These functions generate uniform samples from real projective planes in 4-dimensional space, optionally with noise.
Number of observations.
Standard deviation of (independent multivariate) Gaussian noise.
The real projective plane only embeds into a Euclidean space of dimension at least 4. This embedding is adapted from Wikipedia. The uniform sample is generated through a rejection sampling process as described by Diaconis, Holmes, and Shahshahani (2013).
P Diaconis, S Holmes, and M Shahshahani (2013) Sampling from a Manifold. Advances in Modern Statistical Theory and Applications: A Festschrift in honor of Morris L. Eaton, 102–125. doi: 10.1214/12-IMSCOLL1006
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