IPC분류정보
국가/구분 |
United States(US) Patent
등록
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국제특허분류(IPC7판) |
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출원번호 |
US-0761558
(2001-01-16)
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등록번호 |
US-8253754
(2012-08-28)
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발명자
/ 주소 |
- Snyder, John M.
- Mitchell, Don P.
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출원인 / 주소 |
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대리인 / 주소 |
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인용정보 |
피인용 횟수 :
5 인용 특허 :
7 |
초록
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Spherical-like textures are useful to simulate reflections and to generate arbitrary views from a point. For addressing simplicity, graphics systems typically require rectangular arrays of texture samples but an infinite variety of functions can be used to map these samples to a sphere-like object.
Spherical-like textures are useful to simulate reflections and to generate arbitrary views from a point. For addressing simplicity, graphics systems typically require rectangular arrays of texture samples but an infinite variety of functions can be used to map these samples to a sphere-like object. A new metric is presented for measuring how well various maps use a given number of samples to provide the greatest worst-case frequency content of the image everywhere over the sphere. Using this metric and other important local properties, a comparison is presented of maps used previously in computer graphics as well as other mapping techniques borrowed from cartography. Based on these analysis several novel mapping techniques are presented that are fairly simple to implement and significantly more efficient in terms of the amount of processing and data required, and the quality of the resulting images. The novel metric and mapping techniques can be employed to analyze or otherwise improve the sampling efficiency of mapping textures onto any three-dimensional surface.
대표청구항
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1. A computer-implemented method comprising: providing a first texture map for a first portion of a three-dimensional surface, the first texture map being associated with a first mapping technique;providing a second texture map for a second portion of the three-dimensional surface, the second textur
1. A computer-implemented method comprising: providing a first texture map for a first portion of a three-dimensional surface, the first texture map being associated with a first mapping technique;providing a second texture map for a second portion of the three-dimensional surface, the second texture map being associated with a second mapping technique that is different from the first mapping technique;providing a third texture map for a third portion of the three-dimensional surface, the third texture map being associated with the second mapping technique; andgenerating a multiple-component map set that includes at least a portion of the first, the second and the third texture maps, the first texture map including cylindrical projection information, the second texture map including azimuthal projection information, the third texture map including azimuthal projection information, the first portion separating the second portion and third portion, the cylindrical projection information including plane-chart projection information, and wherein the providing the first texture map includes hexagonally re-parameterizing the cylindrical projection information using a linear transform. 2. The method as recited in claim 1, wherein the azimuthal projection information includes equidistant projection information. 3. The method as recited in claim 1, wherein the first and second texture maps are stretch-invariant and have a sampling requirement definable as: Mcapped(θ)≡Mequi(θ)+Mplane(π/2−θ)=4θ2+2π(π/2−θ)where θ is a transition angle from a defined point on the surface to where the second texture map is adjacent to the first texture map. 4. The method as recited in claim 3, wherein θ is equal to about 45°. 5. The method as recited in claim 1, wherein the linear transform is definable as: Ŝ(u,v)≡S(V(u,v)′)where V≡[kk/201]and k≡2√3/3. 6. The method as recited in claim 1, wherein the cylindrical projection information includes information selected from at least one type of projection information selected from a group comprising plane-chart projection information, equal area information, and Mercator information. 7. The method as recited in claim 1, wherein the azimuthal projection information includes information selected from at least one type of projection information selected from a group comprising equidistant projection information, stereographic projection information, gnomonic projection information, and equal area projection information. 8. The method as recited in claim 1, wherein the first portion is significantly adjacent to both the first and second portions, such that the first portion separates the second and third portions. 9. The method as recited in claim 1, wherein the three-dimensional surface is curvilinear. 10. The method as recited in claim 1, wherein the three-dimensional surface includes a spherical surface. 11. The method as recited in claim 1, wherein providing the first texture map further includes generating the first texture map using the first mapping technique, and providing the second texture map further includes generating the second texture map using the second mapping technique. 12. The method as recited in claim 1, wherein at least one of the first and second texture maps includes information based on a rectangular sampling matrix. 13. The method as recited in claim 1, wherein at least one of the first and second texture maps includes information based on a hexagonal sampling matrix. 14. The method as recited in claim 1, wherein providing the first texture map further includes analyzing the texture map per at least one criterion to determine an appropriate texture resolution. 