TILED PROJECTIONS FOR PLANAR PROCESSING OF ROUND EARTH DATA

• US 20090123088A1
• Filed: 05/08/2008
• Published: 05/14/2009
• Est. Priority Date: 11/14/2007
• Status: Active Grant

• Current Assignee: Microsoft Technology Licensing LLC (Microsoft Corporation)
• Original Assignee: Microsoft Corporation
• Inventors: Kunen, Isaac Kenneth, Kallay, Michael
• Granted Patent: US 8,638,327 B2
• Time in Patent Office: Days
• US Class Current: 382/295
• CPC Class Codes: G06T 3/12 Panospheric to cylindrical image transformations

Abstract

A system and method that facilitates planar processing of round earth data by employing a tiled projection is provided. The tiled projection is a two-step projection from the surface of the earth to a common plane that preserves polygons and polygonal paths. During the first step, the system performs a gnomonic projection to the facets of a circumscribed platonic solid, which maps spherical polygons to spatial polygons on the facets of the solid. During the second step, the system performs a polygon-preserving projection from the facets of the platonic solid to tiles in common plane. Thus, projections from multiple facets of the platonic solid on the common plane are processed by employing a planar algorithm.

Claims

1. A computer implemented system that facilitates tiled projections for planar processing of spherical data, comprising:

a mapping component that projects the spherical data, mapped onto facets of a polyhedron, to a single plane while preserving at least one of polygons or polygonal paths; and

a processing component that employs a planar algorithm to perform a computation on data mapped to the single plane.

2. The computer implemented system of claim 1, wherein the polyhedron is at least one of an octahedron, a tetrahedron or a cube, the polyhedron circumscribes a sphere associated with the spherical data.

3. The computer implemented system of claim 1, wherein the mapping component projects at least one of an entire hemisphere or an entire sphere onto the single plane based in part on the polyhedron employed for the mapping, such that polygons and polygonal paths are preserved during the mapping.

4. The computer implemented system of claim 1, further comprising, a first projection component that maps one or more points on a sphere to one or more points on corresponding facets of the polyhedron by employing a gnomonic projection.

5. The computer implemented system of claim 4, further comprising, a second projection component that maps the one or more points on the corresponding facets to one or more points on corresponding tiles of the single plane by employing at least one of an affine or central projection.

6. The computer implemented system of claim 1, further comprising, a crease vertex addition component that inserts a fake crease vertex on a projection in the single plane at a crease that separates the projection onto two tiles.

7. The computer implemented system of claim 1, further comprising, a node vertex addition component that inserts a fake node vertex on a projection in the single plane at a seam that separates the projection onto two planes.

8. The computer implemented system of claim 1, further comprising, an inverse mapping component that performs a polygon-preserving inverse mapping to map a result of the computation from the single plane to spherical coordinates.

9. The computer implemented system of claim 1, further comprising, a polyhedron selection component that determines a type of polyhedron employed for the mapping based in part on at least one of a user input or an artificial intelligence(AI)-based scheme.

10. A computer implemented method that facilitates mapping of data from a surface of a sphere to a common plane, comprising:

projecting the data that is mapped to facets of a polyhedron, onto the common plane, the projection is polygon-preserving; and

performing an operation on the projection by employing a planar algorithm.

11. The computer implemented method of claim 10, wherein the polyhedron is at least one of an octahedron, a tetrahedron or a cube that circumscribes the sphere.

12. The computer implemented method of claim 10, further comprising, inserting a fake crease vertex on the projection at a crease that separates the projection onto two tiles in the common plane.

13. The computer implemented method of claim 10, further comprising, employing a gnomonic projection to map at least one point from the surface of the sphere to at least one point on one or more corresponding facets of the polyhedron.

14. The computer implemented method of claim 13, further comprising, employing at least one of an affine or central projection to map the at least one point on the one or more corresponding facets to at least one point on one or more corresponding tiles in the common plane.

15. The computer implemented method of claim 10, further comprising, projecting at least one of an entire hemisphere or the entire sphere onto a single plane based in part on the polyhedron employed for mapping.

16. A computer implemented system that facilitates tiled mapping of spherical data to a common plane, comprising:

means for projecting the spherical data that is mapped to facets of a polyhedron onto the common plane, the projection is polygon-preserving; and

means for processing data mapped to the common plane by employing a planar algorithm.

17. The computer implemented system of claim 16, wherein the polyhedron is at least one of an octahedron, a tetrahedron or a cube that circumscribes a sphere.

18. The computer implemented system of claim 16, wherein the projection onto the common plane is at least one of an affine projection or a central projection.

19. The computer implemented system of claim 16, further comprising, means for mapping an arc on a sphere as a straight line in the common plane, when a projection of the arc on the common plane is contained in one tile.

20. The computer implemented system of claim 16, further comprising, means for mapping an arc on the sphere as a broken straight line by inserting one or more fake crease vertex, when a projection of the arc on the common plane is contained in two or more tiles.