Update

collision_detection.md

@@ -5,7 +5,7 @@ Collision detection is an essential problem e.g. of simulating physics of mechan
 There are two main types of collision detection:
 
 - **[discrete](discrete.md)**: Detecting collisions only at one point in time (each engine tick or "frame") -- this is easier but can result in detecting the collisions in wrong ways or missing them completely (imagine a fast flying object that in one moment is wholly in front of a wall and at the next instant wholly behind it). Nevertheless this is completely usable, one just has to be careful enough about the extreme cases.
-- **[continuous](continuous.md)**: Detecting collisions considering the continuous motion of the bodies (still done at discrete ticks but considering the whole motion since the last tick) -- this is more difficult to program and more costly to compute, but also correctly detects collisions even in extreme cases. Sometimes engines perform discrete detection by default and use continuous detection in special cases (e.g. when speeds become very high or in other error-prone situations). Continuous detection can be imagined as a collision detection of a higher dimensional bodies where the added dimension is time -- e.g. detecting collisions of 2D spheres becomes detecting collisions of "tubes" in 3D space. If you don't want to go all the way to implementing continuous collisions, you may consider an in-between solution by detecting collisions in smaller steps (which may also be done only sometimes, e.g. only for high speed bodies or only when an actual discrete collision is detected).
+- **[continuous](continuous.md)**: Detecting collisions considering the continuous motion of the bodies (still done at discrete ticks but considering the whole motion since the last tick) -- this is more difficult to program and more costly to compute, but also correctly detects collisions even in extreme cases. Sometimes engines perform discrete detection by default and use continuous detection in special cases (e.g. when speeds become very high or in other error-prone situations). Continuous detection can be imagined as a collision detection of a higher dimensional bodies where the added dimension is time -- e.g. detecting collisions of 2D circles becomes detecting collisions of "tubes" in 3D space. If you don't want to go all the way to implementing continuous collisions, you may consider an in-between solution by detecting collisions in smaller steps (which may also be done only sometimes, e.g. only for high speed bodies or only when an actual discrete collision is detected).
 
 Collision detection is non-trivial because we need to detect not only the presence of the collision but also its parameters which are typically the exact **point of collision, collision depth and collision [normal](normal.md)** -- these are needed for subsequently resolving the collision (typically the bodies will be shifted along the normal by the collision depth to become separated and [impulses](impulse.md) will be applied at the collision point to update their velocities). We also need to detect **general cases**, i.e. collisions of whole volumes (imagine e.g. a tiny cuboid inside an arbitrarily rotated bigger cone). This is very hard and/or expensive for some complex shapes such as general 3D triangle meshes (which is why we approximate them with simpler shapes). We also want the detection algorithm to be at least reasonably **fast** -- for this reason collision detection mostly happens in two phases: