Pack normal and height data in one float texture

Wow, hard coding night. But in the end I can code two routines that allows me to store normal mapping data and terrain height in one float texture. Remember that in order to perform vertex texture fetch in the vertex shader we need to access to the topology with one float texture.

I coded this in C++ but it's easy portable to GLSL or HLSL.

In this example I store only 2 normal components: X and Y in range 0 to 255. Remember that you must extract third component as follows: sqrt( 1.0 - nx*nx + ny*ny );

Heightmap has custom precision values, due big imprecision of floating point conversion. With 11 bits of precision we can store heights from 0 to 2043. This happened because we loose 4 numbers with this precision. The formula is:

unsigned char hPrecisionBits = 11; // (1<<11) = 2048
unsigned char expectedError = 1 << (hPrecisionBits - 9); // 4
unsigned short maxHeight = (1 << hPrecisionBits) - expectedError; // 2044

//! Gives fractional number
inline float frac( float _value ) {
return _value - floorf( _value );
}

// NX | NY | HEIGHT -> float32
// 8 | 8 | 16
inline float packNormalAndHeight( unsigned char _nx, unsigned char _ny, unsigned short _height, char _hPrecisionBits )
{
return
(_nx / 256.0) +
((_ny / 256.0) / 256.0) +
(_height / ((float)(1<<_hPrecisionBits)) / 65536.0);
}

// float32 -> NX | NY | HEIGHT
// 8 | 8 | 16
inline void unpackNormalAndHeight( float _value, char _hPrecisionBits, float* nx_, float* ny_, float* height_ )
{
*nx_ = floorf( frac( _value ) * 256.0 );
*ny_ = floorf( frac( _value * 256.0 ) * 256.0 );
*height_ = frac( _value * 65536.0 ) * ((float)(1<<_hPrecisionBits));
}


Usage example:

unsigned char hPrecisionBits = 11; // (1<<11) = 2048
unsigned char expectedError = 1 << (hPrecisionBits - 9); // 4
unsigned short maxHeight = (1 << hPrecisionBits) - expectedError; // 2044

// Pack as 8 | 8 | 16
float packedValue = packNormalAndHeight( 231, 137, 2043, hPrecisionBits );

// Unpack from single float
float x,y,h;
unpackNormalAndHeight( packedValue, hPrecisionBits, &x, &y, &h );

Notice that 'expectedError' brings us the amount of error values returned in height function. For example, if our precision bits are 9, expected error will be 1 (135 when we store 136 number). For 10, error will be 2, for 11, will be 4, for 12 will be 8, etc...

I hope it will be useful.