For the most simple of 2D games, I have implemented a posteriori collision detection (overlapping rectangles) on the x/y Cartesian plane, but am now interested in understanding the basics of a priori collision detection...
In the link here, I noticed the reference to Newton’s Method. So, I want to better understand the link b/w finding zeros of an equation and detecting a posteriori collision.
Let's start with the most obvious case of finding roots of an equation: If you have a projectile's trajectory modeled as a quadratic function, you can find the roots to predict at what time the height will equal zero (or any other constant height, actually, by just solving f(x)=C to be f(x)-C=0 and then finding roots of that expression).
So, as I understand, finding the root can tell me the time at which the object will be at any chosen height. More broadly, we basically know the (x,y) location of the object for any given time. But how does root finding, in particular, translate to detecting collisions with another object? (The other object may be stationary, or be moving. If the latter, do you also determine roots/location of this moving object as well? Calculate the (x,y) trajectory of both objects and determine where they will intersect?)
Again, the basic question is where does root finding come into play? Any links to a basic primer on this topic, with a simple example would also be greatly appreciated.
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