如何找到曲线和圆的交点? [英] How to find an intersection of curve and circle?

问题描述

我有一条曲线是从经验数据中得出的，我可以获得一个合理的模型.我需要确定曲线与已知中心和半径的圆相交的点(x，y).以下代码说明了这个问题.

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 and radius. The following code illustrates the question.

x <- c(0.05, 0.20, 0.35, 0.50, 0.65, 0.80, 0.95, 
   1.10, 1.25, 1.40, 1.55, 1.70, 1.85, 2.00, 
   2.15, 2.30, 2.45, 2.60, 2.75, 2.90, 3.05)

y <- c(1.52, 1.44, 1.38, 1.31, 1.23, 1.15, 1.06,
   0.96, 0.86, 0.76, 0.68, 0.61, 0.54, 0.47, 
   0.41, 0.36, 0.32, 0.29, 0.27, 0.26, 0.26)

fit <- loess(y ~ x, control = loess.control(surface = "direct"))
newx <- data.frame(x = seq(0, 3, 0.01))
fitline <- predict(fit, newdata = newx)
est <- data.frame(newx, fitline)

plot(x, y, type = "o",lwd = 2)
lines(est, col = "blue", lwd = 2)

library(plotrix)
draw.circle(x = 3, y = 0, radius = 2, nv = 1000, lty = 1, lwd = 1)

推荐答案

使用sf包中的函数轻松找到交点.

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

计算圆值(受此答案和将预测值和圆值转换为简单特征"(LINESTRING)，并找到它们的交点(a POINT):

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)

将交点添加到图中:

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

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