Game Development of .Nettrix: GDI+ and Collision Detection - Extending the Algorithms to Add a Third Dimension

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There are many advanced algorithms for 3-D collisions described on game-related sites all over the Internet. We’ll not stress the many implications on including a z axis in the collision detection algorithms; instead you just add some simple extensions to the preceding algorithms. This code sample depicts a proximity test with cube-like objects:

float Dx = Math.Abs(r2.x - r1.x);
float Dy = Math.Abs(r2.y - r1.y);
float Dz = Math.Abs(r2.z - r1.z);
…
if (Dx > (r1.extentX+r2.extentX) && (Dy > (r1.extentY+r2.extentY) && (Dz > r1.extentZ+r2.extentZ))
  // The boxes do not overlap.
else
  // The boxes overlap.

The next proximity algorithm extends the circle proximity test to use spheres in a 3-D space.

Dx = Math.Abs(Object1.CenterX - Object2.CenterX);
Dy = Math.Abs(Object1.CenterY - Object2.CenterY);
Dz = Math.Abs(Object1.CenterZ - Object2.CenterZ);
double Distance = Math.Sqrt(Dx*Dx + Dy*Dy + Dz*Dz);

if (Distance > Object1.radius+ Object2.radius)
  // => The circles do not overlap.
else
  // => The circles are overlapping.

The last proximity test is used for Sphere/Cube intersections. You probably already get the idea on how to extend these simple intersection tests. In the case of Arvo’s Algorithm, you simply add a test for the z axis.

…
// Check z axis. If Circle is outside box limits, add to distance.
if (CircleCenterZ < this.MinZ)
  dist += Math.Sqr(CircleCenterZ – this.MinZ);
else if (CircleCenterZ > this.MaxZ)
  dist += Math.Sqr(CircleCenterZ – this.MaxZ);

// Now that distances along x, y, and z axis are added, check if the square
// of the Circle's radius is longer and return the boolean 
         result. return (Radius*Radius) < dist;
return (Radius*Radius) < dist;

In the next sections you’ll see how to apply these theoretical ideas in a real game project.

This chapter is from Beginning .NET Game Programming in C#, by David Weller, et al., (Apress, 2004, ISBN: 1590593197). Check it out at your favorite bookstore today. Buy this book now.

Next: Develop a Real Game Proposal >>
 

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