This is an easy problem if you compute the distance from the corner of the square at the center of the circle (just whether
d is less-than-or-equal to
r), but is it possible to determine from the point opposite that one without computing the distance from the circle's center.
The context is for image processing. I have the four outer corners of a bounding box but any algorithmic solution becomes complex when you need to compute which part of the bounding box a particular point is. However, I know that every point is inside the bounding box, so I'm wondering if it's possible to measure the distance from all four outer points and determine if a point would lie outside a circle based on its distance from those four corners.