# Cube map to cylindrical map

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Does anyone have any idea's or references on any algorithms to convert a cube map to a cylindricaly wrapped rectangular (nxn) map? I'm currently generating a cube map that I wrap around a sphere but I'd like to squish it down to a single texture. Thanks very much.

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The texture u[0..1], v[0..1] maps to theta[0..2pi], phi[-(pi/2)..(pi/2)]

For each pixel in the destination map
Map u, v coordinates to polar theta, phi coordinates

theta = u * pi
phi = -(pi / 2) + (v * pi)

Convert polar coordinates to cartesian coordinates

x = cos(phi) * cos(theta)
y = sin(phi)
z = cos(phi) * sin(theta)

This defines a ray, computing the intersection of the ray with the cube map gives you the point to sample. The intersection can be easily computed, the component with the largest magnitude selects the face, with the sign selecting either positive or negative i.e.

[ 0.7, 0.5, -0.1] selects +x
[-0.7, 0.5, -0.1] selects -x

[ 0.1, 0.4, 0.0] selects +y
[ 0.1, -0.4, 0.0] selects -y

[ 0.1, 0.1, 0.8] selects +z
[ 0.1, 0.1, -0.8] selects -z

The other two components are remapped from [-1..1] to [0..1] and used as the u and v texture coordinates, so in the positive x example above

[0.7, 0.5, -0.1] would sample the +x face at [(0.1 + 1) / 2, (0.5 + 1) / 2]

NOTE : the z component -0.1 becomes 0.1 because of the coordinate system, assuming positive z points out of the screen, the coordinate system you are using will affect the exact mapping of ray components to texture coordinates.

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Hmm, I'm real close but any idea why a cubemap that looks like this:

would produce this:

The loop that generates the texture pixels looks like this (excuse it's sloppiness, I was in a hurry):

	for ( i = 0; i < 256; i++ )	{		for ( j = 0; j < 256; j++ )		{			int offset = ( i * 256 + j ) * 4;			float u = i / 256.0f;			float v = j / 256.0f;			const float pi = 3.14f;			float theta = u * pi;			float phi = -( pi / 2.0f ) + ( v * pi );			float x = cosf( phi ) * cosf( theta );			float y = sinf( phi );			float z = cosf( phi ) * sinf( theta );			int iAxis = 0;			bool bPositive = false;			if ( fabs( x ) > fabs( y ) )			{				if ( fabs( x ) > fabs( z ) )				{					iAxis = 0;					bPositive = x >= 0.0f;					u = z;					v = y;				}				else				{					iAxis = 2;					bPositive = z >= 0.0f;					u = x;					v = y;				}			}			else			{				if ( fabs( y ) > fabs( z ) )				{					iAxis = 1;					bPositive = y >= 0.0f;					u = x;					v = z;				}				else				{					iAxis = 2;					bPositive = z >= 0.0f;					u = x;					v = y;				}			}			D3DCUBEMAP_FACES face = D3DCUBEMAP_FACE_POSITIVE_X;			switch ( iAxis )			{				case 0:					if ( bPositive )					{							face = D3DCUBEMAP_FACE_POSITIVE_X;					}					else					{						face = D3DCUBEMAP_FACE_NEGATIVE_X;					}				break;				case 1:					if ( bPositive )					{							face = D3DCUBEMAP_FACE_POSITIVE_Y;					}					else					{						face = D3DCUBEMAP_FACE_NEGATIVE_Y;					}				break;				case 2:					if ( bPositive )					{							face = D3DCUBEMAP_FACE_POSITIVE_Z;					}					else					{						face = D3DCUBEMAP_FACE_NEGATIVE_Z;					}				break;			}			// Scale/Bias from [-1, 1] into [0, 1].			u = ( u + 1.0f ) * 0.5f * 256.0f;			v = ( v + 1.0f ) * 0.5f * 256.0f;			// Round up and truncate.			u = int( u + 0.5f );			v = int( v + 0.5f );			pCubeTexture->LockRect( face, 0, &SrcLockedRect, NULL, 0 );			pSrcPixels = static_cast< unsigned char * >( SrcLockedRect.pBits );			int iCubeOffset = (int)u * SrcLockedRect.Pitch + (int)v * 4;			// ARGB.			pDestPixels[ offset + 3 ] = pSrcPixels[ iCubeOffset + 3 ];			pDestPixels[ offset + 2 ] = pSrcPixels[ iCubeOffset + 2 ];			pDestPixels[ offset + 1 ] = pSrcPixels[ iCubeOffset + 1 ];			pDestPixels[ offset + 0 ] = pSrcPixels[ iCubeOffset + 0 ];			pCubeTexture->UnlockRect( (D3DCUBEMAP_FACES)face, 0 );		}	}

Thanks again for your help thus far. If I may ask, do you have a reference for this algorithm (or some place I could learn about it)?

