box_set: Evenly spaced samples across a one- or two-dim domain

In mosaicCalc: R-Language Based Calculus Operations for Teaching

Evenly spaced samples across a one- or two-dim domain

Description

This function breaks up a domain in 1- or 2- dimensions into evenly spaced samples. It returns a data frame of the position of the samples, each of which can be considered to correspond to a Riemann bin for the purposes of integration.

Usage

box_set(tilde = NULL, domain, n = 10, sum = FALSE, dx = NULL)

Arguments

tilde	A tilde expression specifying the function to be evaluated on the domain.
domain	Either a one- or two-dimensional domain in the same format as for slice_plot() or contour_plot(), or a data frame with two columns specifying the coordinates of a polygon defining the area.
n	the number of divisions along each of the x- and y-directions. Can be a vector of length 2 giving different numbers for the x and for the y directions.
sum	If TRUE carry out the integral and return the numerical result.
dx	An alternative way of specifying the box size directly. Same for all dimensions.

Value

By default, a data frame listing the location of the samples, the .output. value of the given function at those samples, the spatial extent of the samples (that is, dx for one-dimension or dx and dy for two dimensions. There is also a dA giving the dx or dx*dy depending on the dimension). If sum=TRUE, then returns the sum of .output * dA, that is, the estimate of the integral of the function over the domain.

Examples

box_set(x*y ~ x & y, domain(x=0:1, y=0:1), n = 4)
# approximation to the variance of a uniform [0,1] distribution
box_set((x-.5)^2 ~ x, domain(x=0:1), n=100, sum=TRUE)
# a polygon
poly <- tibble(x = c(1:9, 8:1), y = c(1, 2*(5:3), 2, -1, 17, 9, 8, 2:9))
boxes <- box_set(1 ~ x & y, poly, dx = 1)
gf_polygon(y ~ x, data = poly, color="blue", fill="blue", alpha=0.2) %>%
  gf_rect((y - dy/3) + (y + dy/3) ~ (x - dx/3) + (x + dx/3),
  data = boxes)
# area inside polygon
box_set(1 ~ x & y, poly, n=100)

mosaicCalc documentation built on Sept. 11, 2024, 9:10 p.m.