Discrete pattern, apparatus, method, and program storage device for generating and implementing the discrete pattern

Claim 2

A disease 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, 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 S 1 that is obtained by expression 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 g, 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 r 1 to r 2 , and g av is the average value of g 1 within the range of from r 1 to r 2 ; such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r 1 and r 2 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, wherein said discrete pattern is disposed so that an average radius distribution function in said predetermined blocks becomes sufficiently smooth.

Claim 3

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, 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 S 1 that is obtained by expression 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, g 1 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 r 1 to r 2 , and g av is the average value of g 1 within the range of from r 1 to r 2 ; such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r 1 and r 2 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, wherein said discrete pattern is disposed so that an average radius distribution function in said predetermined blocks becomes sufficiently smooth.

Claim 4

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, 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 S 1 that is obtained by expression 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, g 1 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 r 1 to r 2 , and g av is the average value of g 1 within the range of from r 1 to r 2 ; such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r 1 and r 2 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, wherein said discrete pattern is disposed so that an average radius distribution function in said predetermined blocks becomes sufficiently smooth.

Claim 5

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, 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 S 1 that is obtained by expression (3) 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, g 1 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 r 1 to r 2 , and g av is the average value of g 1 within the range of from r 1 to r 2 , such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r 1 and r 2 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, wherein said discrete pattern is disposed so that an average radius distribution function in said predetermined blocks becomes sufficiently smooth.

Claim 6

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, 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 S 1 that is obtained by expression (3) 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, g 1 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 r 1 to r 2 , and g av is the average value of g 1 within the range of from r 1 to r 2 , such that, when the dots are arranged in a square lattice to satisfy a given filling rate, r 1 and r 2 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, wherein said discrete pattern is disposed so that an average radius distribution function in said predetermined blocks becomes sufficiently smooth.

Claim 7

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, 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 S 1 that is obtained by expression 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, g 1 is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integration value of a(r) over a range of from r 1 to r 2 , and g av is the average value of g 1 within the range of from r 1 to r 2 ; such that, when the dots are arranged in a square lattice to satisfy a given tilling rate, r 1 and r 2 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, wherein said discrete pattern is disposed so that an average radius distribution function in said predetermined blocks becomes sufficiently smooth.

Claim 8

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, 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 S 1 that is obtained by expression 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, g 1 is obtained by dividing the average radial distribution function g(r) of each dot in the area by an integration value of a(r) over a range of from r 1 to r 2 , and g av is the average value of g 1 within the range of from r 1 to r 2 ; such that, when the dots are arranged in a square lattice to satisfy a given tilling rate, r 1 and r 2 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, wherein said discrete pattern is disposed so that an average radius distribution function in said predetermined blocks becomes sufficiently smooth.

Claim 9

A discrete pattern generation method in a computer system to generate a discrete pattern formed of discrete dots disposed two-dimensionally comprising the steps of: providing a predetermined block; providing a filling factor distribution function of said dots; providing areas of said dots; generating at least two dots according to said filling factor distribution function for said predetermined blocks; moving using predetermined functions said generated dots and updating thereof to new coordinate values; judging a distance between dots of which said new coordinate values have been obtained; generating or deleting new dots with regard to said distance; and employing said predetermined functions to update coordinate values of dots including said generated dots.

Claim 10

A discrete pattern generation method in a computer system to generate a discrete pattern formed of discrete dots disposed two-dimensionally comprising the steps of: providing a predetermined block; providing a filling factor distribution function of said dots; providing areas of said dots; generating at least two dots according to said filling factor distribution function for said predetermined blocks; moving using predetermined functions said generated dots and updating thereof to new coordinate values; judging a distance between dots of which said new coordinate values have been obtained; generating or deleting new dots with regard to said distance; and employing said predetermined functions to update coordinate values of dots including said generated dots.

Claim 11

The discrete pattern generation method according to claim 5 , wherein said step of generating dots according to a filling factor distribution function comprises a step of generating dots in a boundary region of said block and a step of generating dots inside said boundary region of said block.