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Ahh, looks like I just wasn't googling the right terms. "Cube map to Spherical" gave me this: http://astronomy.swin.edu.au/~pbourke/projection/spheretexture, which appears to be what you described, but even using his exact algorithm doesn't appear to give me proper results. Can you offer some advice on converting to a left-handed coordinate system for the cartesian conversion? I believe that may be it (and negating my z doesn't quite do it).

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Firstly u[0..2pi] and v[-pi..pi]. It looks like coordinates are the wrong way and your dimensions are incorrect.

Also it looks like you have your u and v sampling a bit messed up, I've had this problem before when blurring cube maps. Take a look at this picture, it should help clarify the relationship between texture and world coordinates :

Here is how you map {x, y, z} to {FACE, u, v} for each of the faces :

+X -> z[-1..1] becomes u[1..0] and y[-1..1] becomes v[1..0]
-X -> z[-1..1] becomes u[0..1] and y[-1..1] becomes v[1..0]

+Y -> x[-1..1] becomes u[0..1] and z[-1..1] becomes v[0..1]
-Y -> x[-1..1] becomes u[0..1] and z[-1..1] becomes v[1..0]

+Z -> x[-1..1] becomes u[0..1] and y[-1..1] becomes v[1..0]
-Z -> x[-1..1] becomes u[1..0] and y[-1..1] becomes v[1..0]

Sorry I didn't have time to look at your code in depth, but hopefully you can work it out from this. Hope that helps.

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No apologies needed, you've been more than helpful and I greatly appreciate it.

I think I almost have this working but one last question; whats the algorithm to transform from spherical to cartesian for a left-handed coordinate system (I'm using Direct3D)?

Many thanks!

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The equation for a RHS is :

x = cos(phi) * cos(theta)
y = sin(phi)
z = cos(phi) * sin(theta)

For a LHS, you simply need to negate the z

There is a slight error in the conversion from u and v to theta and phi that I described (the method I described below for converting u is assuming that u is in the range [-1..1], Which is probably why it appears you are not sampling enough of the cube faces) So for u in the range [0..1] the algorithm is :

theta = 2pi * u
phi = (-pi / 2) + (pi * v)

Have you made any progress on this? Do you have an image of how your destination map is looking now?

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Well I fixed a number of issues so progress yes but still not what I'm expecting. I'm basically stumped at this point...

Here's what I have to show though. The first image maps colors to each face:

       r  g  b +x   [ 1  0  1 ]   i.e. pink-x   [ 0  0  1 ]   i.e. blue+y   [ 1  0  0 ]   i.e. red-y   [ 0  1  0 ]   i.e. green+z   [ 0  1  1 ]   i.e. cyan-z   [ 1  1  0 ]   i.e. yellow

Here's the color info:

The results are just plain wrong.

As far as I know the uv coordinates are valid for the destination texture.
The conversion to spherical signed numbers looks correct.
The conversion from spherical to cartesian (including negation of z for lhs) looks correct.
The "cube intersection" by finding the greatest axis, keeping the sign and matching with the cube face is correct.
The final src uv generation from the specified face looks right, and finally the conversion to actual pixels looks right.

I'm totally stumped. As far as I can tell it looks like an issue with the spherical conversion (although I do now take into account the proper axis and range, the * 2 issue).

If you have any more idea's I'm definitely open to them.

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Sorry for the late reply, OK, it's not looking too bad actually it looks almost there, the main problems I can see are that a) Your Y axis is wrong, +Y should be pointing up b) Your mapping of u seems to be inverted. If you post your current code I can take a look to see if I can pinpoint the error.

