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US 2003/0210210 A1Published application
Discrete pattern, apparatus, method, and program storage device for generating and implementing the discrete pattern
AssigneeInternational Business Machines Corporation
InventorsTsuyoshi Ide, Hideyuki Mizuta, Yoichi Taira, Akiko Nishikai
Life of this patent
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Abstract
A discrete pattern, formed by dots discretely arranged in two dimensions, is provided wherein the dots are generated in a low discrepancy sequence. The dots are preferably generated in a discrete pattern wherein the square of discrepancy D satisfies the formula, D≦0.13N−1.15 (1) Further, the method provides for generation of, and the appartus provides implementation of, a discrete pattern even when the filling factor rapidly changes by automatically generating or deleting dots.
Claims66
A discrete pattern, formed by dots discretely arranged in two dimensions, wherein said dots included in a rectangular area having a longitudinal length of Lx and a transverse length of Ly satisfy expression,
- D≦0.13N−1.15 (1)
- such that, N denotes the number of dots included in a predetermined area, and D is obtained by expression (2), wherein A(x,y) defines the number of dots, of a total of N dots, included in a rectangular area for which a line segment extended from reference coordinates (0,0) to an arbitrary coordinate point (x,y) is a diagonal line,
- 55 D ( L x , L y ;
- N ) = ∫ ∫ L x x L y [ A ( x , y ) N - x y L x L y ] 2 ⅆ x ⅆ y L x L y ( 2 )
- and wherein S1 that is obtained by expression
- 56 S 1 ( r 1 , r 2 ) = ∫ r 1 r 2 ⅆ r | g 1 ( r ;
- r 1 , r 2 ) - g a v | ( 3 )
- is equal to or smaller than 0.7, such that g1 is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integration value of g(r) over a range of from r1 to r2, and gav is the average value of g1 within the range of from r1 to r2;
- such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r1 and r2 are chosen as one and four times the value of the lattice constant Dr respectively;
- and the dot filling rate is a value obtained by multiplying the square of the maximum diameter of a dot by the number of dots, and dividing the product by the size of the area.
7 more elements
An optical member, on which a discrete pattern is formed by dots discretely arranged in two dimensions, wherein said dots included in a rectangular area having a longitudinal length of Lx and a transverse length of Ly satisfy expression,
- D≦0.13N−1.15 (1)
- such that, N denotes the number of dots included in a predetermined area, and D is obtained by expression (2), wherein A(x,y) defines the number of dots, of a total of N dots, included in a rectangular area for which a line segment extended from reference coordinates (0,0) to an arbitrary coordinate point (x,y) is a diagonal line,
- 57 D ( L x , L y ;
- N ) = ∫ ∫ L x x L y [ A ( x , y ) N - x y L x L y ] 2 ⅆ x ⅆ y L x L y ( 2 )
- and wherein S1 that is obtained by expression
- 58 S 1 ( r 1 , r 2 ) = ∫ r 1 r 2 ⅆ r | g 1 ( r ;
- r 1 , r 2 ) - g a v | ( 3 )
- is equal to or smaller than 0.7, such that, g1 is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integration value of g(r) over a range of from r1 to r2, and gav is the average value of g1 within the range of from r1 to r2;
- such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r1 and r2 are chosen as one and four times the value of the lattice constant Dr respectively;
- and the dot filling rate is a value obtained by multiplying the square of the maximum diameter of a dot by the number of dots, and dividing the product by the size of the area.
7 more elements
A light guide plate, used for a light-transmitting liquid crystal display device, on which a discrete pattern is formed by dots discretely arranged in two dimensions, wherein said dots included in a rectangular area having a longitudinal length of Lx and a transverse length of Ly satisfy expression,
- D≦0.13N−1.15 (1)
- such that, N denotes the number of dots included in a predetermined area, and D is obtained by expression (2), wherein A(x,y) defines the number of dots, of a total of N dots, included in a rectangular area for which a line segment extended from reference coordinates (0,0) to an arbitrary coordinate point (x,y) is a diagonal line,
- 59 D ( L x , L y ;
- N ) = ∫ ∫ L x x L y [ A ( x , y ) N - x y L x L y ] 2 ⅆ x ⅆ y L x L y ( 2 )
- and wherein S1 that is obtained by expression (3)
- 60 S 1 ( r 1 , r 2 ) = ∫ r 1 r 2 ⅆ r | g 1 ( r ;
- r 1 , r 2 ) - g a v | ( 3 )
- is equal to or smaller than 0.7, such that, g1 is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integration value of g(r) over a range of from r1 to r2, and gav is the average value of g1 within the range of from r1 to r2, such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r1 and r2 are chosen as one and four times the value of the lattice constant Dr respectively;
- and the dot filling rate is a value obtained by multiplying the square of the maximum diameter of a dot by the number of dots, and dividing the product by the size of the area.
