Quick 'n Dirty Point-Plane Collision Detection

A couple weeks ago I was in a frenzy to implement collision detection in my SkyCop demo. Sure, I planned to go back and study it in more detail at some point, but for the moment I just wanted to get something done so I could avoid flying through enemy ships and start blowing them up. After a few days of searching, I quickly realized that collision detection is no trivial task; it's a field of study all on its own! I started with this flipcode article that served as a good introduction but left me a bit confused. After more research and trial-and-error I had a working example function that I would like to share with anyone needing to feed that same primal urge to get something working quickly.

The function, written in C++ for Direct3D 9, determines if a single point will cross a triangular plane (parameters vP1-vP3 specified in clockwise order). Parameter prevPos is the initial position your character/camera/object moves from and curPos is the position to which it will be moved. For example, if you want to detect if an FPS player will collide with a wall, you would call this function with the camera's initial position as prevPos and its predicted next position [prevPos + (speed * direction)] as curPos. Submit a comment if you have any questions, and keep in mind I will discuss the code in detail in a future post.

Btw, I'm sure there are engines that handle all this stuff for you, but since I haven't gotten into those yet it was a nice exercise for me. And I do apologize for the ugly formatting. I'll work on making code selections look better in future posts!

enum PlanePosition
{
   PlaneFront,
   PlaneBack,
   OnPlane
};

bool IntersectsTriangle(D3DXVECTOR3 prevPos, D3DXVECTOR3 curPos, 
          D3DXVECTOR3 vP1, D3DXVECTOR3 vP2, D3DXVECTOR3 vP3)
{
    float p, d, t, thetaSum;
    PlanePosition prevLoc, curLoc;
    D3DXVECTOR3 ray, v1, v2, v3, vNormal, intersect;
 
    // Compute normal vector for the plane
    v1 = (vP2 - vP1);
    v2 = (vP3 - vP2);
    D3DXVec3Cross(&vNormal, &v1, &v2);
    D3DXVec3Normalize(&vNormal, &vNormal);

    
    // Compute plane distance
    d = - D3DXVec3Dot(&vP1, &vNormal);

    
    // Classify positions using planar equation
    p = (D3DXVec3Dot(&vNormal, &prevPos) + d);
    if ( p > 0.0f ) prevLoc = PlaneFront;
    else if ( p < 0.0f ) prevLoc = PlaneBack;
    else prevLoc = OnPlane;

    
    p = (D3DXVec3Dot(&vNormal, &curPos) + d);
    if( p > 0.0f ) curLoc = PlaneFront;
    else if (p < 0.0f ) curLoc = PlaneBack;
    else curLoc = OnPlane;
        
    if (prevLoc == curLoc) return false;
   
    // Crossed the plane, did intersect occur inside triangle?
    // Get normalized ray
    ray = curPos - prevPos;
    D3DXVec3Normalize(&ray, &ray);

    
    // t = point along ray where intersection occurs
    t = - (d + D3DXVec3Dot(&vNormal, &prevPos)) 
        / D3DXVec3Dot(&vNormal, &ray);

    
    // Get intersection point on the plane
    intersect = prevPos + (ray * t);

    
    // Determine if intersection is within triangle plane
    // Angles around intersection should total 360 degrees (2 PI) 
    v1 = intersect - vP1;
    v2 = intersect - vP2;
    v3 = intersect - vP3;
    D3DXVec3Normalize(&v1, &v1);
    D3DXVec3Normalize(&v2, &v2);
    D3DXVec3Normalize(&v3, &v3);
 
    thetaSum = acos(D3DXVec3Dot(&v1, &v2)) 
             + acos(D3DXVec3Dot(&v2, &v3)) 
             + acos(D3DXVec3Dot(&v3, &v1));

    
    // If sum == 2PI we have an intersection!
    if ((thetaSum >= ((2 * D3DX_PI) - 0.1)) && 
        (thetaSum <= ((2 * D3DX_PI) + 0.1)))
    {
        return true;
    }

    
    return false;
}