Ellipsoidal projection mapping

A method of calculating texture coordinates for a surface, comprising the steps of:

• (a) calculating an inertial ellipsoid of the surface;
• (b) calculating a transformation that aligns said inertial ellipsoid and a projective body, wherein said projective body is an ellipsoid including eight octants;
• (c) adjusting the relative orientation and position between the surface and said projective body according to said transformation;
• (d) projecting the surface onto said projective body;
• and
• (e) mapping said projective body to a texture rectangle, wherein said texture rectangle includes eight texture sub-rectangles, and wherein said mapping step comprises the step of mapping each octant to a unique texture sub-rectangle.

A method of calculating texture coordinates for a surface, comprising the steps of:

• (a) selecting an ellipsoidal projective body;
• (b) aligning the centers of gravity of the surface and said projective body;
• (c) projecting the surface onto said ellipsoidal projective body using ellipsoidal coordinates;
• and
• (d) mapping said ellipsoidal projective body to a texture rectangle.

A method of calculating texture coordinates for a surface, comprising the steps of:

• (a) selecting an ellipsoidal projective body, wherein said ellipsoidal projective body includes eight octants;
• (b) projecting the surface onto said ellipsoidal projective body using ellipsoidal coordinates;
• and
• (c) mapping said ellipsoidal projective body to a texture rectangle, wherein said texture rectangle includes eight texture sub-rectangles, and wherein said mapping step comprises the step of mapping each octant to a unique texture sub-rectangle.

A computer program product comprising a computer usable medium having computer program logic stored therein, wherein said computer program logic comprises:

• receiving means for enabling a computer to receive a surface;
• aligning means for enabling said computer to align the centers of gravity of the surface and a projective body;
• first calculating means for enabling said computer to calculate an inertial ellipsoid of said surface;
• second calculating means for enabling said computer to calculate a transformation that aligns said inertial ellipsoid and said projective body, said transformation comprising a rotation of said inertial ellipsoid;
• adjusting means for enabling said computer to adjust the relative orientation between said surface and said projective body according to said transformation;
• projection means for enabling said computer to project said surface onto said projective body;
• and
• mapping means for enabling said computer to map said projective body to a texture rectangle.

A computer program product comprising a computer usable medium having computer program logic stored therein, wherein said computer program logic comprises:

• receiving means for enabling a computer to receive a surface;
• first calculating means for enabling said computer to calculate an inertial ellipsoid of said surface;
• second calculating means for enabling said computer to calculate a transformation that aligns said inertial ellipsoid and a projective body, wherein said projective body is an ellipsoid including eight octants;
• adjusting means for enabling said computer to adjust the relative orientation and position between said surface and said projective body according to said transformation;
• projection means for enabling said computer to project said surface onto said projective body;
• and
• mapping means for enabling said computer to map said projective body to a texture rectangle, wherein said texture rectangle includes eight texture sub-rectangles, and wherein said mapping means maps each octant to a unique texture sub-rectangle.