Claim 12

The discrete pattern generation method according to claim 6 , wherein said step of employing predetermined functions to move dots comprises a step of moving dots along said boundary region and a step of moving said dots two-dimensionally inside said boundary region.

Claim 13

The discrete pattern generation method according to claim 5 , wherein said step of generating dots according to a tilling factor distribution function comprises a step of employing a low-discrepancy sequence method to generate dots.

Claim 14

The discrete pattern generation method according to claim 5 , wherein said discrete pattern is a binarized pattern of an optical intensity modulation element or a variable-density image of an optical component.

Claim 15

A program for making a computer to execute the steps of: providing a predetermined block; providing said filing factor distribution function of dots; providing said area of dots; generating at least two dots according to said filling factor distribution function for said predetermined blocks; moving employing predetermined functions said generated dots and updating thereof to new coordinate values; judging a distance between said dots of which said new coordinate values have been obtained; generating or deleting new dots with regard to said distance; and employing said predetermined functions to update coordinate values of dots including said generated dots.

Claim 16

A program for making a computer to execute the steps of: providing a predetermined block; providing said filing factor distribution function of dots; providing said area of dots; generating at least two dots according to said filling factor distribution function for said predetermined blocks; moving employing predetermined functions said generated dots and updating thereof to new coordinate values; judging a distance between said dots of which said new coordinate values have been obtained; generating or deleting new dots with regard to said distance; and employing said predetermined functions to update coordinate values of dots including said generated dots.

Claim 17

The program according to claim 10 , wherein said step of generating dots according to a filling factor distribution function comprises a step of generating dots in a boundary region of said block and a step of generating dots inside said boundary region of said block.

Claim 18

The program according to claim 11 , wherein said step of employing predetermined functions to move dots comprises a step of moving dots along said boundary region and a step of moving said dots two-dimensionally inside said boundary region.

Claim 19

The program according to claim 10 , wherein said step of generating dots according to a filling factor distribution function comprises a step of generating a low-discrepancy sequence method for generation.

Claim 20

The program according to claim 10 , wherein said discrete pattern is binarized patterns of optical intensity modulation elements or variable-density images of optical components.

Claim 21

A computer readable storage medium storing a computer executable program, said program making said computer to execute a generation method for discrete patterns formed of discrete dots disposed two-dimensionally, said storage medium making a computer system to execute the steps of: providing a predetermined block; providing a filling factor distribution function of said dots; providing areas of said dots; generating at least two dots according to said filling factor distribution function for said predetermined blocks; moving using predetermined functions said generated dots and updating thereof to new coordinate values; judging a distance between dots of which said new coordinate values have been obtained; generating or deleting new dots with regard to said distance; and employing said predetermined functions to update coordinate values of dots including said generated dots.

Claim 22

A computer readable storage medium storing a computer executable program, said program making said computer to execute a generation method for discrete patterns formed of discrete dots disposed two-dimensionally, said storage medium making a computer system to execute the steps of: providing a predetermined block; providing a filling factor distribution function of said dots; providing areas of said dots; generating at least two dots according to said filling factor distribution function for said predetermined blocks; moving using predetermined functions said generated dots and updating thereof to new coordinate values; judging a distance between dots of which said new coordinate values have been obtained; generating or deleting new dots with regard to said distance; and employing said predetermined functions to update coordinate values of dots including said generated dots.

Claim 23

The storage medium according to claim 15 , wherein said step of generating dots according to a filling factor distribution function comprises a step of generating dots in a boundary region of said block and a step of generating dots inside said boundary region of said block.

Claim 24

The storage medium according to claim 15 , wherein said step of employing predetermined functions to move dots comprises a step of moving dots along said boundary region and a step of moving said dots two-dimensionally inside said boundary region.

Claim 25

The storage medium according to claim 15 , wherein said step of generating dots according to a filling factor distribution function comprises a step of employing a low-discrepancy sequence method to generate dots.

