A Low Distortion Map Between Disk and Square

This paper appears in issue Volume 2, Number 3.
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Abstract

This paper presents a map between squares and disks that associates concentric squares with concentric circles. This map preserves adjacency and fractional area, and has proven useful in many sampling applications where correspondences must be maintained between the two shapes. The paper also provides code to compute the map that minimizes branching and is robust for all inputs. Finally, it extends the map to the hemisphere. Though this map has been used in publications before, details of its computation have never previously been published.

Author Information

Peter Shirley, University of Utah, CS Dept, 3190 MEB, Salt Lake City, UT 84112 shirley@cs.utah.edu

Kenneth Chiu, Indiana University/CS Dept, Lindley Hall, Bloomington, IN chiuk@cs.indiana.edu

Source Code

Downloadable C source code implements the maps between disk and square described in this paper.

BibTeX Entry

@article{ShirleyChiu97,
  author = "Peter Shirley and Kenneth Chiu",
  title = "A Low Distortion Map Between Disk and Square",
  journal = "journal of graphics, gpu, and game tools",
  volume = "2",
  number = "3",
  pages = "45-52",
  year = "1997",
}