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)
n | Number of observations. |
---|---|
sd | 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
set.seed(22764L) # real projective plane embedding in 4-space x <- sample_projective_plane(120) pairs(x, asp = 1, pch = 19, cex = .5)