如何计算一个点是否在一个圆内

Question

I am given a constructor:

Circle::Circle(const Point& c, float r) {
    x_ = c.getX();
    y_ = c.getY();
    r_ = r;
}

All values have been initialised as shown. In the parameter I have Point& - This just allows me to get the x and y coords using a function from a different class. Also, I have "r" which will take in the radius value.

Using this I want to check whether that: If o is a circle, it returns true if and only if p is on the inside or the boundary of the circle

For example,

I am given: Point p(1,2); & Circle c(p,3);

I want to check if Point(3.9,2) is on the inside or on the boundary of Circle c(p,3);

For extra reference, I will provide the Point Constructor :

Point::Point(float x, float y) {
    x_ = x;
    y_ = y;
}

Initialised constructor to allow me to create getter and setters for use in other classes.

In my function I have tried this:

bool Circle::contains(const Point& p) const {

    bool results; 
    if( ( (getX()-p.getX() ) * ( getX()-p.getX() ) ) + ( ( (getY()-p.getY() ) * ( getY()-p.getY() ) ) <= (getR()*getR())))


    {
        results = true;
    }
else {results = false;}
return results;
}

This did not work.

Test Case I am given:

    Point p(1,2);
Circle c(p,3);
if (!c.contains(p)) errorOut_("c does not contain p?",1);
if (!c.contains(Point(3.9,2))) errorOut_("c does not contain (3.9,2)?",1);
if (!c.contains(Point(3.1,4.1))) errorOut_("c does not contain (3.1,4.1)?",1);
if (!c.contains(Point(-1.1,4.1))) errorOut_("c does not contain (-1.1,4.1)?",1);
if (!c.contains(Point(-1.1,-0.1))) errorOut_("c does not contain (-1.1,-0.1)?",1);
if (!c.contains(Point(3.1,-0.1))) errorOut_("c does not contain (3.1,-0.1)?",1);
if (c.contains(Point(3.2,4.2))) errorOut_("c contains (3.2,4.2)?",1);
if (c.contains(Point(-1.2,4.2))) errorOut_("c contains (-1.2,4.2)?",1);
if (c.contains(Point(-1.2,-0.2))) errorOut_("c contains (-1.2,-0.2)?",1);
if (c.contains(Point(3.2,-0.2))) errorOut_("c contains (3.2,-0.2)?",1);

The result:

fail1: c contains (-1.2,4.2)?
fail1: c contains (-1.2,-0.2)?
fail1: c contains (3.2,-0.2)?

Answer 1

To check whether point lies inside circle, you need to implement this formula (strict < if you don't need points at circumerence):

 (px-cx)*(px-cx) + (py-cy)*(py-cy) <= r*r

Squared distance from point to center should be less than squared radius (to avoid sqrt calculation)

For your example

(3.9-1)^2+(2-2)^2 = 8.41 < 3*3=9   - inside

Corrected your function:

bool Circle::contains(const Point& p) const {
    return ( ( (getX()-p.getX() ) * ( getX()-p.getX() ) ) + 
             ( ( (getY()-p.getY() ) * ( getY()-p.getY() ) ) <= (getR()*getR())))
}