Method for determining weighting factors for the color calculation of a color value of texels for a footprint

1. A method for displaying an image of an object on a display device, the image comprising at least one pixel, the method comprising:

determining weighting factors for the color calculation of a color value of texels for a footprint covering a plurality of texels in a texel grid, wherein the footprint is a projection of the object, and wherein determining the weighting factors comprises:

(a) determining form information of the footprint;

(b) determining edges of the footprint;

(c) approximating the edges determined in step (b) by a staircase function;

(d) determining the texels of the texel grid contacted by the staircase function; and

(e) determining a weighting factor for each texel containing a portion of the staircase function depending on a subarea of the respective texel covered by the footprint; and

displaying an image of said object on said display device wherein said image include the determined texel color values.

2. The method according to claim 1 , wherein in step (d) a texel contacted by the staircase function is determined based on the starting points and/or end points of the vertical portions of the staircase function.

3. The method according to claim 1 , wherein in step (e) a uniform weighting value is associated with the texels of the texel grid not contacted by the staircase function and covered by the footprint.

4. The method according to claim 1 , wherein in step (e) the weighting factor for each texel is associated with a data structure.

5. The method according to claim 1 , wherein the staircase function for each edge of the footprint includes a plurality of steps, a plurality of horizontal step elements and a plurality of vertical step elements,

wherein each edge includes a plurality of subsequent edge portions of equal length,

wherein a horizontal edge is present when the end points of the edge portions of the edge intersect a horizontal step element of the staircase function,

wherein a vertical edge is present when the end points of the edge portions of the edge intersect a vertical step element of the staircase function,

wherein a horizontal edge includes a number of vertical step elements, the number being equal to the number of steps of the staircase function,

wherein a vertical edge includes a number of vertical step elements, the number being larger than the number of the steps of the staircase function by an additional vertical step element, and

wherein the additional vertical step element is used for calculating the weighting factors of a neighboring edge having the same vertical position.

6. The method according to claim 1 , wherein determining the subarea of the texel, following step (e), includes determining the texel subarea determined by the staircase function and covered by the footprint.

7. The method according to claim 6 , wherein the weighting factor determined in step (e) is determined by the ratio of the texel subarea to the texel overall area.

8. The method according to claim 1 , wherein an enlargement offset (r) is associated with the footprint,

wherein following step (a), based on the enlargement offset, the footprint is enlarged by offsetting the edges of the footprint outwardly from the current edge footprint positions by a distance depending on the enlargement offset,

wherein the offset edges are determined in step (b),

wherein the offset edges are approximated in step (c) by a staircase function, and

wherein in step (e) a weighting factor for each texel containing an offset edge is determined depending on the subarea of the respective texel covered by the enlarged footprint.

9. The method according to claim 8 , wherein gaps resulting due to the enlargement of the footprint are filled by horizontal and vertical edges.

10. The method according to claim 9 , wherein in step (e) the weighting factor for each texel containing an incorporated vertical edge is determined depending on a subarea of the respective texel covered by the enlarged footprint.

11. The method according to claim 8 , wherein enlarging the footprint includes offsetting the edge end points in the horizontal direction and the vertical direction by the same distances determined by the enlargement offset.

12. The method according to claim 1 , wherein the weighting factors for all the edges of the footprint are produced in parallel.

13. A method for displaying an image of an object on a display device, the image comprising at least one pixel, the method comprising:

determining weighting factors for the color calculation of a color value of texels for a footprint covering a plurality of texels in a texel grid, wherein the footprint is a projection of the object, and wherein determining the weighting factors comprises:

(a) determining form information of the footprint;

(b) determining edges of the footprint;

(c) approximating the edges determined in step (b) by a staircase function;

(d) determining the texels of the texel grid contacted by the staircase function;

(e) determining a weighting factor for each texel containing a portion of the staircase function depending on a subarea of the respective texel covered by the footprint;

wherein an enlargement offset (r) is associated with the footprint,

wherein following step (a), based on the enlargement offset, the footprint is enlarged by offsetting the edges of the footprint to the outside outwardly from the current edge footprints positions by a distance depending on the enlargement offset,

wherein the offset edges are determined in step (b),

wherein the offset edges are approximated in step (c) by a staircase function, and

wherein in step (e) a weighting factor for each texel containing an offset edge is determined depending on the subarea of the respective texel covered by the enlarged footprint; and

displaying an image of said object on said display device wherein said image include the determined texel color values.

14. A method for displaying an image of an object on a display device, the image comprising at least one pixel, the method comprising:

determining weighting factors for the color calculation of a color value of texels for a footprint covering a plurality of texels in a texel grid, wherein the footprint is a projection of the object, and wherein determining the weighting factors comprises:

(a) determining form information of the footprint, wherein an enlargement offset (r) is associated with the footprint;

(b) determining edges of the footprint;

(c) approximating the edges determined in step (b) by a staircase function;

(d) determining the texels of the texel grid contacted by the staircase function; and

(e) determining a weighting factor for each texel containing a portion of the staircase function depending on a subarea of the respective texel covered by the footprint,

wherein following step (a), based on the enlargement offset, the footprint is enlarged by offsetting the edges of the footprint outwardly from the current edge footprint positions by a distance depending on the enlargement offset,

wherein the offset edges are determined in step (b),

wherein the offset edges are approximated in step (c) by a staircase function, and

wherein in step (e) a weighting factor for each texel containing an offset edge is determined depending on the subarea of the respective texel covered by the enlarged footprint; and

displaying an image of said object on said display device wherein said image include the determined texel color values.

15. The method according to claim 14 , wherein gaps resulting due to the enlargement of the footprint are filled by horizontal and vertical edges.

16. The method according to claim 15 , wherein in step (e) a weighting factor for each texel containing an incorporated vertical edge is determined depending on a subarea of the respective texel covered by the enlarged footprint.

17. The method according to claim 14 , wherein enlarging the footprint includes offsetting the edge end points in the horizontal direction and the vertical direction by the same distances determined by the enlargement offset.