Efficiently building a matrix to rotate one vector to another

Authors:
Tomas Möller;John F. Hughes
Affiliations:
U.C. Berkeley and Chalmers University of Technology, Department of Computer Engineering, 412 96 Gothenburg, Sweden;Brown University, Computer Science Department, 115 Waterman Street, Providence, RI
Venue:
Journal of Graphics Tools
Year:
1999

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Abstract

We describe an efficient (no square roots or trigonometric functions) method to construct the 3 × 3 matrix that rotates a unit vector f into another unit vector t, rotating about the axis f × t. We give experimental results showing this method is faster than previously known methods. An implementation in C is provided.