6 more elements
A side light device comprising:
- a light guide plate, on which a discrete pattern is formed by dots discretely arranged in two dimensions, wherein said dots included in a rectangular area having a longitudinal length of Lx and a transverse length of Ly satisfy expression,
- D≦0.13N−1.15 (1)
- such that, N denotes the number of dots included in a predetermined area, and D is obtained by expression (2), wherein A(x,y) defines the number of dots, of a total of N dots, included in a rectangular area for which a line segment extended from reference coordinates (0,0) to an arbitrary coordinate point (x,y) is a diagonal line,
- 61 D ( L x , L y ;
- N ) = ∫ ∫ L x x L y [ A ( x , y ) N - x y L x L y ] 2 ⅆ x ⅆ y L x L y ( 2 )
- and wherein S1 that is obtained by expression
- 62 S 1 ( r 1 , r 2 ) = ∫ r 1 r 2 ⅆ r | g 1 ( r ;
- r 1 , r 2 ) - g av | ( 3 )
- is equal to or smaller than 0.7, such that, g1 is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integration value of g(r) over a range of from r1 to r2, and gav is the average value of g1 within the range of from r1 to r2;
- such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r1 and r2 are chosen as one and four times the value of the lattice constant Dr respectively;
- and the dot filling rate is a value obtained by multiplying the square of the maximum diameter of a dot by the number of dots, and dividing the product by the size of the area;
- said light device further comprising:
- a light source for projecting light onto said light guide plate;
- and
- a reflector for reflecting said light projected by said light source and transmitting said reflected light to said light guide plate.
12 more elements
The light-transmitting liquid crystal display device comprising:
- a side light device functioning as a backlight unit;
- said side light device comprising:
- a light guide plate, on which a discrete pattern is formed by dots discretely arranged in two dimensions, wherein said dots included in a rectangular area having a longitudinal length of Lx and a transverse length of Ly satisfy expression,
- D≦0.13N−1.15 (1)
- such that, N denotes the number of dots included in a predetermined area, and D is obtained by expression (2), wherein A(x,y) defines the number of dots, of a total of N dots, included in a rectangular area for which a line segment extended from reference coordinates (0,0) to an arbitrary coordinate point (x,y) is a diagonal line,
- 63 D ( L x , L y ;
- N ) = ∫ ∫ L x × L y [ A ( x , y ) N - xy L x L y ] 2 dxdy L x L y ( 2 )
- and wherein S1 that is obtained by expression
- 64 S 1 ( r 1 , r 2 ) = ∫ r 1 r 2 ⅆ r | g 1 ( r ;
- r 1 , r 2 ) - g av | ( 3 )
- is equal to or smaller than 0.7, such that, g1 is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integration value of g(r) over a range of from r1 to r2, and gav is the average value of g1 within the range of from r1 to r2;
- such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r1 and r2 are chosen as one and four times the value of the lattice constant Dr respectively;
- and the dot filling rate is a value obtained by multiplying the square of the maximum diameter of a dot by the number of dots, and dividing the product by the size of the area;
- said light device further comprising:
- a light source for projecting light onto said light guide plate;
- and
- a reflector for reflecting said light projected by said light source and transmitting said reflected light to said light guide plate.
14 more elements
A discrete pattern generation method for generating a discrete pattern wherein dots are discretely arranged in two dimensions comprising the steps of:
- providing a predetermined area;
- determining the number of dots to be arranged in said predetermined area;
- and
- determined the position coordinates of said dots, so that said dots included in a rectangular area having a longitudinal length of Lx and a transverse length of Ly satisfy expression,
- D≦0.13N−1.15 (1)
- such that, N denotes the number of dots included in a predetermined area, and D is obtained by expression (2), wherein A(x,y) defines the number of dots, of a total of N dots, included in a rectangular area for which a line segment extended from reference coordinates (0,0) to an arbitrary coordinate point (x, y) is a diagonal line,
- 65 D ( L x , L y ;
- N ) = ∫ ∫ L x × L y [ A ( x , y ) N - xy L x L y ] 2 dxdy L x L y ( 2 )
- and wherein S1 that is obtained by expression
- 66 S 1 ( r 1 , r 2 ) = ∫ r 1 r 2 ⅆ r | g 1 ( r ;
- r 1 , r 2 ) - g av | ( 3 )
- is equal to or smaller than 0.7, such that, g1 is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integration value of g(r) over a range of from r1 to r2, and gav is the average value of g1 within the range of from r1 to r2;
- such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r1 and r2 are chosen as one and four times the value of the lattice constant Dr respectively;
- and the dot filling rate is a value obtained by multiplying the square of the maximum diameter of a dot by the number of dots, and dividing the product by the size of the area;
- setting said position coordinates as initial positions;
- and
- changing said position coordinates of said dots so that said dots for which said position coordinates are determined do not overlap each other.
