如何在闪亮或R代码中计算两个圆的相交面积

Question

谁有关于如何计算两个圆的交点面积的闪亮代码或 R 代码？

用户界面

图书馆（闪亮）

为绘制直方图的应用程序定义 UI

shinyUI(fluidPage(

# 应用程序标题 titlePanel("选择你的概率"),

# 带有滑动条输入箱数的侧边栏 侧边栏布局（ 侧边栏面板（

  sliderInput("radius",
              "Probability of A",
              min = 0,
              max = 0.4,
              value = 0.2),
  sliderInput("radius2",
              "Probability of B",
              min = 0,
              max = 0.4,
              value = 0.2)
),
mainPanel(
  plotOutput("distPlot")
)

) ))

服务器

图书馆（闪亮） 图书馆（情节） 图书馆（网格）

定义绘制直方图所需的服务器逻辑

shinyServer（函数（输入，输出）{

输出$distPlot

isolate({
  plot(c(-1,1),c(-1,1), type = 'n')


})

draw.circle(-0.25,0,input$radius)
draw.circle(0.25,0,input$radius2)

})

})

Answer 1

你可以用这个：

circle_intersection <- function(x1, y1, r1, x2, y2, r2){
  rr1 <- r1 * r1
  rr2 <- r2 * r2
  d <- sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1))
  
  if (d > r2 + r1) # Circles do not overlap
  {
    return(0)
  } else if (d <= abs(r1 - r2) && r1 >= r2){ # Circle2 is completely inside circle1  
    return(pi*rr2)
  } else if (d <= abs(r1 - r2) && r1 < r2){ # Circle1 is completely inside circle2
    return(pi*rr1)
  } else { # Circles partially overlap
    phi <- (acos((rr1 + (d * d) - rr2) / (2 * r1 * d))) * 2
    theta <- (acos((rr2 + (d * d) - rr1) / (2 * r2 * d))) * 2
    area2 <- 0.5 * theta * rr2 - 0.5 * rr2 * sin(theta)
    area1 <- 0.5 * phi * rr1 - 0.5 * rr1 * sin(phi)
    return(area1 + area2)
  }
}

circle_intersection(-0.25,0,0.2,0.25,0,0.2)  # 0 (Circles do not overlap)
circle_intersection(-0.25,0,0.2,-0.25,0,0.1) # 0.031 (Circle2 is completely inside circle1)
circle_intersection(-0.25,0,0.1,-0.25,0,0.2) # 0.031 (Circle1 is completely inside circle2)
circle_intersection(-0.25,0,0.3,0.25,0,0.4)  # 0.06641675 (Circles partially overlap)