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Sir Sapo

Terrain Collision

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What is the method used to determine the height of the ground is at a certain x,y point on a heightmap? I heard somewhere that you have to find what square in the grid an object is and then somehow average the height of those 4 points together to get the final height, is this correct?

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A gridcell consist out of 4 points. If you take the average height of each point, then you got the relative height of the gridcell itself.

A heightmap usually is a 8-bit bitmap, meaning every pixels can have a ranged value between 0 and 255. You could say to your engine, that value 127 is the sealevel for example and every value higher or lower is 1.0f or 100.0f in absolute z-coordinates higher or lower.
Every pixel in that bitmap could be a point in the gridfield.

I hope this is what would like to know, else feel free to ask.

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Basically yeah, that's the process. You get the 4 points for that cell and do a bilinear interpolation.

Here's my source for the meat of the algo:

//the x and y coords are all either int(x) or int(x)+1
//use all 4 combos
//x0 <= x <= x1
//z0 <= z <= z1
int x0, z0, x1, z1;
x0 = int(x);
x1 = x0 + 1;
z0 = int(z);
z1 = z0 + 1;

//we are just slightly off the edge of the terrain if x1 or z1 is off the terrain
if( x0 < 0.0 || z0 < 0.0 )
return std::numeric_limits<float>::min();

if( x1 >= m_Width || z1 >= m_Height )
return std::numeric_limits<float>::min();


float h00, h01, h10, h11;
h00 = m_Heights[x0*m_Height+z0];
h01 = m_Heights[x0*m_Height+z1];
h10 = m_Heights[x1*m_Height+z0];
h11 = m_Heights[x1*m_Height+z1];

//NOTE: The faces are indexed like this:
//one tri is h00, h01, h10
//other tri is h01, h10, h11 --- NOT h00 in this tri
//This is important; most terrain engines appear to wind the verts along the other diagonal

//find distance from camera to x0,z0
float tx, ty;
tx = x - x0;
ty = z - z0;

//Now, how do we figure out the height from all this info?
//We could try a bilerp...
float txty = tx * ty;
float Height = h00 * (1.0f - ty - tx + txty)
+ h10 * (tx - txty)
+ h11 * txty
+ h01 * (ty - txty);

return Height;



Fairly simple...get the four points, look up the heights, get the factors on x and z, and average them all together. If you work out the sum of the 4 factors, you'll find they add up to 1.

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