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Given a point (pX, pY) and a circle with a known center (cX,cY) and radius (r), what is the shortest amount of code you can come up with to find the point on the circle closest to (pX, pY) ?
I've got some code kind of working but it involves converting the circle to an equation of the form (x - cX)^2 + (y - cY)^2 = r^2 (where r is radius) and using the equation of the line from point (pX, pY) to (cX, cY) to create a quadratic equation to be solved.
Once I iron out the bugs it'll do, but it seems such an inelegant solution.
545
The closest pair is the minimum of the closest pairs within each half and the closest pair between the two halves. To split the point set in two, we find the x-median of the points and use that as a pivot. Finding the closest pair of points in each half is subproblem that is solved recursively.
Distance Formula for a Point and the Center of a Circle: d=√(x−h)2+(y−k)2 d = ( x − h ) 2 + ( y − k ) 2 , where (x, y) is the point and (h,k) is the center of the circle. This formula is derived from the Pythagorean Theorem.
where P is the point, C is the center, and R is the radius, in a suitable "mathy" language:
V = (P - C); Answer = C + V / |V| * R; where |V| is length of V.
OK, OK
double vX = pX - cX; double vY = pY - cY; double magV = sqrt(vX*vX + vY*vY); double aX = cX + vX / magV * R; double aY = cY + vY / magV * R; easy to extend to >2 dimensions.
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i would make a line from the center to the point, and calc where that graph crosses the circle oO i think not so difficult
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answered Oct 01 '22 11:10
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