P.S

Limitation of Sphere Mapping

Although sphere mapping is generally convincing, it is not generally correct. Most of the artifacts come from the fact that the sphere map is generated at a single point and then applied over a large number of points. Objects with interreflections cannot be handled correctly. If reflected objects are close to the reflective object, their reflections should appear differently when viewed from different points on the reflector. Using sphere maps, this will not happen. Sphere mapping results are only correct if we assume that all the reflective objects are infinitely far from the reflective object.

Fixing the eye point along the vector (0, 0, 1) also leads to incorrect results. The same normal in eyespace will always map to the same location in the sphere map. A normal which points directly at the eyepoint maps to the center of the sphere map. A normal which points directly away from the user maps to the circle around the sphere map. Two important advantages of this simplification are that it significantly reduces the cost of computing r and that it ensures that the parts of the sphere map which have the best filtering are mapped to the primitives which face the user. In general, primitives which face the user will cover large areas in screen space and will be the focus of the user's attention.

Interpolation of the texture coordinates also leads to artifacts. Texture coordinates are computed at the vertices and linearly interpolated across the polygon. Unfortunately, the sphere map is not in a linear space, so this interpolation is not correct. Additionally, the linear interpolation will not take into account the fact that the points at the edge of the circle all map to the same location. Coordinates may be interpolated within the circle of the sphere map when they should be interpolated across the boundary.

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