Calculate curvature for 3 Points (x,y)

Question

I have a two dimensional euclidean space. Three points are given.

For example (p2 is the middle point):

Point2D p1 = new Point2D.Double(177, 289);
Po         


        

Answer 1

C/C++

// https://www.mathopenref.com/coordtrianglearea.html
float getAreaOfTriangle(Point2f A, Point2f B, Point2f C)
{
    return fabs(
            (A.x * (B.y - C.y) + B.x * (C.y - A.y) + C.x * (A.y - B.y)) / 2);
}

float getDistFromPtToPt(Point2f pt1, Point2f pt2)
{
    return sqrt((pt2.x - pt1.x) * (pt2.x - pt1.x) +
                (pt2.y - pt1.y) * (pt2.y - pt1.y));
}


// https://en.wikipedia.org/wiki/Menger_curvature
float
getCurvatureUsingTriangle(Point2f pt1, Point2f pt2, Point2f pt3, bool bDebug)
{
    float fAreaOfTriangle = getAreaOfTriangle(pt1, pt2, pt3);
    float fDist12 = getDistFromPtToPt(pt1, pt2);
    float fDist23 = getDistFromPtToPt(pt2, pt3);
    float fDist13 = getDistFromPtToPt(pt1, pt3);
    float fKappa = 4 * fAreaOfTriangle / (fDist12 * fDist23 * fDist13);
    return fKappa;
}