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Allen Chou

Member Since 15 Jul 2010
Offline Last Active May 24 2014 11:01 PM

Topics I've Started

Interpolating Quaternions with Circular Blending

18 April 2014 - 02:52 PM

Hi, all:

 

I wrote a post on interpolating quaternions with circular blending.

 

http://allenchou.net/game-math-series/

 

Circular blending is an interpolation technique that produces "quaternion curves" with C1 continuity, as opposed to the commonly used piece-wise slerp technique that has only C0 continuity.

 

Here's a video comparing the two techniques.

 

https://www.youtube.com/watch?v=rsx9BGZiX_E


I gave a lecture on constraint-based physics, and here are the slides.

18 April 2014 - 12:51 AM

Hi, all:

This is my last semester at DigiPen Institute of Technology, so I decided to give a lecture to my fellow schoolmates on constraint-based physics to pass down a few things I know about implementing game physics.

Here are the slides I used:
http://allenchou.net/slides-constraint-based-physics/

Below are the main points I went over in this lecture:

  • The flow chart of a typical physics engine.
  • How to derive velocity constraints.
  • Contact constraints, including normal and tangential resolutions.
  • Solving multiple constraints simultaneously (block-solving).

You don't really need to implement a full-blown physics engine with narrow phase, broad phase, and other fancy stability features like contact caching and warm starting, just in order to get something cool. In the end, I presented a simple constraint, the mouse constraint, as an exercise homework.

I encourage anyone who hasn't done any physics-related stuff to try implementing mouse constraints with a simple semi-implicit Euler integrator; you will end up with something you can drag around, reacting and looking physically "correct".

If you are not familiar with motion dynamics, I also wrote two posts on its fundamentals and implementation examples, please do check them out:
http://allenchou.net/2013/12/game-physics-motion-dynamics-fundamentals/
http://allenchou.net/2013/12/game-physics-motion-dynamics-implementations/

Lastly, here's a full list of the posts I have written on game physics:
http://allenchou.net/game-physics-series/

As always, please tell me if you think I've got something wrong. Thanks smile.png


Quaternion Basics

09 April 2014 - 02:05 AM

Hi, all:

 

I've written a post on quaternion basics.

 

http://allenchou.net/2014/04/game-math-quaternion-basics/

 

It covers the basic operations of quaternions and slerp.

 

I hope some people find this post useful smile.png


My Game Math Series (Ongoing & Seeking New Topic Recommendations)

03 March 2014 - 11:21 PM

Hi, everyone:

 

Recently, I decided to start a game math series on my blog.
Please tell me what you'd like to read to help me plan out what to write about.

 

Thanks smile.png

 

Below is a list of written posts and planned topics:

 

http://allenchou.net/game-math-series/

 

Vector Math

Linear Algebra

 

Coordinate Systems

  • Complex Numbers (Planned)
  • Polar Coordinates (Planned)

Quaternions

  • Quaternion Basics (Planned)
  • Quaternions as 3D Rotations (Planned)

Misc. Polyhedon-Related Posts for Game Physics

19 February 2014 - 08:04 PM

Hi, everyone:

 

I wrote a couple of miscellaneous posts on polyhedron-related stuff for my game physics series on my blog.

 

The first post explains how you can use the half edge data structure to implement a better support function for polyhedrons utilizing a hill-climbing approach, as opposed to the most obvious brute-force approach. It also shows an example implementation of dynamic half edge data structure.

http://allenchou.net/2014/02/game-physics-implementing-support-function-for-polyhedrons-using-half-edges/

 

The second post demonstrates 3 options for updating the AABBs of polyhedrons, namely the brute-force approach, approximation by local AABB, and the support function approach. This posts also touches on their pros and cons.

http://allenchou.net/2014/02/game-physics-updating-aabbs-for-polyhedrons/

 

Here's a list of all posts of the game physics series that lead up to these two posts.

http://allenchou.net/game-physics-series/

 

I hope you like it smile.png


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