boolean isInRectangle(double centerX, double centerY, double radius, 
    double x, double y)
{
        return x >= centerX - radius && x <= centerX + radius && 
            y >= centerY - radius && y <= centerY + radius;
}    

//test if coordinate (x, y) is within a radius from coordinate (center_x, center_y)
public boolean isPointInCircle(double centerX, double centerY, 
    double radius, double x, double y)
{
    if(isInRectangle(centerX, centerY, radius, x, y))
    {
        double dx = centerX - x;
        double dy = centerY - y;
        dx *= dx;
        dy *= dy;
        double distanceSquared = dx + dy;
        double radiusSquared = radius * radius;
        return distanceSquared <= radiusSquared;
    }
    return false;
}

这样效率更高，可读性更强。它避免了昂贵的平方根运算。我还添加了一个检查，以确定点是否在圆的边界矩形内。

矩形检查是不必要的，除非有许多点或许多圆。如果大多数点都在圆圈内，边框检查实际上会使事情变慢!

像往常一样，一定要考虑您的用例。

你应该检查圆心到点的距离是否小于半径

使用Python

if (x-center_x)**2 + (y-center_y)**2 <= radius**2:
    # inside circle

我使用下面的代码为初学者像我一样:)。

公共类incirkel {

public static void main(String[] args) {
    int x; 
    int y; 
    int middelx; 
    int middely; 
    int straal; {

// Adjust the coordinates of x and y 
x = -1;
y = -2;

// Adjust the coordinates of the circle
middelx = 9; 
middely = 9;
straal =  10;

{
    //When x,y is within the circle the message below will be printed
    if ((((middelx - x) * (middelx - x)) 
                    + ((middely - y) * (middely - y))) 
                    < (straal * straal)) {
                        System.out.println("coordinaten x,y vallen binnen cirkel");
    //When x,y is NOT within the circle the error message below will be printed
    } else {
        System.err.println("x,y coordinaten vallen helaas buiten de cirkel");
    } 
}



    }
}}

下面是解决这个问题的简单java代码:

以及它背后的数学:https://math.stackexchange.com/questions/198764/how-to-know-if-a-point-is-inside-a-circle

boolean insideCircle(int[] point, int[] center, int radius) {
    return (float)Math.sqrt((int)Math.pow(point[0]-center[0],2)+(int)Math.pow(point[1]-center[1],2)) <= radius;
}

求圆心到所给点之间的距离。如果它们之间的距离小于半径，则该点在圆内。 如果它们之间的距离等于圆的半径，那么这个点就在圆的周长上。 如果距离大于半径，则该点在圆外。

int d = r^2 - ((center_x-x)^2 + (center_y-y)^2);

if(d>0)
  print("inside");
else if(d==0)
  print("on the circumference");
else
  print("outside");

iOS 15，接受的答案写在Swift 5.5

func isInRectangle(center: CGPoint, radius: Double, point: CGPoint) -> Bool
{
    return point.x >= center.x - radius && point.x <= center.x + radius &&
    point.y >= center.y - radius && point.y <= center.y + radius
}

//test if coordinate (x, y) is within a radius from coordinate (center_x, center_y)
func isPointInCircle(center: CGPoint,
                     radius:Double, point: CGPoint) -> Bool
{
    if(isInRectangle(center: center, radius: radius, point: point))
    {
        var dx:Double = center.x - point.x
        var dy:Double = center.y - point.y
        dx *= dx
        dy *= dy
        let distanceSquared:Double = dx + dy
        let radiusSquared:Double = radius * radius
        return distanceSquared <= radiusSquared
    }
    return false
}