Textured sphere and spherical environment map rendering using texture map double indirection

A method for generating texture map indices for rotating the view of a textured sphere along a first axis and a second axis while rendering said textured sphere, said method comprising the steps of:

• a) generating a screen look-up table representing an orthogonal view of a first sphere in a display window, said screen look-up table having a plurality of entries representing first sphere parameters (u,v);
• b) generating a parametric look-up table representing a mapping of said first sphere parameters (u,v) to a second sphere, said second sphere rotated by N degrees about an axis perpendicular to the poles of said first sphere, where N is not zero, said parametric look-up table having a plurality of entries representing second sphere parameters (u',v'), and
• c) for each entry (u,v) in said screen look-up table,
• combining a first offset with said entry (u,v) to create an index into said parametric look-up table, therein causing rotation of said textured sphere along said first axis,
• retrieving an entry (u',v') from said parametric look-up table based on said index, and
• combining a second offset with said entry (u',v') of said parametric look-up table to create a texture map index, therein causing rotation of said textured sphere along said second axis.

A method for generating texture map indices while rendering a view of a spherical environment map projected on a sphere with the viewing position at the center of said sphere for panning along a first axis and a second axis, said method comprising the steps of:

• a) generating a screen look-up table representing a view of a first sphere having a viewing position at the center of said first sphere, said screen look-up table having a plurality of entries representing first sphere parameter (u,v);
• b) generating a parametric look-up table representing a mapping of said first sphere parameters (u,v) to a second sphere, said second sphere rotated by N degrees about an axis perpendicular to the poles of said first sphere, where N is not zero, said parametric look-up table having a plurality of entries representing second sphere parameters (u',v')
• for each entry (u,v) in said screen look-up table,
• combining a first offset with said entry (u,v) to create an index into said parametric look-up table, therein causing panning of said projected spherical environment map along said first axis,
• retrieving an entry (u',v') into said parametric look-up based on said index,
• combining a second offset with said entry (u',v') of said parametric look-up table to create a texture map index, therein causing panning of said projected spherical environment map along said second axis.

A method of accessing texture map information for rotating the view of a textured sphere along a first axis and a second axis while rendering said textured sphere, said method comprising the steps of:

• a) generating a screen look-up table representing a first sphere having a first orientation, said first sphere having a plurality of first sphere parameters (u,v), u corresponding to a position along the equator of said first sphere, v corresponding to a position between the poles of said first sphere, said screen look-up table having a plurality of first storage locations, each of said plurality of first storage locations corresponding to one of said plurality of first sphere parameters, each of said plurality of first storage locations for storing values corresponding to one of a plurality of second sphere parameters (u',v');
• b) generating a parametric look-up table representing a second sphere having a second orientation rotated 90.degree. from an axis perpendicular to an axis between the poles of said first sphere, said second sphere having said plurality of second sphere parameters (u',v'), said parametric look-up table having a plurality of second storage locations, each of said plurality of second storage locations corresponding to one of said plurality of second sphere parameters, each of said second plurality of storage locations for storing one of a plurality of indices to said texture map, and
• c) for each of said first sphere parameters (u,v), performing the following steps,
• providing a u offset, said u offset representative of a translation in a first direction,
• generating an address corresponding to (u+u offset, v),
• accessing a parametric look-up table index corresponding to said (u+u offset, v), said parametric look-up table index corresponding to one of said plurality of second sphere parameters (u',v'),
• providing a u' offset, said u' offset representative of a translation in a second direction, said second direction being 90.degree. from said first direction,
• generating a texture map index corresponding to (u'+u' offset, v'), and
• accessing said texture map at a location corresponding to said texture map index.