A fast algorithm for general raster rotation
Proceedings on Graphics Interface '86/Vision Interface '86
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
A fast algorithm for general raster rotation
Graphics gems
Permutation warping for data parallel volume rendering
PRS '93 Proceedings of the 1993 symposium on Parallel rendering
AFNI: software for analysis and visualization of functional magnetic resonance neuroimages
Computers and Biomedical Research
Three-dimensional rotations by three shears
Graphical Models and Image Processing
Optimizing the resampling of registered images
Handbook of medical imaging
Fast rotation of volume data on data parallel architectures
VIS '91 Proceedings of the 2nd conference on Visualization '91
Optimal filter design for volume reconstruction and visualization
VIS '93 Proceedings of the 4th conference on Visualization '93
Convolution-based interpolation for fast, high-quality rotation of images
IEEE Transactions on Image Processing
Solving inverse configuration space problems by adaptive sampling
Computer-Aided Design
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Algorithms for rotation of 2D images by multiple shearing transformations are well known; algorithms which use as few as four shears to perform an arbitrary 3D rotation on a 3D volume have also been described. By using Fourier transform methods to implement these shears, rotations can be performed completely reversibly and without loss of information. This is of great utility when the rotated data are used as input to statistical calculations, for example in human brain imaging. In general, six different patterns of four shears can be used to implement a given 3D rotation. We examine the mathematical and implementation details of these rotation algorithms. This paper provides a classification of these patterns, demonstrates that a consistent scheme must be used to select shear patterns for various rotations, and presents several such consistent schemes.