Camera Keyframing using Linear Interpolation of Matrices

Amy Hawkins and Cindy M. Grimm
Washington University in St. Louis

This paper appears in issue Volume 12, Number 3.
Purchase this issue from the akpeters.com web site.

Abstract

Alexa’s method for linearly interpolating matrices is well-suited for application to camera matrices. This paper discusses implementation issues that arise when applying this method to camera interpolation. We show how to include the perspective matrix, even though Alexa’s operators cannot be applied directly to it. We discuss cases where Alexa’s operators fail to converge and show how to work around this problem. Additionally, we present implementation details for three interpolation methods: linear, spline-based smooth approximation, and smooth interpolation using subdivision.

We also discuss general issues with implementing Alexa’s method. We note changes to his provided pseudocode and discuss suitable values for epsilon to maximize efficiency. Finally, we show examples of the technique and describe a quality metric that can be used to compare our technique to camera parameter interpolation.

Author Information

Amy Hawkins, Department of Computer Science and Engineering, One Brookings Drive, St. Louis, MO 63105 aeh1@alum.wustl.edu

Cindy M. Grimm, Department of Computer Science and Engineering, One Brookings Drive, St. Louis, MO 63105 cmg@cse.wustl.edu

Animation

A video which shows the two examples discussed in the paper can be found here.

Source Code

We provide our source code for computing the matrix exponential, logarithm, and square root.

Executable

The program, including sample interpolation files and scenefiles, can be found here. A quick and dirty user's guide for the program is available here.

BibTeX Entry

@article{HawkinsGrimm07,
  author = "Amy Hawkins and Cindy M. Grimm",
  title = "Camera Keyframing using Linear Interpolation of Matrices",
  journal = "journal of graphics tools",
  volume = "12",
  number = "3",
  pages = "55-69",
  year = "2007",
}