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Here ya go.

	for ( y = 0; y < iHeight; y++ )	{		for ( x = 0; x < iWidth; x++ )		{			int offset = y * DestLockedRect.Pitch + x * 4;			float u = x / (float)iWidth;			float v = y / (float)iHeight;			const float pi = D3DX_PI;			float theta = 2.0f * u * pi;			float phi = ( -pi / 2.0f ) + ( v * pi );			vSamp.x = cosf( phi ) * cosf( theta );			vSamp.y = sinf( phi );			vSamp.z = cosf( phi ) * sinf( theta );			int iAxis = 0;			bool bPositive = false;			// Find the prominent axis.			if ( fabs( vSamp.x ) > fabs( vSamp.y ) )			{				if ( fabs( vSamp.x ) > fabs( vSamp.z ) )				{					iAxis = 0;					bPositive = vSamp.x >= 0.0f;				}				else				{					iAxis = 2;					bPositive = vSamp.z >= 0.0f;				}			}			else			{				if ( fabs( vSamp.y ) > fabs( vSamp.z ) )				{					iAxis = 1;					bPositive = vSamp.y >= 0.0f;				}				else				{					iAxis = 2;					bPositive = vSamp.z >= 0.0f;				}			}			D3DCUBEMAP_FACES face = D3DCUBEMAP_FACE_POSITIVE_X;			char chColor[ 3 ] = { 255, 255, 255 };			// Retrive the cube map uv coordinate.			switch ( iAxis )			{				case 0:					if ( bPositive )					{							face = D3DCUBEMAP_FACE_POSITIVE_X;						u = vSamp.z;						v = vSamp.y;						chColor[ 0 ] = 255;		chColor[ 1 ] = 0;		chColor[ 2 ] = 255;					}					else					{						face = D3DCUBEMAP_FACE_NEGATIVE_X;						u = -vSamp.z;						v = vSamp.y;						chColor[ 0 ] = 0;		chColor[ 1 ] = 0;		chColor[ 2 ] = 255;					}				break;				case 1:					if ( bPositive )					{							face = D3DCUBEMAP_FACE_POSITIVE_Y;						u = vSamp.x;						v = vSamp.z;						chColor[ 0 ] = 255;		chColor[ 1 ] = 0;		chColor[ 2 ] = 0;					}					else					{						face = D3DCUBEMAP_FACE_NEGATIVE_Y;						u = vSamp.x;						v = -vSamp.z;						chColor[ 0 ] = 0;		chColor[ 1 ] = 255;		chColor[ 2 ] = 0;					}				break;				case 2:					if ( bPositive )					{							face = D3DCUBEMAP_FACE_POSITIVE_Z;						u = -vSamp.x;						v = vSamp.y;						chColor[ 0 ] = 0;		chColor[ 1 ] = 255;		chColor[ 2 ] = 255;											}					else					{						face = D3DCUBEMAP_FACE_NEGATIVE_Z;						u = vSamp.x;						v = vSamp.y;						chColor[ 0 ] = 255;		chColor[ 1 ] = 255;		chColor[ 2 ] = 0;					}				break;				default: assert( 0 ); break;			}			// Scale/Bias from [-1, 1] to [0, 1].			u = ( u + 1.0f ) / 2.0f;			v = ( v + 1.0f ) / 2.0f;			// Map to exact cube map face pixels, round up, then truncate.			u = int( u * 256.0f + 0.5f );			v = int( v * 256.0f + 0.5f );			pCubeTexture->LockRect( face, 0, &SrcLockedRect, NULL, 0 );			pSrcPixels = static_cast< unsigned char * >( SrcLockedRect.pBits );			int iCubeOffset = (int)v * SrcLockedRect.Pitch + (int)u * 4;			// ARGB.#if 1			pDestPixels[ offset + 3 ] = pSrcPixels[ iCubeOffset + 3 ];			pDestPixels[ offset + 2 ] = pSrcPixels[ iCubeOffset + 2 ];			pDestPixels[ offset + 1 ] = pSrcPixels[ iCubeOffset + 1 ];			pDestPixels[ offset + 0 ] = pSrcPixels[ iCubeOffset + 0 ];#else						pDestPixels[ offset + 3 ] = 255;			pDestPixels[ offset + 2 ] = chColor[ 0 ];			pDestPixels[ offset + 1 ] = chColor[ 1 ];			pDestPixels[ offset + 0 ] = chColor[ 2 ];#endif			pCubeTexture->UnlockRect( face, 0 );		}	}

It's odd but it also doesn't look like those central, planar xz directions are actually warping properly. If you spot anything let me know, I'm really hoping to put this sucker to bed.

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