Distance Constraint
The next equality constraint we will derive is the distance constraint. A distance constraint can be used to join two bodies at a fixed distance. It can also be used as a spring between two bodies.
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Category: Game Development
Point-to-Point Constraint
As the first entry after the Equality Constraints post, we will perform the derivation of the Point-to-Point constraint, which models a Revolute Joint, in 2D.
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Equality Constraints
After the first release of the dyn4j project, I felt that it would be good to pass along what I learned about constrained dynamics.
This is not an easy subject and aside from purchasing books there’s not much information out there about it for those of us not accustomed to reading research papers or theses.
In this post I plan to solve a velocity constraint generally. Later posts will be for the individual types of constraints.
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EPA (Expanding Polytope Algorithm)
In the last few posts we learned about using GJK for collision detection, distance between shapes, and finding the closest points. It was stated that GJK must be augmented, to find collision information like the penetration depth and vector, with another algorithm. One such algorithm is EPA.
I plan to cover the EPA algorithm and mention an alternative.
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GJK – Distance & Closest Points
The last installment talked about the GJK algorithm as it pertains to collision detection. The original algorithm actually is used to obtain the distance and closest points between two convex shapes.
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GJK (Gilbert–Johnson–Keerthi)
Today I’m going to talk about the other collision detection algorithm packaged with the dyn4j project. You can find a lot of GJK documentation but much of it is really technical mostly because they are research papers. I strongly recommend this video tutorial and to be honest you may not even need to read any further after watching. But if you feel you need more information after watching the video please read on.
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SAT (Separating Axis Theorem)
This is a post I have been meaning to do for some time now but just never got around to it. Let me first start off by saying that there are a ton of resources on the web about this particular collision detection algorithm. The problem I had with the available resources is that they are often vague when explaining some of the implementation details (probably for our benefit).
I plan to explain the algorithm and also fill in some of the blanks that I had when implementing this myself.
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