinal axis rotation limits can also be defined for locations in the reach cone. Calculations to determine whether a segment is within the reach cone are based on the relation of the segment longitudinal axis to the planes defining the reach cone and are done in the local coordinate space of the segment. The calculations have no discernible effect on the speed of interactive display or animation.

Author Information

Jane Wilhelms, University of California, Santa Cruz, Computer Science Department, Santa Cruz, CA 95064 wilhelms@cse.ucsc.edu

Allen Van Gelder, University of California, Santa Cruz, Computer Science Department, Santa Cruz, CA 95064 avg@cse.ucsc.edu

Source Code

The authors provide downloadable C source code for the main reach code joint-limit routines as well as procedures to construct a reach cone directly in three dimensions: jointLimits.tar.gz (15K gzip-compressed tar format)

Technical Report

The referenced technical report, which contains more detailed bibliography and background information, is available here: Jane Wilhelms and Allen Van Gelder. “Efficient Spherical Joint Limits with Reach Cones.” Technical Report, UCSC, April 2001. [514K PDF] [1013K PostScript gzip]

Images

The following images are from Figure 6 of the paper. Click on a thumbnail to view a large version.

[Thumbnail of Figure 6(left)] [Thumbnail of Figure 6(right)]

Left: The reach cones of the right side of the body. On the upper arm reach cone, the range of allowable z-axis rotation is color-coded (green denotes a lesser range and red a larger). Right: The upper arm reach cone, with the slice containing the arm defined by three triangles. Red and green are consecutive radial slices in counterclockwise order; blue is the reach-cone boundary.

BibTeX Entry

@article{WilhelmsVanGelder01,
  author = "Jane Wilhelms and Allen Van Gelder",
  title = "Fast and Easy Reach-Cone Joint Limits",
  journal = "journal of graphics, gpu, and game tools",
  volume = "6",
  number = "2",
  pages = "27-41",
  year = "2001",
}