The Voronoi diagram is just the dual graph of the Delaunay triangulation. So, the edges of the Voronoi diagram are along the perpendicular bisectors of the edges of the Delaunay triangulation, so compute those lines. Then, compute the vertices of the Voronoi diagram by finding the intersections of adjacent edges. Finally, the edges are then … Read more
It’s possible to check if a point is inside a sector with only integer arithmetic and the basic operations of addition, subtraction and multiplication. For a point to be inside a circular sector, it has to meet the following tests: It has to be positioned counter-clockwise from the start “arm” of the sector. It has … Read more
As already said: there is no exact representation of the circle using Bezier curves. To complete the other answers : for Bezier curve with n segments the optimal distance to the control points, in the sense that the middle of the curve lies on the circle itself, is (4/3)*tan(pi/(2n)). So for 4 points it is … Read more
Here is how I would do it: bool intersects(CircleType circle, RectType rect) { circleDistance.x = abs(circle.x – rect.x); circleDistance.y = abs(circle.y – rect.y); if (circleDistance.x > (rect.width/2 + circle.r)) { return false; } if (circleDistance.y > (rect.height/2 + circle.r)) { return false; } if (circleDistance.x <= (rect.width/2)) { return true; } if (circleDistance.y <= (rect.height/2)) … Read more
There’s a nice approach to this problem that uses vector cross products. Define the 2-dimensional vector cross product v × w to be vx wy − vy wx. Suppose the two line segments run from p to p + r and from q to q + s. Then any point on the first line is representable as p + t r (for a scalar parameter t) and any point … Read more