Method for determining an intuitively defined spatial relationship among physical entities
First Claim
1. A method for determining whether a specified spatial relationship exists among physical spatial entities comprising the steps of:
- (a) determining sets of elements forming a representation of each of a plurality of spatially significant descriptors which describe each of said physical spatial entities;
(b) determining with processing means intersections between the sets of elements of every combination of descriptors between different ones of said spatial entities;
(c) categorizing with said processing means relationships between every combination of descriptors based upon the intersections of the corresponding sets of elements and the descriptors themselves;
(d) combining with said processing means said relationships categorized in said step (c) to determine a unique mathematical relationship that exists between said spatial entities; and
(e) determining with said processing means whether said unique mathematical relationship between said spatial entities matches any one of a plurality of desired mathematical relationships which collectively define said specified spatial relationship, to determine that said spatial entities have said specified spatial relationship.
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Abstract
Apparatus and method for determining whether a specific spatial relationship exists among physical spatial entities. First, spatially significant descriptors such as the interior and boundary of the physical spatial entities are selected and sets of elements forming a representation of each of the descriptors for each spatial entity is determined. Intersections are then determined between the sets of elements for every combination of descriptors and these intersections are categorized. The categorized relationships are then combined to determine a unique mathematical relationship between the spatial entities. The specific spatial relationship to be analyzed is broken down into the set of desired mathetmatical relationships. According to the present invention, it is then determined whether the unique mathematical relationship between the spatial entities matches any of the desired mathematical relationships used to define the specific relationship, to determine whether or not the spatial entities have the specific relationship.
9 Citations
50 Claims
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1. A method for determining whether a specified spatial relationship exists among physical spatial entities comprising the steps of:
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(a) determining sets of elements forming a representation of each of a plurality of spatially significant descriptors which describe each of said physical spatial entities; (b) determining with processing means intersections between the sets of elements of every combination of descriptors between different ones of said spatial entities; (c) categorizing with said processing means relationships between every combination of descriptors based upon the intersections of the corresponding sets of elements and the descriptors themselves; (d) combining with said processing means said relationships categorized in said step (c) to determine a unique mathematical relationship that exists between said spatial entities; and (e) determining with said processing means whether said unique mathematical relationship between said spatial entities matches any one of a plurality of desired mathematical relationships which collectively define said specified spatial relationship, to determine that said spatial entities have said specified spatial relationship. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17)
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18. A method for determining whether a specific spatial relationship exists between first and second physical spatial entities comprising the steps of:
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(a) determining, with processing mans, sets of elements forming a representation of a boundary for each of said first and second spatial entities; (b) determining with processing means sets of elements forming a representation of an interior for each of said first and second spatial entities; (c) determining with said processing means intersections between the sets of elements of;
(1) said boundary of said first spatial entity and said boundary of said second spatial entity, (2) said interior of said first spatial entity and said interior of said second spatial entity;
(3) said boundary of said first spatial entity and said interior of said second spatial entity and (4) said interior of said first spatial entity and said boundary of said second spatial entity;(d) determining with said processing means the number of elements in each set specifying the boundary and interior of said first and second spatial entities; (e) categorizing with said processing means relationships between each of boundary and interior of said first spatial entity and both of boundary and interior of said second spatial entity, respectively, based upon at least one of set intersection, symmetric difference, set differences and dimension, said categorizing being based on said determining step (c) and said generating step (d); (f) generating with said processing means a unique one of a plurality of codes, based upon said categorizing step (e), which uniquely identifies said relationships; and (g) determining with said processing means whether said unique code matches any one of a plurality of desired codes which collectively define said specified spatial relationship, to determine that said spatial entities have said specified spatial relationship. - View Dependent Claims (19, 20, 21, 22, 23, 24, 25)
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26. Apparatus for determining whether a specified spatial relationship exists among physical spatial entities comprising:
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means for storing representations of said spatial entities; means, coupled to said storing means, for entering said representations of said spatial entities into said storing means; and analyzing means, coupled to said storing means, for;
(1) determining sets of elements forming a representation of each of a plurality of spatially significant descriptors which describe each of said physical spatial entities;
(2) determining intersections between the sets of elements of every combination of descriptors between different ones of said spatial entities;
(3) categorizing relationships between every combination of descriptors based upon the intersections of the corresponding sets of elements and the descriptors themselves;
(4) combining said categorized relationships to determine a unique mathematical relationship that exists between said spatial entities; and
(5) determining whether said unique mathematical relationship between said spatial entities matches any one of a plurality of desired mathematical relationships which collectively define said specified spatial relationship, to determine that said spatial entities have said specified spatial relationship. - View Dependent Claims (27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42)
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43. Apparatus for determining whether a specific spatial relationship exists between first and second physical spatial entities comprising:
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means for storing representations of said physical spatial entities; means, coupled to said storing means, for entering said representations into said storing means; and analyzing means, coupled to said storing means, for;
(1) determining sets of elements forming a representation of a boundary for each of said first and second spatial entities;
(2) determining sets of elements forming a representation of an interior for each of said first and second spatial entities;
(3) determining intersections between the sets of elements of;
(a) said boundary of said first spatial entity and said boundary of said second spatial entity, (b) said interior of said first spatial entity and said interior of said second spatial entity, (c) said boundary of said first spatial entity and said interior of said second spatial entity and (d) said interior of said first spatial entity and said boundary of said second spatial entity;
(4) determining the number of elements in each set specifying the boundary and interior of said first and second spatial entities;
(5) categorizing relationships between each of boundary and interior of said first spatial entity and both of boundary and interior of said second spatial entity, respectively, based upon at least one of set intersection, symmetric difference, set differences and dimension, said categorizing being based on said intersection determining function and said data generating function;
(6) generating a unique one of a plurality of codes, based upon said categorization, which uniquely identifies said relationships; and
(7) determining whether said unique code matches any one of a plurality of desired codes which collectively define said specified spatial relationship, to determine that said spatial entities have said specified spatial relationship. - View Dependent Claims (44, 45, 46, 47, 48, 49, 50)
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Specification