How to find an intersection of curve and circle?

Question

I have a curve, derived from empirical data, and I can obtain a reasonable model of it. I need to identify a point (x, y) where the curve intersects a circle of known center

Answer 1

It's straightforward to find the intersection using functions from the sf package.

Calculate the circle values (inspired by this answer and as done by @Onyambu)

circ <- function(xc = 0, yc = 0, r = 1, n = 100){
  v <- seq(0, 2 * pi, len = n)
  cbind(x = xc + r * cos(v),
        y = yc + r * sin(v))
}

m <- circ(xc = 3, yc = 0, r = 2)

Convert the predicted values and the circle values to "simple features" (LINESTRING), and find their intersection (a POINT):

library(sf)
int <- st_intersection(st_linestring(as.matrix(est)),
                       st_linestring(m))
int
# POINT (1.2091 0.8886608)

Add the intersection to your plot:

plot(x, y, type = "o", lwd = 2)
lines(est, col = "blue", lwd = 2)
lines(m)
points(int[1], int[2], col = "red", pch = 19)