I understand you think that a physics library is overkill for this, but many of the problems you're running into are already solved. The choice is yours to use the right tool for the job, or try coding your own solution.

Priyank Jain wrote:
Now, to do collision detection between the Ball (which I am considering to be a 
point for now, and thus a line given its velocity) and the World, I'd want a 
way for the line to be checked against the PAT transformed Bboxes. Any 
suggestions on how I should approach this (any callback that I should define or 
what)?

A bounding box (axis-aligned) is just two points. So you just need to transform those two points by the PAT's matrix.

Also, as per the API, I can retrieve the bounding box of a Geode and bounding 
sphere of a Node. Thus, if I were to use the above hierarchy, I would have 3 
bounding spheres for left/center/right Transform. What I really want is a 
bounding box for these 3, since the BS would be a very loose fit for the 
collision detection. So, do you recommend me organizing the hierarchy in any 
other way ?

Don't use the bounding sphere. Just use the bounding box of the Geode.

FYI, osgBullet has facilities to bridge the gap between OSG's inherently relative coordinate system and the inherently absolute coordinate system required for collision detection. osgBullet also has facilities for creating collision shapes from scene graphs, so even if the bounding box isn't axis-aligned, you can still create an exact collision shape.
   -Paul
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