R/real-projective-plane.r
real-projective-planes.Rd
These functions generate uniform samples from real projective planes in 4-dimensional space, optionally with noise.
sample_projective_plane(n, sd = 0)
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