Encoding normal vectors using optimized spherical coordinates

We present a method for encoding unit vectors based on spherical coordinates that out-performs existing encoding methods both in terms of accuracy and encoding/decoding time. Given a tolerance ϵϵ, we solve a simple, discrete optimization problem to find a set of points on the unit sphere that can trivially be indexed such that the difference in angle between the encoded vector and the original are no more than ϵϵ apart. To encode a unit vector, we simply compute its spherical coordinates and round the result based on the prior optimization solution. We also present a moving frame method that further reduces the amount of data to be encoded when vectors have some coherence. Our method is extremely fast in terms of encoding and decoding both of which take constant time O(1). The accuracy of our encoding is also comparable or better than previous methods for encoding unit vectors.

Graphical abstractFigure optionsDownload full-size imageDownload high-quality image (295 K)Download as PowerPoint slideHighlights► A computationally efficient method for encoding and decoding 3D unit vectors. ► Computation time is constant and independent of the required accuracy. ► A differential encoding method using moving frames that drastically increases compression rates.