System and method for contiguous images from polygons

• US 20050062763A1
• Filed: 10/13/2004
• Published: 03/24/2005
• Est. Priority Date: 02/27/2002
• Status: Active Grant

• Current Assignee: AT&T Corporation (AT&T, Inc.)
• Original Assignee: AT&T Corporation (AT&T, Inc.)
• Inventors: Panse, Christian, Keim, Daniel, North, Stephen Charles
• Granted Patent: US 7,286,144 B2
• Time in Patent Office: Days
• US Class Current: 345/647
• CPC Class Codes: G09B 29/00 Maps; Plans; Charts; Diagrams, e.g. route diagram star maps G09B27/04; devices for holding or supporting maps A47B97/02; for computing purposes G06G1/14, G09B1/16; display boards G09F
• CPC Class Codes: G09B 29/001 Planning boards
• CPC Class Codes: G09B 29/005 Map projections or methods associated specifically therewith

Abstract

A system, method and computer-readable media are disclosed for generating an image from another image of contiguous polygons and a vector containing values to which areas of corresponding polygons are scaled. The method embodiment relates to generating an image from a plurality of contiguous polygons having vertices. The method comprises calculating a shape value associated with a polygon, calculating an altered shape value associated with an altered polygon, the altered polygon being an altered version of the polygon, calculating a shape distortion by comparing the shape value and the altered shape value and determining whether to accept the altered polygon based on the calculated shape distortion.

Claims

1. A method for generating an image from a plurality of contiguous polygons having vertices, the method comprising:

calculating a shape value associated with a polygon;

calculating an altered shape value associated with an altered polygon, the altered polygon being an altered version of the polygon;

calculating a shape distortion by comparing the shape value and the altered shape value; and

determining whether to accept the altered polygon based on the calculated shape distortion.

2. The method of claim 1, wherein the image is a cartogram.

3. The method of claim 1, wherein calculating a shape value associated with a polygon comprises:

determining a curvature function of the polygon; and

performing a Fourier transform of the first curvature function to calculate the shape value.

4. The method of claim 1, wherein calculating an altered shape value associated with an altered polygon further comprises:

repositioning one of the vertices of the polygon to produce the altered polygon;

determining an altered curvature function of the altered polygon; and

performing a Fourier transform of the altered curvature function to calculate the altered shape value.

5. A system for generating an image from a plurality of contiguous polygons having vertices, the system comprising:

means for calculating a shape value associated with a polygon;

means for calculating an altered shape value associated with an altered polygon, the altered polygon being an altered version of the polygon;

means for calculating a shape distortion by comparing the shape value and the altered shape value; and

means for determining whether to accept the altered polygon based on the calculated shape distortion.

6. The system of claim 5, wherein the image is a cartogram.

7. The system of claim 5, wherein the means for calculating a shape value associated with a polygon comprises:

means for determining a curvature function of the polygon; and

means performing a Fourier transform of the first curvature function to calculate the shape value.

8. The system of claim 5, wherein the means for calculating an altered shape value associated with an altered polygon further comprises:

means for repositioning one of the vertices of the polygon to produce an altered polygon;

means for determining an altered curvature function of the altered polygon; and

means for performing a Fourier transform of the altered curvature function to calculate the altered shape value.

9. A method for generating a second image from a first image of a plurality of contiguous first polygons with vertices, the second image having a plurality of second polygons corresponding to the plurality of first polygons, the first polygons having areas proportional to values contained in a data vector, the method comprising:

identifying a vertex having adjacent polygons for repositioning;

determining an area error of the adjacent polygons based on corresponding data vector values;

determining a shape error of the adjacent polygons; and

deciding whether to reposition the identified vertex based on the shape error and the area error.

10. The method of claim 9, wherein determining a shape error of the adjacent polygons is based on a Fourier transformation of a curvature function of a perimeter of each polygon.

11. The method of claim 9, wherein the first image is cartogram and the second image is a map.

12. A computer-readable medium storing instructions for controlling a computing device to generate an image from a plurality of contiguous polygons having vertices, the instructions comprising:

calculating a shape value associated with a polygon;

calculating an altered shape value associated with an altered polygon, the altered polygon being an altered version of the polygon;

calculating a shape distortion by comparing the shape value and the altered shape value; and

determining whether to accept the altered polygon based on the calculated shape distortion.

13. The computer-readable medium of claim 12, wherein the image is a cartogram.

14. The computer-readable medium of claim 12, wherein calculating a shape value associated with a polygon comprises:

determining a curvature function of the polygon; and

performing a Fourier transform of the first curvature function to calculate the shape value.

15. The computer-readable medium of claim 12, wherein calculating an altered shape value associated with an altered polygon further comprises:

repositioning one of the vertices of the polygon to produce an altered polygon;

determining an altered curvature function of the altered polygon; and

performing a Fourier transform of the altered curvature function to calculate the altered shape value.

16. A system for generating a second image from a first image of a plurality of contiguous first polygons with vertices, the second image having a plurality of second polygons corresponding to the plurality of first polygons, the first polygons having areas proportional to values contained in a data vector, the system comprising:

means for identifying a vertex having adjacent polygons for repositioning;

means for determining an area error of the adjacent polygons based on corresponding data vector values;

means for determining a shape error of the adjacent polygons; and

means for deciding whether to reposition the identified vertex based on the shape error and the area error.

17. The system of claim 16, wherein the means for determining a shape error of the adjacent polygons is based on a Fourier transformation of a curvature function of a perimeter of each polygon.

18. The system of claim 16, wherein the first image is cartogram and the second image is a map.

19. A system for generating an image from a plurality of contiguous polygons having vertices, the system comprising:

a module that calculates a shape value associated with a polygon;

a module that calculates an altered shape value associated with an altered polygon, the altered polygon being an altered version of the polygon;

a module that calculates a shape distortion by comparing the shape value and the altered shape value; and

a module that determines whether to accept the altered polygon based on the calculated shape distortion.

20. The system of claim 19, wherein the image is a cartogram.

21. The system of claim 19, wherein the module that calculates a shape value associated with a polygon further determines a curvature function of the polygon and performs a Fourier transform of the first curvature function to calculate the shape value.

22. The system of claim 19, wherein the module that calculates an altered shape value associated with an altered polygon further repositions one of the vertices of the polygon to produce an altered polygon, determines an altered curvature function of the altered polygon and performs a Fourier transform of the altered curvature function to calculate the altered shape value.