14 more elements
A program for executing a method for generating a discrete pattern wherein dots are discretely arranged in two dimensions, said program comprising the steps of:
- providing a predetermined area;
- determining the number of dots to be arranged in said predetermined area;
- and
- determined the position coordinates of said dots, so that said dots included in a rectangular area having a longitudinal length of Lx and a transverse length of Ly satisfy expression,
- D≦0.13N−1.15 (1)
- such that, N denotes the number of dots included in a predetermined area, and D is obtained by expression (2), wherein A(x,y) defines the number of dots, of a total of N dots, included in a rectangular area for which a line segment extended from reference coordinates (0,0) to an arbitrary coordinate point (x, y) is a diagonal line,
- 67 D ( L x , L y ;
- N ) = ∫ ∫ L x × L y [ A ( x , y ) N - xy L x L y ] 2 dxdy L x L y ( 2 )
- and wherein S1 that is obtained by expression
- 68 S 1 ( r 1 , r 2 ) = ∫ r 1 r 2 ⅆ r | g 1 ( r ;
- r 1 , r 2 ) - g av | ( 3 )
- is equal to or smaller than 0.7, such that, g1 is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integration value of g(r) over a range of from r1 to r2, and gav is the average value of g1 within the range of from r1 to r2;
- such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r1 and r2 are chosen as one and four times the value of the lattice constant Dr respectively;
- and the dot filling rate is a value obtained by multiplying the square of the maximum diameter of a dot by the number of dots, and dividing the product by the size of the area;
- setting said position coordinates as initial positions;
- and
- changing said position coordinates of said dots so that said dots for which said position coordinates are determined do not overlap each other.
14 more elements
A computer-readable storage medium, on which a program is stored that executes a method for generating a discrete pattern wherein dots are discretely arranged in two dimensions, said method comprising the steps of:
- providing a predetermined area;
- determining the number of dots to be arranged in said predetermined area;
- and
- determined the position coordinates of said dots, so that said dots included in a rectangular area having a longitudinal length of Lx and a transverse length of Ly satisfy expression,
- D≦0.13N−1.15 (1)
- such that, N denotes the number of dots included in a predetermined area, and D is obtained by expression (2), wherein A(x,y) defines the number of dots, of a total of N dots, included in a rectangular area for which a line segment extended from reference coordinates (0,0) to an arbitrary coordinate point (x, y) is a diagonal line,
- 69 D ( L x , L y ;
- N ) = ∫ ∫ L x × L y [ A ( x , y ) N - xy L x L y ] 2 dxdy L x L y ( 2 )
- and wherein S1 that is obtained by expression
- 70 S 1 ( r 1 , r 2 ) = ∫ r 1 r 2 ⅆ r | g 1 ( r ;
- r 1 , r 2 ) - g av | ( 3 )
- is equal to or smaller than 0.7, such that, g1 is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integrated value of g(r) over a range of from r1 to r2, and gav is the average value of g1 within the range of from r1 to r2;
- such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r1 and r2 are chosen as one and four times the value of the lattice constant Dr respectively;
- and the dot filling rate is a value obtained by multiplying the square of the maximum diameter of a dot by the number of dots, and dividing the product by the size of the area;
- setting said position coordinates as initial positions;
- and
- changing said position coordinates of said dots so that said dots for which said position coordinates are determined do not overlap each other.
14 more elements
A discrete pattern generation system, for generating the discrete pattern, comprising:
- means for providing the discrete pattern, said discrete pattern, formed by dots discretely arranged in two dimensions, wherein said dots included in a rectangular area having a longitudinal length of Lx and a transverse length of Ly satisfy expression,
- D≦0.13N−1.15 (1)
- such that, N denotes the number of dots included in a predetermined area, and D is obtained by expression (2), wherein A(x,y) defines the number of dots, of a total of N dots, included in a rectangular area for which a line segment extended from reference coordinates (0,0) to an arbitrary coordinate point (x,y) is a diagonal line,
- 71 D ( L x , L y ;
- N ) = ∫ ∫ L x × L y [ A ( x , y ) N - xy L x L y ] 2 dxdy L x L y ( 2 )
- and wherein S1 that is obtained by expression
- 72 S 1 ( r 1 , r 2 ) = ∫ r 1 r 2 ⅆ r [LeftBracketingBar] g 1 ( r ;
- r 1 , r 2 ) - g av [RightBracketingBar] ( 3 )
- is equal to or smaller than 0.7, such that g1 is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integration value of g(r) over a range of from r1 to r2, and gav is the average value of g1 within the range of from r1 to r2;
- such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r1 and r2 are chosen as one and four times the value of the lattice constant Dr respectively;
- and the dot filling rate is a value obtained by multiplying the square of the maximum diameter of a dot by the number of dots, and dividing the product by the size of the area;
- storage means for storing the position coordinates of the dots that form said discrete pattern;
- printer means for outputting said position coordinates included in said recording means;
- and
- pattern receiving elements wherein said discrete pattern is formed by said printer means.
12 more elements
Dependencies are inferred from the claim text.