15. The method as recited in claim 1, wherein providing the first texture map further includes analyzing the texture map per at least one metric criterion to determine a requisite number of texture maps in addition to the first texture map. 16. A computer storage device providing computer instructions suitable for performing steps comprising: providing a first texture map for a first portion of a three-dimensional surface, the first texture map being associated with a first mapping technique;providing a second texture map for a second portion of the three-dimensional surface, the second texture map being associated with a second mapping technique that is different from the first mapping technique;providing a third texture map for a third portion of the three-dimensional surface, the third texture map being associated with the second mapping technique, and wherein the third texture map includes azimuthal projection information for the third portion; andgenerating a multiple-component map set that includes at least a portion of the first and the second texture map, the first texture map including at least one of cylindrical projection information or Mercator projection information for the first portion, the second texture map including at least one of azimuthal projection information or stereographic projection information for the second portion,wherein: the first texture map includes cylindrical projection information for the first portion, and the second texture map includes azimuthal projection information for the second portion,the multiple-component map set is a three-component map set,the second and third portion are two poles, the first portion is the area between the second and third portions,the cylindrical projection information includes plane-chart projection information, andthe providing the first texture map further includes means for hexagonally re-parameterizing the cylindrical projection information using a linear transform. 17. The computer storage device as recited in claim 16, wherein the azimuthal projection information includes equidistant projection information. 18. The computer storage device as recited in claim 16, wherein the first and second texture maps are stretch-invariant and have a sampling requirement definable as: Mcapped(θ)≡Mequi(θ)+Mplane(π/2−θ)=4θ2+2π(π/2−θ)where θ is a transition angle from a defined point on the surface to where the second texture map is adjacent to the first texture map. 19. The computer storage device as recited in claim 18, wherein θ is equal to about 45°. 20. The computer storage device as recited in claim 16, wherein the linear transform is definable as: Ŝ(u,v)≡S(V(u,v)′)where V≡[kk/201]and k≡2√3/3. 21. The computer storage device as recited in claim 16, wherein the first texture map includes Mercator projection information for the first portion, and the second texture map includes stereographic projection information for the second portion. 22. The computer storage device as recited in claim 21, further comprising computer instructions suitable for performing the step of: providing a third texture map for a third portion of the three-dimensional surface, the third texture map being associated with the second mapping technique, and wherein the third texture map includes stereographic projection information for the third portion. 23. The computer storage device as recited in claim 21, wherein the first and second texture maps are conformal and have a sampling requirement definable as: Mcapped(θ)≡Mstereo(θ)+MMercator(π/2−θ)=16 tan2(θ/2)+π ln((1+cos θ)/(1−cos θ))where θ is a transition angle from a defined point on the surface to where the second texture map is adjacent to the first texture map. 24. The computer storage device as recited in claim 23, wherein θ is equal to about 47.8°. 25. The computer storage device as recited in claim 16, wherein the cylindrical projection information includes information selected from at least one type of projection information selected from a group comprising plane-chart projection information, equal area information, and Mercator information. 26. The computer storage device as recited in claim 16 wherein the azimuthal projection information includes information selected from at least one type of projection information selected from a group comprising equidistant projection information, stereographic projection information, gnomonic projection information, and equal area projection information. 27. The computer storage device as recited in claim 16, wherein the first portion is significantly adjacent to both the first and second portions, such that the first portion separates the second and third portions. 28. The computer storage device as recited in claim 16, wherein the three-dimensional surface is curvilinear. 29. The computer storage device as recited in claim 16, wherein the three-dimensional surface includes a spherical surface. 30. The computer storage device as recited in claim 16, wherein providing the first texture map further includes generating the first texture map using the first mapping technique, and providing the second texture map further includes generating the second texture map using the second mapping technique. 31. The computer storage device as recited in claim 16, wherein at least one of the first and second texture maps includes information based on a rectangular sampling matrix. 32. The computer storage device as recited in claim 16, wherein at least one of the first and second texture maps includes information based on a hexagonal sampling matrix. 33. The computer storage device as recited in claim 16, wherein providing the first texture map further includes analyzing the texture map per at least one criterion to determine an appropriate texture resolution. 