Category Archives: Polygons

Closest Points Between Polygons

Here we examine an algorithm that computes the pair of points that are closest to each other while still being inside each of a pair of polygons. The name of the algorithm that solves this problem is called the Lemke Algorithm. The Lemke Algorithm is able to solve a set of simultaneous equations that define mathematically the set of constraints described above. … Continue reading …

Separating Axes

Here we continue our exploration of polygons and collision detection. This sketch detects the intersection of two convex polygons using the method of separating axes. The method of separating axes considers each edge of a given polygon, and determines the projection of the extreme vertices of another polygon onto the line defined by the endpoints of the edge. … Continue reading …

Axis Projection

Here we continue our exploration of polygons, and specifically the projection of their extreme vertices on an arbitrary line or axis. What do I mean by extreme vertices? I mean the pair of vertices that are the most nearly aligned with a given line or axis. How do we determine that pair of vertices? … Continue reading …

Convex Hull

Convex Hull. This week I’ve decided to explore polygons. It’s essential to understand how to represent polygons for two-dimensional physical simulations. As its name implies, this sketch is a visualization of a Graham Scan: an algorithm for computing the convex hull of a finite set of points. … Continue reading …