Claim 26

The storage medium according to claim 15 , wherein said discrete pattern is binarized patterns of light intensity modulation elements of optical components or a variable-density image.

Claim 27

A discrete pattern generation system for generating discrete patterns comprising: an execution means for the method according to claim 5 ; a storage means to store position coordinates of dots forming said generated discrete pattern; a printer means to output position coordinates stored in said storage means; and a pattern acceptance element to which discrete pattern is formed by said printer means.

Claim 28

The discrete pattern generation system according to claim 20 , wherein said system generates a binarized pattern of an optical intensity modulation element or a variable-density image of an optical component.

Claim 29

A binarized pattern generation method for generating a binarized patterns of a variable-density image formed of discrete dots disposed two-dimensionally, said binary pattern generation method making a computer system to execute the steps of: providing a predetermined block; determining a number of dots disposed in said predetermined block; determining said dot position coordinates so that said dots contained in a rectangular block having a lateral size of Lx and a longitudinal size of Ly satisfy formula (1): D≦0.13N −1.15 (1) (wherein N in formula (1) denotes a number of dots contained in said block and D is given by formula (2) in the condition in that a number of dots contained in a rectangular region having a diagonal line extending from a reference coordinate ( 0 , 0 ) to an arbitrary coordinate (x, y) is A (x, y): D ⁡ ( L x , L y ; N ) = ∫ ∫ L x ⁢ xL y ⁢ [ A ⁡ ( x , y ) N - xy L x ⁢ L y ] 2 ⁢ dxdy L x ⁢ L y ( 2 ) and S 1 given by formula (3) is equal to or less than 0.7: S 1 ⁡ ( r 1 , r 2 ) = ∫ r 1 r 2 ⁢ ⅆ r | g 1 ⁡ ( r ; r 1 , r 2 ) - g av | , ( 3 ) wherein g 1 in formula (3) is a value obtained from dividing an average radius distribution function g(r) by an integral value ranging from r 1 to r 2 and g av is a mean value of g 1 ranging from r 1 to r 2 . When dots are disposed in a shape of a tetragonal lattice to satisfy a given filling factor, r 1 and r 2 are specified to an equal value and a quadruple value of a lattice constant Dr, respectively. A filling factor of dots is the value defined in that a square of a maximum diameter of a dot is multiplied by a number of dots, then thus calculated value is divided by an area of said region); setting said predetermined position coordinates as initial positions; changing said dot position coordinates so that dots of which said position coordinates have been determined do not overlap with each other; and employing a plurality of said boundary conditions to adjoin said predetermined blocks to generate a discrete pattern of a predetermined size.

Claim 30

A binarized pattern generation method for generating a binarized patterns of a variable-density image formed of discrete dots disposed two-dimensionally, said binary pattern generation method making a computer system to execute the steps of: providing a predetermined block; determining a number of dots disposed in said predetermined block; determining said dot position coordinates so that said dots contained in a rectangular block having a lateral size of Lx and a longitudinal size of Ly satisfy formula (1): D≦0.13N −1.15 (1) (wherein N in formula (1) denotes a number of dots contained in said block and D is given by formula (2) in the condition in that a number of dots contained in a rectangular region having a diagonal line extending from a reference coordinate ( 0 , 0 ) to an arbitrary coordinate (x, y) is A (x, y): D ⁡ ( L x , L y ; N ) = ∫ ∫ L x ⁢ xL y ⁢ [ A ⁡ ( x , y ) N - xy L x ⁢ L y ] 2 ⁢ dxdy L x ⁢ L y ( 2 ) and S 1 given by formula (3) is equal to or less than 0.7: S 1 ⁡ ( r 1 , r 2 ) = ∫ r 1 r 2 ⁢ ⅆ r | g 1 ⁡ ( r ; r 1 , r 2 ) - g av | , ( 3 ) wherein g 1 in formula (3) is a value obtained from dividing an average radius distribution function g(r) by an integral value ranging from r 1 to r 2 and g av is a mean value of g 1 ranging from r 1 to r 2 . When dots are disposed in a shape of a tetragonal lattice to satisfy a given filling factor, r 1 and r 2 are specified to an equal value and a quadruple value of a lattice constant Dr, respectively. A filling factor of dots is the value defined in that a square of a maximum diameter of a dot is multiplied by a number of dots, then thus calculated value is divided by an area of said region); setting said predetermined position coordinates as initial positions; changing said dot position coordinates so that dots of which said position coordinates have been determined do not overlap with each other; and employing a plurality of said boundary conditions to adjoin said predetermined blocks to generate a discrete pattern of a predetermined size.