34. The computer storage device as recited in claim 16, wherein providing the first texture map further includes analyzing the texture map per at least one metric criterion to determine a requisite number of texture maps in addition to the first texture map. 35. A computing device comprising: one or more processors;memory to store computer-program instructions executable by the one or more processors; andlogic module configured to: provide a first texture map for a first portion of a three-dimensional surface, the first texture map being associated with a first mapping technique and a second texture map for a second portion of the three-dimensional surface, the second texture map being associated with a second mapping technique that is different from the first mapping technique,output graphically displayable information based on at least a portion of the first and second texture maps, the first texture map including at least one of cylindrical projection information or Mercator projection information for the first portion, and the second texture map including at least one of azimuthal projection information or stereographic projection information for the second portion, andprovide a third texture map for a third portion of the three-dimensional surface, the third texture map being associated with the second mapping technique,wherein the first texture map includes cylindrical projection information for the first portion, and the second texture map includes azimuthal projection information for the second portion,the third texture map includes azimuthal projection information for the third portion,the cylindrical projection information includes plane-chart projection information, andthe cylindrical projection information in the first texture map has been hexagonally re-parameterized the using a linear transform. 36. The computing device as recited in claim 35, wherein the azimuthal projection information includes equidistant projection information. 37. The computing device as recited in claim 35, wherein the first and second texture maps are stretch-invariant and have a sampling requirement definable as: Mcapped(θ)≡Mequi(θ)+Mplane(π/2−θ)=4θ2+2π(π/2−θ)where θ is a transition angle from a defined point on the surface to where the second texture map is adjacent to the first texture map. 38. The computing device as recited in claim 37, wherein θ is equal to about 45°. 39. The computing device as recited in claim 35, wherein the linear transform is definable as: Ŝ(u,v)≡S(V(u,v)′)where V≡[kk/201]and k≡2√3/3. 40. The computing device as recited in claim 35, wherein the first texture map includes Mercator projection information for the first portion, and the second texture map includes stereographic projection information for the second portion. 41. The computing device as recited in claim 40, wherein the logic is further configured to provide a third texture map for a third portion of the three-dimensional surface, the third texture map being associated with the second mapping technique, and wherein the third texture map includes stereographic projection information for the third portion. 42. The computing device as recited in claim 40, wherein the first and second texture maps are conformal and have a sampling requirement definable as: Mcapped(θ)≡Mstereo(θ)+MMercator(π/2−θ)=16 tan2(θ/2)+π ln((1+cos θ)/(1−cos θ))where θ is a transition angle from a defined point on the surface to where the second texture map is adjacent to the first texture map. 43. The computing device as recited in claim 42, wherein θ is equal to about 47.8°. 44. The computing device as recited in claim 35, wherein the cylindrical projection information includes information selected from at least one type of projection information selected from a group comprising plane-chart projection information, equal area information, and Mercator information. 45. The computing device as recited in claim 35, wherein the azimuthal projection information includes information selected from at least one type of projection information selected from a group comprising equidistant projection information, stereographic projection information, gnomonic projection information, and equal area projection information. 46. The computing device as recited in claim 35, wherein the first portion is significantly adjacent to both the first and second portions, such that the first portion separates the second and third portions. 47. The computing device as recited in claim 35, wherein the three-dimensional surface is curvilinear. 48. The computing device as recited in claim 35, wherein the three-dimensional surface includes a spherical surface. 49. The computing device as recited in claim 35, wherein the logic is further configured to analyze the texture map per at least one criterion to determine an appropriate texture resolution when providing the first texture map. 50. The computing device as recited in claim 35, wherein the logic is further configured to analyze the texture map per at least one metric criterion to determine a requisite number of texture maps in addition to the first texture map when providing the first texture map. 51. The computing device as recited in claim 35, wherein at least one of the first and second texture maps includes information based on a rectangular sampling matrix. 52. The computing device as recited in claim 35, wherein at least one of the first and second texture maps includes information based on a hexagonal sampling matrix. 53. A computer-implemented method comprising: providing a first texture map for a first portion of a three-dimensional surface, the first texture map being associated with a first mapping technique;providing a second texture map for a second portion of the three-dimensional surface, the second texture map being associated with a second mapping technique that is different from the first mapping technique, the first texture map including Mercator projection information for the first portion, and the second texture map including stereographic projection information for the second portion;providing a third texture map for a third portion of the three-dimensional surface, the third texture map being associated with the second mapping technique, and the third texture map including stereographic projection information for the third portion; andgenerating a multiple-component map set that includes at least a portion of the first, the second and the third texture map, wherein the first and second texture maps are conformal and have a sampling requirement definable as: Mcapped(θ)≡Mstereo(θ)+MMercator(π/2−θ)=16 tan2(θ/2)+π ln((1+cos θ)/(1−cos θ))where θ is a transition angle from a defined point on the surface to where the second texture map is adjacent to the first texture map. 54. The method as recited in claim 53, wherein θ is equal to about 47.8°.
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