1/3/2023 0 Comments Vector 2d collision![]() ![]() This is an extremely simple calculation once you understand the intuition behind it. Check if the origin lies inside the Minkowski boxįinding the minkowski difference algorithmically.Find the Minkowski difference (which is just a rectangle) of the two bounding boxes.Now our algorithm for doing collision detection should be super clear! All we have to do is: Therefore, if the Minkowski difference of box A and box B contains the origin, the two boxes must be share a point, and are colliding! If two boxes contain the same point, then when we subtract those two points, we’ll get the origin. The beauty of the Minkowski method is that it encodes this condition perfectly. What does it mean for two boxes to collide? Well, one way of formulating the answer to that is that there exists some point which lies inside both boxes. Now, the question becomes: How can we leverage this to do collision detection? The answer is pretty simple. You can see that something which sounds confusing like ‘subtract every point on one shape from every point on another shape’ really has a straightforward geometric interpretation in this context. Ditto for the bottom right corner and the purple rectangle from step two. There we go! That’s the Minkowski difference of these two rectangles! The top right of this black rectangle is exactly the green rectangle from step one. To visualize the rest of the shape, we can just fill in the middle! If you do this process for all four corners, you end up with this: Hence, doing this little process on the corners gives us the extremes of the Minkowski difference. From these two corners, we can see that every point between the top of the green rectangle and the bottom of the purple rectangle is included in the Minkowski difference. The purple rectangle is the same as the green rectangle, but shifted down by the height of the blue rectangle. For our case of axis-aligned rectangles, simply subtracting the corners and filling in the gaps will give us exactly what we need. That wasn’t so bad! But aren’t there infinitely many points on a rectangle? How are we going to subtract ALL of them, given that my computer only runs at about 3 GHz? The answer is that we don’t need to do all of the infinitely many points to see where this is going, thankfully. The green rectangle is the resulting shape. The black vector is the vector we’re subtracting. Start with subtracting the bottom left corner of the blue from every point on the red. We’re going to find the Minkowski difference of the blue rectangle and the red rectangle. Geometrically, the Minkowski difference of two 2D shapes is the shape produced when you subtract every point on one shape from every point on the other shape. Minkowski Difference what is a minkowski difference? The methods in this article can be extended to more general cases, too. This guide uses the case where your game geometry is 2D, axis aligned rectangles, which can cover pretty much any 2D game that only needs basic collision detection. ![]() The intent is to give you a solid intuition for a concept that is very fundamental in many collision detection algorithms, as well as what problems you need to solve to extend my basic presentation of it! #Vector 2d collision how to#This post is going to explain the basic idea behind a Minkowski difference – what they are, how to visualize them geometrically, and a simple case of leveraging them for collision detection. finding the minkowski difference algorithmically.\boldsymbol sim = Simulation ( nparticles, radii, styles ) sim. The elastic collision between two particles occurs when their centres are separated by the sum of their radii and the collision event changes their velocities to: Particles move within the domain $0 \le x < 1$, $0 \le y < 1$ and are reflected (elastically) off the edges (walls) of this domain. Each "particle" of the simulation is represented by an instance of the Particle class and depicted as a circle with a fixed radius which undergoes elastic collisions with other particles.Ī Particle's position and velocity vectors are represented by NumPy arrays r and v, but their components can be retrieved and set by using the shortcuts Particle.x, Particle.y etc., implemented as class properties. The animation is carried out using Matplotlib's FuncAnimation method and is implemented by the class Simulation. This small Python project is a physical simulation of two-dimensional physics. ![]()
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