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Please help me chose Physics and collision engine

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Hello!

Before all I'll state some info:
-I made a 2d game engine complete with physics, graphics, entity system, sounds etc before.
-I want to expand and move onto the 3D world
-Contrary to the last engine I want to use third party libs to help me.

I've decided on Horde3D for graphics, Fmod for Sound, custom model and map format.
Right now I want to chose a physics and collision engine.

[b]Here's what I want from it:
[/b]
[list][*][b]C++[/b][*]3D[*]Pretty optimized (my game won't be very physics heavy but the faster the better)[*]Great handling of collisions (things can't fall though floor nor sink into it like it often happens in ODE)[*]It must let me cast rays, polygons, check if a box at a given place [b]would[/b] collide and other such things (I'd use this for AI and other such things).[*]it must be able to use convex meshes for collision check.[*]physics-wise it should either enable concave meshes or let one object be made out of several convex ones.[*]I can use it without paying royalties or having to release the source code to my program.[*]not a complete pain to use.[*]should be able to handle physics by its own but also allow me to step in when I need it.[/list]
[b]What I want to accomplish in my game:[/b]
[list][*]physically reactive animated ragdolls for characters (see one of the Overgrowth fighting videos, you notice they go limp from hits but quickly resume their stance)[*]physics based AI[*]semi-physics based movement (eg: if the player is controling a bird I want it to fly realistically, unlike WoW where it can just stop in mid air)[*]buoyancy[*]being able to destroy houses/towers or other constructions made from preset destructibe geometry pieces.[/list]
As you can see my biggest focus is on characters and the amount of control I can have over the behavior of each individual part, I don't know the favs and cons of the existing engines which is why I'm asking you for help. So far I've only tried ODE (since yesterday) and I've seen that it's not the best collision handling engine (things like to sink into each other a bit ). I saw somewhere that it can be used with SOLID to do the collision detection and solution, but I still haven't seen SOLID's features.

So, I'm asking you for your input, which engine do you use or used in the past, which do you think is the best , what are its shortcomings, what are its strengths ,how it compares to others, etc.
I'd also love if someone explained to me how are such libraries integrated into the game engine itself. I did a 2d polygon based collision system for my last engine but it was pretty much well integrated into the entity system from the start so I didn't learn much about adding a 3rd party one.

Also if any of you could point me to open source 3d games that use the physics engines so I could learn from them I would be grateful.


[b]Tl;dr version:[/b]
I need a good physics and collision engine, help me chose!.

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Your options pretymuch are[url="http://bulletphysics.org/wordpress/"] Bullet[/url], [url="http://www.havok.com/index.php?page=havok-physics"]Havok[/url], or [url="http://www.nvidia.com/object/physx_new.html"]Physx[/url].

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I would normally suggest Tokamak(www.[b]tokamakphysics[/b].com/) and listen to people complain that it doesn't support soft bodies and other minor details (although, IMHO, its ragdoll physics are the best), but then you said you wanted to use it for physics based A.I. So definitely look at Havok(Stated above), its free version should fit your needs just fine.

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