Code-Bin #221 - Compressing Normals (and other unit vectors)

Compressing Normals (and other unit vectors)
Posted by: aav | February 7, 2009 @ 4:12pm

Revision 1 - Original post on February 7, 2009 @ 4:07pm

C++ Code

void TraceLine( float3 n, int3* pPoints, int& size )  
{  
	int x1 = 0;  
	int y1 = 0;  
	int z1 = 0;  
	int x2 = n.x * (2<<24);  
	int y2 = n.y * (2<<24);  
	int z2 = n.z * (2<<24);

int xd, yd, zd;  
	int x, y, z;  
	int ax, ay, az;  
	int sx, sy, sz;  
	int dx, dy, dz;

dx = x2 - x1;  
	dy = y2 - y1;  
	dz = z2 - z1;

ax = abs(dx) << 1;  
	ay = abs(dy) << 1;  
	az = abs(dz) << 1;

sx = sign(dx);  
	sy = sign(dy);  
	sz = sign(dz);

x = x1;  
	y = y1;  
	z = z1;

size = 0;

if (ax >= max(ay, az))            /* x dominant */  
	{  
		yd = ay - (ax >> 1);  
		zd = az - (ax >> 1);

while( x*x < 127*127 )  
		{  
			pPoints[size++] = int3( x, y, z );

if (yd >= 0)  
			{  
				y += sy;  
				yd -= ax;  
			}

if (zd >= 0)  
			{  
				z += sz;  
				zd -= ax;  
			}

x += sx;  
			yd += ay;  
			zd += az;  
		}  
	}  
	else if (ay >= max(ax, az))            /* y dominant */  
	{  
		xd = ax - (ay >> 1);  
		zd = az - (ay >> 1);

while( y*y < 127*127 )  
		{  
			pPoints[size++] = int3( x, y, z );

if (xd >= 0)  
			{  
				x += sx;  
				xd -= ay;  
			}

if (zd >= 0)  
			{  
				z += sz;  
				zd -= ay;  
			}

y += sy;  
			xd += ax;  
			zd += az;  
		}  
	}  
	else if (az >= max(ax, ay))            /* z dominant */  
	{  
		xd = ax - (az >> 1);  
		yd = ay - (az >> 1);

while( z*z < 127*127 )  
		{  
			pPoints[size++] = int3( x, y, z );

if (xd >= 0)  
			{  
				x += sx;  
				xd -= az;  
			}

if (yd >= 0)  
			{  
				y += sy;  
				yd -= az;  
			}

z += sz;  
			xd += ax;  
			yd += ay;  
		}  
	}

assert( size <= 128 );

for( ; size < 128; size++ )  
	{  
		pPoints[size] = int3(0,0,0);  
	}  
}

void NormalToUByte4( float3 n, unsigned char* pOutVec )  
{  
	n = normalize(n);

//  
	// Find the candidate points.  
	//  
	int3 points[128];  
	int pointCount = 0;

TraceLine( n, &points[0], pointCount );

int3 best( 0, 0, 0 );  
	float bestError = std::numeric_limits<float>::max();

for( int i = 0; i < pointCount; i++ )  
	{  
		float3 cf = normalize( float3( points[i].x, points[i].y, points[i].z ) );

float err = acos( dot( n, cf ) ); // Don't need the acos here really. Just to see the error in radians.

if( err < bestError )  
		{  
			bestError = err;  
			best = points[i];  
		}  
	}

best.x = max( 0, min( 255, best.x + 128 ) );  
	best.y = max( 0, min( 255, best.y + 128 ) );  
	best.z = max( 0, min( 255, best.z + 128 ) );

#ifdef BENCHMARK  
	float3 bf = normalize( float3(best.x,best.y,best.z) );

std::cout << " Input vector: " << n.x << ", " << n.y << ", " << n.z << std::endl;  
	std::cout << " Result vec I: " << best.x << ", " << best.y << ", " << best.z << std::endl;  
	std::cout << " Result vec F: " << bf.x << ", " << bf.y << ", " << bf.z << std::endl;  
	std::cout << "        Error: " << bestError << std::endl;  
	std::cout << std::endl;  
#endif

pOutVec[0] = best.x;  
	pOutVec[1] = best.y;  
	pOutVec[2] = best.z;  
	pOutVec[3] = 0;  
}

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