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Anteru
Anteru
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Your normals should be in tangent space, that way you can apply them onto any surface for which you can create a tangent space (trivial for spheres.) Basically the normal map describes how the normal differs from the actual normal on a small patch on the surface. The tangent space is what you probably try to get with your Jacobian matrix -- for a sphere, you can create a tangent space coordinate system at any given point by using the normal at the point and two perpendicular vectorvectors -- just orient them consistently (for instance, along u and v) and youryou're done. You can then translate your incoming light vector into tangent space (or the other way round) and light with the new normal. The advantage is that your normal map will work on any object with a defined tangent space and UV mapping.

On the cube, your tangent space for each face is simply that face itself (i.e. if you have a face which has a normal -Z for instance, and your tangent space up is +Y, you just rotate that normal using a matrix which maps -Z to +Y.)

Your normals should be in tangent space, that way you can apply them onto any surface for which you can create a tangent space (trivial for spheres.) Basically the normal map describes how the normal differs from the actual normal on a small patch on the surface. The tangent space is what you probably try to get with your Jacobian matrix -- for a sphere, you can create a tangent space coordinate system at any given point by using the normal at the point and two perpendicular vector -- just orient them consistently (for instance, along u and v) and your done. You can then translate your incoming light vector into tangent space (or the other way round) and light with the new normal. The advantage is that your normal map will work on any object with a defined tangent space and UV mapping.

On the cube, your tangent space for each face is simply that face itself (i.e. if you have a face which has a normal -Z for instance, and your tangent space up is +Y, you just rotate that normal using a matrix which maps -Z to +Y.)

Your normals should be in tangent space, that way you can apply them onto any surface for which you can create a tangent space (trivial for spheres.) Basically the normal map describes how the normal differs from the actual normal on a small patch on the surface. The tangent space is what you probably try to get with your Jacobian matrix -- for a sphere, you can create a tangent space coordinate system at any given point by using the normal at the point and two perpendicular vectors -- just orient them consistently (for instance, along u and v) and you're done. You can then translate your incoming light vector into tangent space (or the other way round) and light with the new normal. The advantage is that your normal map will work on any object with a defined tangent space and UV mapping.

On the cube, your tangent space for each face is simply that face itself (i.e. if you have a face which has a normal -Z for instance, and your tangent space up is +Y, you just rotate that normal using a matrix which maps -Z to +Y.)

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Anteru
Anteru
  • 399
  • 2
  • 7

Your normals should be in tangent space, that way you can apply them onto any surface for which you can create a tangent space (trivial for spheres.) Basically the normal map describes how the normal differs from the actual normal on a small patch on the surface. The tangent space is what you probably try to get with your Jacobian matrix -- for a sphere, you can create a tangent space coordinate system at any given point by using the normal at the point and two perpendicular vector -- just orient them consistently (for instance, along u and v) and your done. You can then translate your incoming light vector into tangent space (or the other way round) and light with the new normal. The advantage is that your normal map will work on any object with a defined tangent space and UV mapping.

On the cube, your tangent space for each face is simply that face itself (i.e. if you have a face which has a normal -Z for instance, and your tangent space up is +Y, you just rotate that normal using a matrix which maps -Z to +Y.)