real-projective-planes | R Documentation |
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. \Sexpr[results=rd]{tools:::Rd_expr_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)
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