Exact height value

How do you want to interpolate? linearly?

Looking at just the horizontal components draw a line through the point parallel to one side. Then find the height of each end of that line. Then find the height of the point. If you are t percent of the way from a to b then a linear interpolation is y=a+t*(b-a).

A simple mistake, but in the last post it's not t percent. The percentage ofcourse is 100*t.

You need some interpolator order. Linear or cubic are commonly used. Linear is very cheap, but looks pretty bad (all angles and sharp creases). Cubic is a little more expensive, but looks much better (soft and smooth). Cubic allows you to extract more detail by using multiple samples from within the same "cell" in the height field.

The trick is, as someone said, to first interpolate along the integer grid lines (say, integer X values), to get reference points along the other grid line (say, the Y line) to interpolate between.

For linear interpolation, the pseudo-code looks like so:

I(F,x,y) {  xi = floor(x);  yi = floor(y);  xt = x - xi;  yt = y - yi;  y0 = F[xi][yi]*(1-xt)+F[xi][yi+1]*xt;  y1 = F[xi+1][yi]*(1-xt)+F[xi+1][yi+1]*xt;  return y0*(1-yt)+y1*yt;}

For cubic, it looks something like (taken from some old terrain code I wrote):

    inline float hermite4( float frac, float * ptr )    {      const float    c     = (ptr[2] - ptr[0]) * 0.5f;      const float    v     = ptr[1] - ptr[2];      const float    w     = c + v;      const float    a     = w + v + (ptr[3] - ptr[1]) * 0.5f;      const float    b     = w + a;      return ((((a * frac) - b) * frac + c) * frac + ptr[1]);    }    static float do_sample( unsigned char const * data, uint pitch, uint x, uint z, float xp, float zp )    {      assert( xp < 1 && zp < 1 );      assert( xp >= 0 && zp >= 0 );      assert( x > 0 && z > 0 );      float xx[ 4 ];      float yy[ 4 ];      for( int iz = 0; iz < 4; ++iz ) {        unsigned char const * data2 = data + x - 1 + (iz + z - 1) * pitch;        for( int ix = 0; ix < 4; ++ix ) {          xx[ ix ] = data2[ ix ];        }        yy[ iz ] = hermite4( xp, xx );      }      float sv = (hermite4( zp, yy ) - 128.f) * (1.f / 128.f);      return sv;    }

No, 50% of the way from a to b in half way from a to b and not 50 times the distance from a to b.

he meant that, yes, half way would be 50%, but the value of t would be .5

Thank you guys. That helped! :-)