Game Development Reference
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b = L * cos((90-Alpha) *3.14/180); // projection of barrel onto x-z plane
Lx = b * cos(Gamma * 3.14/180); // x-component of barrel length
Ly = L * cos(Alpha * 3.14/180); // y-component of barrel length
Lz = b * sin(Gamma * 3.14/180); // z-component of barrel length
cosX = Lx/L;
cosY = Ly/L;
cosZ = Lz/L;
// These are the x and z coordinates of the very end of the cannon barrel
// we'll use these as the initial x and z displacements
xe = L * cos((90-Alpha) *3.14/180) * cos(Gamma * 3.14/180);
ze = L * cos((90-Alpha) *3.14/180) * sin(Gamma * 3.14/180);
// Now we can calculate the position vector at this time
s.i = Vm * cosX * time + xe;
s.j = (Yb + L * cos(Alpha*3.14/180)) + (Vm * cosY * time) −
(0.5 * g * time * time);
s.k = Vm * cosZ * time + ze;
// Check for collision with target
// Get extents (bounding coordinates) of the target
tx1 = X - Length/2;
tx2 = X + Length/2;
ty1 = Y - Height/2;
ty2 = Y + Height/2;
tz1 = Z - Width/2;
tz2 = Z + Width/2;
// Now check to see if the shell has passed through the target
// We're using a rudimentary collision detection scheme here where
// we simply check to see if the shell's coordinates are within the
// bounding box of the target. This works for demo purposes, but
// a practical problem is that you may miss a collision if for a given
// time step the shell's change in position is large enough to allow
// it to "skip" over the target.
// A better approach is to look at the previous time step's position data
// and to check the line from the previous position to the current position
// to see if that line intersects the target bounding box.
if( (s.i >= tx1 && s.i <= tx2) &&
(s.j >= ty1 && s.j <= ty2) &&
(s.k >= tz1 && s.k <= tz2) )
return 1;
// Check for collision with ground (x-z plane)
if(s.j <= 0)
return 2;
// Cut off the simulation if it's taking too long
// This is so the program does not get stuck in the while loop
if(time>3600)
return 3;
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