Saturday 8 August 2009
Two interesting problems I've had to solve this week...
Given a point p and a radius r, consider the family of circles Ct, where t is a positive real number, with centres tp and radii tr. Given a point q, find the smallest value of t such that the circle Ct contains q. You may assume |p| < r. This came up while I was optimizing repeating radial gradients for Mac.
Given a set of non-overlapping axis-aligned rectangles in the plane, and a 2D vector v, order the rectangles in a sequence so that translating each rectangle one by one by v does not have any overlapping rectangles in the intermediate states. Does such an order always exist? This came up while I worked on optimizing scrolling.