Find the intercept of a line with the unit circle

Vectorised over its arguments: each `(x0, y0)` -> `(x1, y1)` pair gives one row of the result.

Usage

line_circle_intercept(x0, y0, x1, y1)

Arguments

x0, y0

Starting coordinates of the vector.

x1, y1

Ending coordinates of the vector.

Value

A tibble with the intersection point closest to `(x1, y1)`.

Examples

# A ray from the origin through (2, 0) hits the unit circle at (1, 0)
line_circle_intercept(0, 0, 2, 0)
#> # A tibble: 1 × 2
#>   x_int y_int
#>   <dbl> <dbl>
#> 1     1     0

# Vectorised: multiple rays at once
line_circle_intercept(c(0, 0), c(0, 0), c(2, 0), c(0, 3))
#> # A tibble: 2 × 2
#>   x_int y_int
#>   <dbl> <dbl>
#> 1     1     0
#> 2     0     1