I am involved in the development of an open source game featuring theme park construction and operation. For this game I want to make a quadtree map for collisions to prevent two solid objects from going in the same space. ( I have considered octrees, but they don't seem useful in relatively flat space. Quadtrees would be sufficient.) That part is mostly figured out, except for the core collision testing for each object in the tree. Triangles are very precise, and would correspond to the object's graphics almost exactly. The problem is that the algorithm is a little "involved" - both for me and the processor. For spheres I easily do a single-line function based off of distance-squared. Boxes, as long as they are axis-aligned, would be a simple case of comparing bounds. I've looked over a few texts explaining triangle intersection, and they involve multiple steps and a lot of linear algebra. I generally understand the math and geometry behind it, but it seems too complex for my needs.

I would like a certain degree of precision (perhaps within a third of a meter or so), but with small radii and more points in the "cloud", I could make collisions somewhat accurate with variable-radius spheres. Axis-aligned boxes would require more comparisons, but not as many as triangles would. Plus I would still need a lot of "grains" to make the map accurate. Should I go for simple computations and high memory usage, or multiple step matrix and vector processing with lower memory usage? I would like graphical collision to be close to physical collision, but not exact. The polygon counts for large roller coaster track go into the 100K+ range. The number of objects on a map will be huge. Think along the lines of RollerCoaster Tycoon or SimCity. This game aspires to something of that scale, if not bigger.

I am using Irrlicht game library for this game. I know there are some collision checks in that engine, but they seem tied to graphics scenes. I may want to make the collision geometry for certain objects (like ride track) simpler than their graphical mesh geometry. I figured a custom tree would be needed for this task. With STL dynamic structures, that should be a piece of cake. But if someone can point me to a better way, I would be glad. I don't like reinventing the wheel if I don't need to.

Any general advice on collisions in 3D would be appreciated.

Personally I would go with whatever gave the tightest fit to the object. You don't want to use a sphere bounding radius when the object is cube shaped. Just have a couple predefined bouding shapes and pick or choose for each object. Your could use bounding meshes for complex objects, but this would be memory and cpu intensive.

I was thinking about that. Each occupancy in the tree could have a tag giving it's shape type. I think vertical cylinders may be easy to include as well. Any shape with simple bound checking would work.

Frankly, I don't understand why you'd need accurate clash checking for a theme park sim. What are the objects whose clashes you need to prevent?

Spherical collision is great performance-wise, but some meshes may be hard to sum up as a mere sphere and produce silly collisions depending on the radius you apply to them. The key to maximizing performance is skipping the sqrt on your distance call, and instead squaring the other side of the comparison equation... So that

[source lang="cpp"]
typedef struct
{
float x, y, z;
} vec3_t;

typedef struct
{
vec3_t origin;
float radius;
// etc properties...
} object_t;

// returns 1 if colliding, returns 0 if not..
int ObjectsColliding(object_t *a, object_t *b)
{
vec3_t delta;
float dist_sqr, sizes_sqr;;

delta.x = a->origin.x - b->origin.x;
delta.y = a->origin.y - b->origin.y;
delta.z = a->origin.z - b->origin.z;

dist_sqr = delta.x * delta.x + delta.y * delta.y + delta.z * delta.z;
sizes_sqr = a->radius + b->radius;
sizes_sqr *= sizes_sqr; // this is faster than sqrt(dist_sqr)

if(dist_sqr < sizes_sqr)
return 1;

return 0;
}
[/source]

Alternatively you could use axis-aligned bounding boxes but then everything collides as rectangular prisms (ala Quake1/2).
Or a combination of a vertical axis-aligned bounding 'space' (eg: a height) combined with an XY pythag collision to produce cylindrical collisions, which is better suited for bipedal type character collisions.. Or you can even implement all three options to be used with specific objects that each is better suited for, requiring that you implement detection for each possible type of collision (sphere/sphere, sphere/bbox, sphere/cylinder, bbox/bbox, bbox/cylinder, cylinder/cylinder).

I'm going to try Bullet. I didn't really want a full physics simulator, just something for space occupancy to prevent overlapping items. I'll see if Bullet has something to that effect.

Frankly, I don't understand why you'd need accurate clash checking for a theme park sim. What are the objects whose clashes you need to prevent?

Maybe "collision" is the wrong word. I meant overlap avoidance of objects. Although there may be mini games involving free bodies that need physics and collisions. All I need is a simple boolean function that tells me if there is something where I want to place an object. Location of contact and force are irrelevant.