Rotational symmetry detection for configurations of discrete curves
First Claim
1. A medium configured for determining an underlying rotational symmetry group of a configuration of discrete curves, wherein the medium is configured to perform:
- receiving a configuration of discrete closed curves;
determining a plurality of configuration rotational symmetry sub-groups of the configuration, wherein each of the plurality of configuration rotational symmetry sub-groups is associated with one or more of the discrete curves, and wherein the plurality of configuration rotational symmetry sub-groups are based on each discrete curve'"'"'s distance from a configuration center of mass, equivalence class, rotational symmetry group, and sub-configuration rotational symmetry group; and
if no discrete curves having a distance from the configuration center of mass of substantially zero also have a rotational symmetry group of one;
computing a greatest common divisor (GCD) of the plurality of configuration rotational symmetry sub-groups, wherein the GCD comprises an underlying rotation symmetry group of the configuration; and
outputting the underlying rotation symmetry group of the configuration.
5 Assignments
0 Petitions
Accused Products
Abstract
System and method for characterizing configurations of discrete curves based on detected symmetries in the configuration. A configuration of discrete closed curves is received. A plurality of configuration rotational symmetry sub-groups of the configuration are determined, each associated with one or more of the discrete curves, and based on each curve'"'"'s distance from a configuration center of mass, equivalence class, rotational symmetry group, and sub-configuration rotational symmetry group. The configuration rotational symmetry sub-groups are determined by normalizing the configuration, including determining a configuration center of mass, determining the equivalence class and rotational symmetry group for each discrete curve, determining one or more subsets of the discrete curves based on each discrete curve'"'"'s equivalence class and distance from the configuration center of mass, and determining configuration rotational symmetry sub-groups for each of the subsets based on each curve'"'"'s rotational symmetry group, and relative orientations of the discrete curves in the subset.
6 Citations
60 Claims
-
1. A medium configured for determining an underlying rotational symmetry group of a configuration of discrete curves, wherein the medium is configured to perform:
-
receiving a configuration of discrete closed curves;
determining a plurality of configuration rotational symmetry sub-groups of the configuration, wherein each of the plurality of configuration rotational symmetry sub-groups is associated with one or more of the discrete curves, and wherein the plurality of configuration rotational symmetry sub-groups are based on each discrete curve'"'"'s distance from a configuration center of mass, equivalence class, rotational symmetry group, and sub-configuration rotational symmetry group; and
if no discrete curves having a distance from the configuration center of mass of substantially zero also have a rotational symmetry group of one;
computing a greatest common divisor (GCD) of the plurality of configuration rotational symmetry sub-groups, wherein the GCD comprises an underlying rotation symmetry group of the configuration; and
outputting the underlying rotation symmetry group of the configuration. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 33, 34)
-
-
18. A system for determining an underlying rotational symmetry group of a configuration of discrete curves, the system comprising:
-
means for receiving a configuration of discrete closed curves;
means for determining a plurality of configuration rotational symmetry sub-groups of the configuration, wherein each of the plurality of configuration rotational symmetry sub-groups is associated with one or more of the discrete curves, and wherein the plurality of configuration rotational symmetry sub-groups are based on each discrete curve'"'"'s distance from a configuration center of mass, equivalence class, rotational symmetry group, and sub-configuration rotational symmetry group;
means for computing a greatest common divisor (GCD) of the plurality of configuration rotational symmetry sub-groups, wherein the GCD comprises an underlying rotation symmetry group of the configuration; and
means for outputting the underlying rotation symmetry group of the configuration.
