If you're going for a do-it-yourself solution, I'd suggest the following.
Terrain
Preferably have the terrain be a grid, with just each vertex varying in height. The result is a bunch of quads, each with the same dimensions in the (x, y) plane. Vertices have varying (z) values to make up the slopes. The grid arrangement allows you to easily determine which triangles you will have to test for intersection when performing collision checks.
If that's not an option (terrain pre-built in modeling package), you'll probably want to use an in-memory grid anyway, and store a list of triangles that are (partially) inside each cell.
Checking for collision
The easiest approach would be to consider your actors points in space. Then you'd determine the height of the terrain at that point as follows:
- Determine grid cell the point is in
- Get triangles associated with cell
- Get the triangle containing the point (in the (x, y) plane)
- Get height of triangle/plane at point
In the case of the "pure grid" terrain, step 3 involves just a single point/plane check to determine which of the 2 triangles we need. Otherwise, you'd have to do a point-in-triangle check for each triangle (you can probably re-use point/plane checks or use BSP for further optimization).
Step 4 pseudo-code:
point = [ x, y, z ] // actor position
relativePt = point - triangle.vertices[0]
normal = triangle.plane.normal
distance = relativePt DOT normal // (this is a dot-product)
intersection = [
point.x,
point.y,
point.z + distance / normal.z ]
This calculates the intersection of the ray straight up/down from the actor position with the triangle's plane. So that's the height of the terrain at that (x, y) position. Then you can simply check if the actor's position is below that height, and if so, set its z-coordinate to the terrain height.
Objects (houses, trees, ... )
Give each object 1 or more convex collision volumes that together roughly correspond to its actual shape (see this page on UDN to see how the Unreal Engine works with collision hulls for objects).
You will have to use some spatial subdivision technique to quickly determine which of all world objects to check for collision when moving an actor. If most movement is in 2 dimensions (for example, just terrain and some houses), you could use a simple grid or a quadtree (which is like a grid with further subdivisions). A 3-dimensional option would be the octree.
The point of the spatial subdivision is the same as with the terrain organized as a grid: To associate place objects with cells/volumes in space so you can determine the set of objects to check for a collision, instead of checking for collision with all objects.
Checking for collision
- Get the "potential collision objects" using the spatial subdivision technique you've used; f.e. get the objects in the actor's current grid cell.
- For each convex collision volume of each object:
- Using the separating axis theorem, determine if the actor intersects with the collision volume. See my answer to a different post for some implementation hints (that question is about the 2D case, but the code largely applies; just read "edge" as "plane").
- If collision occurs, use the normal of one of the "offending planes" to move the actor to just next to that plane.
Note: In this case, model your actor's collision volume as a box or 3-sided cylinder or so.
Also, you may want to consider building a BSP tree for each object and use axis-aligned bounding boxes for your actors instead. But that's getting a little beyond the scope of this answer. If your objects will have more complicated collision volumes, that will be faster.
Final thoughts
Well, this is already a really long answer, and these are just some broad strokes. Collision is a pretty broad topic, because there are so many different approaches you can take depending on your needs.
For example, I haven't covered "trace collision", which is detecting collision when an actor moves. Instead, the above suggestion on objects checks if an actor is inside an object. This may or may not suit your needs.
I also just realized I haven't covered actor-vs-actor collision. Perhaps that's best done as colliding 2 circles in the (x, y) plane, with an additional check to see if their vertical spaces intersect.
Anyway, I really gotta wrap this up. Hopefully this will at least point you in the right direction.
