System and method for generating a low discrepancy curve in a region
First Claim
1. A method for generating a curve in a region, the method comprising:
- generating an unbounded Low Discrepancy Point;
applying one or more boundary conditions to the unbounded Low Discrepancy Point to generate a bounded Low Discrepancy Point, wherein the bounded Low Discrepancy Point is located within the region;
repeating said generating and said applying one or more boundary conditions one or more times, thereby generating a Low Discrepancy Sequence in the region;
storing the Low Discrepancy Sequence; and
generating output comprising the Low Discrepancy Sequence, wherein the Low Discrepancy Sequence defines the curve in the region.
5 Assignments
0 Petitions
Accused Products
Abstract
A system and method for generating a curve in a region, e.g., a Low Discrepancy Curve. The method may generate an unbounded Low Discrepancy Point (LDP); apply one or more boundary conditions to the unbounded LDP to generate a bounded LDP located within the region; repeat said generating and said applying one or more boundary conditions one or more times, generating a Low Discrepancy Sequence (LDS) in the region; store the LDS; and generate output comprising the LDS, wherein the LDS defines the curve in the region. The method may scan the region according to the defined curve. In generating the unbounded LDP, the method may select two or more irrational numbers, a step size epsilon (ε), and a starting position; initialize a current position to the starting position; and increment components of the current position based on ε and the irrational numbers to generate the unbounded LDP.
-
Citations
38 Claims
-
1. A method for generating a curve in a region, the method comprising:
-
generating an unbounded Low Discrepancy Point;
applying one or more boundary conditions to the unbounded Low Discrepancy Point to generate a bounded Low Discrepancy Point, wherein the bounded Low Discrepancy Point is located within the region;
repeating said generating and said applying one or more boundary conditions one or more times, thereby generating a Low Discrepancy Sequence in the region;
storing the Low Discrepancy Sequence; and
generating output comprising the Low Discrepancy Sequence, wherein the Low Discrepancy Sequence defines the curve in the region. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19)
-
-
20. A method for generating a curve in a region, the method comprising:
-
selecting two or more irrational numbers;
selecting a step size epsilon (ε
);
selecting a starting position;
initializing a current position to the starting position;
incrementing each term of the current position based on a factor of ε and
one of the irrational numbers to generate an unbounded Low Discrepancy Point, wherein each term corresponds to a dimension of the region;
applying boundary conditions to one or more terms of the unbounded Low Discrepancy Point in response to said incrementing to generate a bounded Low Discrepancy Point, wherein the bounded Low Discrepancy Point is located within the region;
setting the current position to the bounded Low Discrepancy Point;
storing the bounded Low Discrepancy Point;
repeating said incrementing, said applying boundary conditions, said setting the current position, and said storing one or more times, thereby generating a Low Discrepancy Sequence in the region; and
generating output comprising the Low Discrepancy Sequence, wherein the Low Discrepancy Sequence defines the curve in the region. - View Dependent Claims (21)
-
-
22. A method for generating a Low Discrepancy Curve in a region, the method comprising:
-
selecting a starting position (x01, . . . x0n);
initializing a current position (x1, . . . xn) to the starting position;
incrementing each term (xi) of the current position by (ε
*α
1) to generate an unbounded Low Discrepancy Point (y1, . . . yn), wherein each term (xi) corresponds to a dimension of the region;
applying boundary conditions to each term (yi) of the unbounded Low Discrepancy Point (y1, . . . yn) in response to said incrementing to generate a bounded Low Discrepancy Point (z1, . . . zn);
setting the current position (x1, . . . xn) to the bounded Low Discrepancy Point (z1, . . . zn);
storing the bounded Low Discrepancy Point (z1, . . . zn);
repeating said incrementing, said applying boundary conditions, said setting the current position, and said storing until a stopping condition is reached, thereby generating a second Low Discrepancy Sequence in the region; and
generating output, wherein said output comprises the second Low Discrepancy Sequence, wherein the second Low Discrepancy Sequence defines the Low Discrepancy Curve in the region.
-
-
23. A memory medium which is operable to store program instructions for generating a curve in a region, wherein said program instructions are executable to perform:
-
generating an unbounded Low Discrepancy Point;
applying one or more boundary conditions to the unbounded Low Discrepancy Point to generate a bounded Low Discrepancy Point, wherein the bounded Low Discrepancy Point is located within the region;
repeating said generating and said applying one or more boundary conditions one or more times, thereby generating a Low Discrepancy Sequence in the region;
storing the Low Discrepancy Sequence; and
generating output comprising the Low Discrepancy Sequence, wherein the Low Discrepancy Sequence defines the curve in the region. - View Dependent Claims (24, 25, 26, 27, 28, 29, 30, 31, 32, 33)
-
-
34. A system for generating a curve in a region, comprising:
-
a CPU; and
a memory medium which is operable to store one or more software programs;
wherein said CPU is operable to execute said one or more software programs to perform;
generating an unbounded Low Discrepancy Point;
applying one or more boundary conditions to the unbounded Low Discrepancy Point to generate a bounded Low Discrepancy Point, wherein the bounded Low Discrepancy Point is located within the region;
repeating said generating and said applying one or more boundary conditions one or more times, thereby generating a Low Discrepancy Sequence in the region;
storing the Low Discrepancy Sequence; and
generating output comprising the Low Discrepancy Sequence, wherein the Low Discrepancy Sequence defines the curve in the region. - View Dependent Claims (35, 36, 37, 38)
-
Specification