我有一对点，我想找到一个由这两个点确定的已知r的圆。我将在模拟中使用它，并且x和y可能有边界（例如-200、200的框）。
It is known半径的平方是
(x-x1)^2 + (y-y1)^2 = r^2
(x-x2)^2 + (y-y2)^2 = r^2
我现在想解决这个非线性方程组，以获得两个潜在的圆心。我尝试使用软件包
BB。这是我微不足道的尝试，只给出了一点。我想得到的是两种可能的观点。在任何可能的情况下，任何指向正确方向的指示都将免费赠送啤酒。library(BB)
known.pair <- structure(c(-46.9531139599816, -62.1874917150412, 25.9011462171242,
16.7441676243879), .Dim = c(2L, 2L), .Dimnames = list(NULL, c("x",
"y")))
getPoints <- function(ps, r, tr) {
# get parameters
x <- ps[1]
y <- ps[2]
# known coordinates of two points
x1 <- tr[1, 1]
y1 <- tr[1, 2]
x2 <- tr[2, 1]
y2 <- tr[2, 2]
out <- rep(NA, 2)
out[1] <- (x-x1)^2 + (y-y1)^2 - r^2
out[2] <- (x-x2)^2 + (y-y2)^2 - r^2
out
}
slvd <- BBsolve(par = c(0, 0),
fn = getPoints,
method = "L-BFGS-B",
tr = known.pair,
r = 40
)
您可以通过以下代码以图形方式看到此代码，但是您将需要一些额外的软件包。
library(sp)
library(rgeos)
plot(0,0, xlim = c(-200, 200), ylim = c(-200, 200), type = "n", asp = 1)
points(known.pair)
found.pt <- SpatialPoints(matrix(slvd$par, nrow = 1))
plot(gBuffer(found.pt, width = 40), add = T)
附录
谢谢大家的宝贵意见和代码。我提供了张贴者的回答时间，张贴者用代码补充了他们的回答。
test replications elapsed relative user.self sys.self user.child sys.child
4 alex 100 0.00 NA 0.00 0 NA NA
2 dason 100 0.01 NA 0.02 0 NA NA
3 josh 100 0.01 NA 0.02 0 NA NA
1 roland 100 0.15 NA 0.14 0 NA NA
最佳答案
这是其他人都提到的解决问题的基本几何方法。我使用polyroot来获得所得二次方程的根，但是您可以轻松地直接使用二次方程。
# x is a vector containing the two x coordinates
# y is a vector containing the two y coordinates
# R is a scalar for the desired radius
findCenter <- function(x, y, R){
dy <- diff(y)
dx <- diff(x)
# The radius needs to be at least as large as half the distance
# between the two points of interest
minrad <- (1/2)*sqrt(dx^2 + dy^2)
if(R < minrad){
stop("Specified radius can't be achieved with this data")
}
# I used a parametric equation to create the line going through
# the mean of the two points that is perpendicular to the line
# connecting the two points
#
# f(k) = ((x1+x2)/2, (y1+y2)/2) + k*(y2-y1, x1-x2)
# That is the vector equation for our line. Then we can
# for any given value of k calculate the radius of the circle
# since we have the center and a value for a point on the
# edge of the circle. Squaring the radius, subtracting R^2,
# and equating to 0 gives us the value of t to get a circle
# with the desired radius. The following are the coefficients
# we get from doing that
A <- (dy^2 + dx^2)
B <- 0
C <- (1/4)*(dx^2 + dy^2) - R^2
# We could just solve the quadratic equation but eh... polyroot is good enough
k <- as.numeric(polyroot(c(C, B, A)))
# Now we just plug our solution in to get the centers
# of the circles that meet our specifications
mn <- c(mean(x), mean(y))
ans <- rbind(mn + k[1]*c(dy, -dx),
mn + k[2]*c(dy, -dx))
colnames(ans) = c("x", "y")
ans
}
findCenter(c(-2, 0), c(1, 1), 3)