Generate one point on arbitrary combination of hyperplanes

Given a hyperplane arrangement (specified by ineqmat) and a subset of those hyperplanes (specified numerically as the rows of ineqmat), determine some point that lies on the intersection of those hyperplanes. If the chosen hyperplanes do not all intersect in at least one point, returns NAs and throws a warning. This function exists mostly for the sake of calculations about a hyperplane arrangement itself, not for musical applications: its results are often not very scale-like (e.g., they often fail optc_test()).

Usage

point_on_flat(rows, card, ineqmat = NULL, edo = 12, rounder = 10)

Arguments

rows

Integer vector: which rows of ineqmat should be taken as hyperplanes defining the target flat?

card

Integer: the number of notes in your desired scale.

ineqmat

Specifies which hyperplane arrangement to consider. By default (or by explicitly entering "mct") it supplies the standard "Modal Color Theory" arrangements of getineqmat(), but can be set to strings "white," "black", "gray", "roth", "infrared", "pastel", "rosy", "infrared", or "anaglyph", giving the ineqmats of make_white_ineqmat(), make_black_ineqmat(), make_gray_ineqmat(), make_roth_ineqmat(), make_infrared_ineqmat(), make_pastel_ineqmat(), make_rosy_ineqmat(), make_infrared_ineqmat(), or make_anaglyph_ineqmat(). For other arrangements, this parameter accepts explicit matrices.

edo

Number of unit steps in an octave. Defaults to 12.

rounder

Numeric (expected integer), defaults to 10: number of decimal places to round to when testing for equality.

Value

Numeric vector of length card which lies on the specified hyperplanes. If the intersection of the hyperplanes is empty, throws a warning and returns a vector of NAs with length card.

See also

match_flat() and populate_flat() are intended for more concretely musical applications, returning a set on the chosen flat which is similar to an input set.

Examples

# Works essentially like an inverse of whichsvzeroes():
test_set <- sc(5, 32)
whichsvzeroes(test_set)
#> [1]  5  8 10
generated_point <- point_on_flat(c(5, 8, 10), card=5)
whichsvzeroes(generated_point)
#> [1]  5  8 10

# But note that the given point might lie on any face of the flat:
signvector(test_set)
#>  [1] -1 -1  1 -1  0 -1 -1  0 -1  0 -1 -1 -1  1  1
signvector(generated_point)
#>  [1]  1  1 -1  1  0  1  1  0  1  0  1  1  1 -1 -1

# Works for other hyperplane arrangements:
point_on_flat(c(2, 3, 6), card=3, ineqmat="roth")
#> [1] -6 -6  0
point_on_flat(c(2, 4), card=4, ineqmat="black")
#> [1] 0.02795603 3.00000000 0.46938430 9.00000000

# Not all combinations of hyperplanes admit a solution:
try(point_on_flat(c(1, 2, 3), card=3, ineqmat="roth"))
#> Warning: Intersection of specified hyperplanes is empty.
#> [1] NA NA NA