-
-
19. A method for determining an underlying rotational symmetry group of a configuration of discrete curves, the method comprising:
-
receiving a configuration of discrete closed curves;
determining a plurality of configuration rotational symmetry sub-groups of the configuration, wherein each of the plurality of configuration rotational symmetry sub-groups is associated with one or more of the discrete curves, and wherein the plurality of configuration rotational symmetry sub-groups are based on each discrete curve'"'"'s distance from a configuration center of mass, equivalence class, rotational symmetry group, and sub-configuration rotational symmetry group; and
if no discrete curves having a distance from the configuration center of mass of substantially zero also have a rotational symmetry group of one;
computing a greatest common divisor (GCD) of the plurality of configuration rotational symmetry sub-groups, wherein the GCD comprises an underlying rotation symmetry group of the configuration; and
outputting the underlying rotation symmetry group of the configuration. - View Dependent Claims (20, 21, 22)
-
-
23. A medium configured for determining rotational symmetry groups of a configuration of discrete curves, wherein the medium is configured to perform:
-
receiving a configuration of discrete curves, wherein the configuration comprises a plurality of discrete closed curves;
normalizing the configuration, including determining a configuration center of mass;
determining a rotational symmetry group for each discrete curve;
determining an equivalence class for each discrete curve;
determining one or more subsets of the plurality of discrete curves based on each discrete curve'"'"'s equivalence class and distance from the configuration center of mass, wherein each subset comprises one or more discrete curves at a respective distance from the configuration center of mass;
determining one or more configuration rotational symmetry groups for each of the one or more subsets based on each discrete curve'"'"'s rotational symmetry group, and relative orientations of the discrete curves in the subset; and
outputting the determined one or more configuration rotational symmetry groups for each of the one or more subsets. - View Dependent Claims (24, 25, 26, 27, 28, 29, 30, 31, 32)
-
-
35. A method for determining rotational symmetry groups of a configuration of discrete curves, the method comprising:
-
receiving a configuration of discrete curves, wherein the configuration comprises a plurality of discrete closed curves;
normalizing the configuration, including determining a configuration center of mass;
determining a rotational symmetry group for each discrete curve;
determining an equivalence class for each discrete curve;
determining one or more subsets of the plurality of discrete curves based on each discrete curve'"'"'s equivalence class and distance from the configuration center of mass, wherein each subset comprises one or more discrete curves at a respective distance from the configuration center of mass;
determining one or more configuration rotational symmetry groups for each of the one or more subsets based on each discrete curve'"'"'s rotational symmetry group, and relative orientations of the discrete curves in the subset; and
outputting the determined one or more configuration rotational symmetry groups for each of the one or more subsets. - View Dependent Claims (36, 37, 38, 39, 40, 41)
-
-
42. A system for determining rotational symmetry groups of a configuration of discrete curves, comprising:
-
means for receiving a configuration of discrete curves, wherein the configuration comprises a plurality of discrete closed curves;
means for normalizing the configuration, including determining a configuration center of mass;
means for determining a rotational symmetry group for each discrete curve;
means for determining an equivalence class for each discrete curve;
means for determining one or more subsets of the plurality of discrete curves based on each discrete curve'"'"'s equivalence class and distance from the configuration center of mass, wherein each subset comprises one or more discrete curves at a respective distance from the configuration center of mass;
means for determining one or more configuration rotational symmetry groups for each of the one or more subsets based on each discrete curve'"'"'s rotational symmetry group, and relative orientations of the discrete curves in the subset; and
means for outputting the determined one or more configuration rotational symmetry groups for each of the one or more subsets. - View Dependent Claims (48, 49, 50)
-
-
43. A medium configured for determining rotational symmetry sub-groups of a configuration of substantially equivalent discrete curves, wherein the medium is configured to perform:
-
receiving a configuration of discrete curves, wherein the configuration of discrete curves comprises a plurality of discrete curves, and wherein each of the plurality of discrete curves are closed;
normalizing the configuration of discrete curves;
determining a plurality of respective orientations between respective pairs of the discrete curves;
determining one or more finite sub-groups of the plurality of discrete curves based on the configuration and the plurality of respective orientations, wherein the one or more finite sub-groups corresponds to a respective one or more rotational symmetry sub-groups of the configuration; and
outputting the one or more rotational symmetry sub-groups of the configuration. - View Dependent Claims (44, 45, 46, 47, 51, 52)
-
-
53. A method for determining rotational symmetry sub-groups of a configuration of substantially equivalent discrete curves, the method comprising:
-
receiving a configuration of discrete curves, wherein the configuration of discrete curves comprises a plurality of discrete curves, and wherein each of the plurality of discrete curves are closed;
normalizing the configuration of discrete curves;
determining a plurality of respective orientations between respective pairs of the discrete curves;
determining one or more finite sub-groups of the plurality of discrete curves based on the configuration and the plurality of respective orientations, wherein the one or more finite sub-groups corresponds to a respective one or more rotational symmetry sub-groups of the configuration; and
outputting the one or more rotational symmetry sub-groups of the configuration. - View Dependent Claims (54, 55, 56, 57, 58, 59)
-
-
60. A system for determining rotational symmetry sub-groups of a configuration of substantially equivalent discrete curves, the system comprising:
-
means for receiving a configuration of discrete curves, wherein the configuration of discrete curves comprises a plurality of discrete curves, and wherein each of the plurality of discrete curves are closed;
means for normalizing the configuration of discrete curves;
means for determining a plurality of respective orientations between respective pairs of the discrete curves;
means for determining one or more finite sub-groups of the plurality of discrete curves based on the configuration and the plurality of respective orientations, wherein the one or more finite sub-groups corresponds to a respective one or more rotational symmetry sub-groups of the configuration; and
means for outputting the one or more rotational symmetry sub-groups of the configuration.
-
Specification