#Vector 2d collision how to
#Vector 2d collision code

Wikipedia has a fantastic animation showing what happens in a 2D collision on their elastic collision page. This situation is very rare for large objects or even molecules, but generally holds for atoms.Īll collisions conserve momentum, which is the main tool for determining the motion resulting from a collision. Before we get ahead of ourselves, let’s create a Vector class with some useful linear algebra methods so we can work easily in a coordinate plane. The game seems to function correctly but Im not entirely sure my algorithm is correct.

#Vector 2d collision how to

In my last post, I discussed how to determine if any two convex shapes in two dimensions overlap. One object can lose all of its energy, but it must then transfer that energy to the other particle. I came up with an algorithm to calculate the resultant vector of the puck once it meets a paddle. Kenton Hamaluik Building a Collision Engine Part 2: 2D Penetration Vectors (). That is, the kinetic energy of the two particles before and after remains the same. You might wonder why we don’t check the BC line - this is because we can implicitly rule out the origin being along its perpendicular.This page is more simulations than calculations, because they are more fun.Ĭollisions between two objects are elastic only if there is no loss of kinetic energy. The implementation of the support function is quite simple:Ĭlass Polygon implements IShape Since the Minkowski Difference is shape a farthest point - shape b farthest point having the point of shape b being sampled from the opposite direction results in a support point that is as far as possible in the direction provided.

The reason we take points from opposite directions is so that we get a point on the Minkowski Difference that will result in the largest area, so there’s a better chance we can encapsulate the origin. Using these two farthest points a support point can be calculated on the Minkowski Difference shape. The support function then takes a point from each shape, the farthest in two opposite directions. The support function takes the two shapes being compared, and the direction you want to check in. The support function is a way to sample a point on the edge of the Minkowski Difference - without building the entire shape. In order to avoid this GJK uses two key concepts support functions and simplexes. Calculating Minkowski Differences could take a long time, especially if you are checking if two shapes with many points are intersecting. Taking these concepts the GJK algorithm optimises them. Minkowski Difference of Shape A and B: Note AD in the table and chart refers to A - D

Taking the values of shape A and shape B we can calculate the Minkowski Difference: The Minkowski Difference has the interesting property that if the two shapes are intersecting/overlapping the resulting Minkowski Difference will contain the origin. This is referred to in resources I’ve seen as the ‘Minkowski Difference’. GJK utilises a form of the Minkowski Sum that instead of A + B, it’s A - B. Minkowski Sum of Shape A and B: Note AD in the table and chart refers to A + DĪ nice way to think about the Minkowski Sum is imagine you take Shape A and trace the outline of Shape B with it, the shape it would result in would be the Minkowski Sum. If we take these values we can plot them on a graph and see the shape it results in. Taking the values of shape A and shape B we can calculate the Minkowski sum: For a review of vector algebra, necessary to understand the topic, you can also see the arti c le of this site. The Minkowski Sum is calculated by adding all the points of two shapes. This article describes the primitive geometric forms used in 2D collisions, with references to the features provided by the Unity’s 2D Physics engine. GJK uses a concept called the Minkowski Sum. It is fast, and is implemented using a generic ‘support function’ which allows for a more general approach - you can treat polygons and curved shapes such as ellipses in the same way. GJK is an algorithm designed to determine if two convex shapes are intersecting. We can solve 2D collision problems using Conservation of Momentum by just applying Vector Components. This post is written based on this article and the video it recommends:

#Vector 2d collision code

The code samples make use of some structures I have created and won’t detail in this post, but they are simple and you can see them in the GitHub repo:Īll the code this post uses is in a GitHub repo here: I’ve been trying to learn how collision detection works this lead me to the Gilbert-Johnson-Keerthi (GJK) algorithm.Īll code samples in this post are in TypeScript.