Claim 31

The binarized pattern generation method according to claim 22 , wherein said step of changing position coordinates comprising the steps of: calculating repulsion regarding a predetermined dot from another dot existing in the vicinity of said dot; displacing said predetermined dot according to a magnitude of said repulsion; a step of calculating repulsion regarding said displaced dot; and summing up repulsion regarding dots within a predetermined range.

Claim 32

The binarized pattern generation method according to claim 22 , wherein said step of changing position coordinates employs repulsion which remains steady as against said distance between dots at a wavelength equal to or less than a principal wavelength and decreases according to increase of said distance between dots exceeding a predetermined value.

Claim 33

A computer executable program for making a computer system to execute a generation method for binarized patterns of a variable-density image formed of discrete dots disposed two-dimensionally, said program making said computer system execute the steps of: providing a predetermined block; determining a number of dots disposed in said predetermined block; determining said dot position coordinates so that said dots contained in a rectangular block having a lateral size of Lx and a longitudinal size of Ly satisfy formula (1): D≦0.13N −1.15 (1) (wherein N in formula (1) denotes a number of dots contained in said block and D is given by formula (2) in the condition that a number of dots contained in a rectangular region having a diagonal line extending from a reference coordinate ( 0 , 0 ) to an arbitrary coordinate (x, y) is A (x, y): D ⁡ ( L x , L y ; N ) = ∫ ∫ L x ⁢ xL y ⁢ [ A ⁡ ( x , y ) N - xy L x ⁢ L y ] 2 ⁢ dxdy L x ⁢ L y ( 2 ) and S 1 given by formula (3) is equal to or less than 0.7: S 1 ⁡ ( r 1 , r 2 ) = ∫ r 1 r 2 ⁢ ⅆ r | g 1 ⁡ ( r ; r 1 , r 2 ) - g av | , ( 3 ) wherein g 1 in formula (3) is a value obtained from dividing an average radius distribution function g(r) by an integral value ranging from r 1 to r 2 and g av is a mean value of g 1 ranging from r 1 to r 2 , when dots are disposed in a shape of a tetragonal lattice to satisfy a given filling factor, r 1 and r 2 are specified to an equal value and a quadruple value of a lattice constant Dr, respectively. A filling factor of dots is the value in the condition that a square of a maximum diameter of a dot is multiplied by a number of dots, then thus calculated value is divided by an area of said region); setting said predetermined position coordinates as initial positions; changing said dot position coordinates so that dots of which said position coordinates have been determined do not overlap with each other; and employing a plurality of predetermined boundary conditions to adjoin said predetermined blocks to generate discrete patterns of predetermined sizes.

Claim 34

A computer executable program for making a computer system to execute a generation method for binarized patterns of a variable-density image formed of discrete dots disposed two-dimensionally, said program making said computer system execute the steps of: providing a predetermined block; determining a number of dots disposed in said predetermined block; determining said dot position coordinates so that said dots contained in a rectangular block having a lateral size of Lx and a longitudinal size of Ly satisfy formula (1): D≦0.13N −1.15 (1) (wherein N in formula (1) denotes a number of dots contained in said block and D is given by formula (2) in the condition that a number of dots contained in a rectangular region having a diagonal line extending from a reference coordinate ( 0 , 0 ) to an arbitrary coordinate (x, y) is A (x, y): D ⁡ ( L x , L y ; N ) = ∫ ∫ L x ⁢ xL y ⁢ [ A ⁡ ( x , y ) N - xy L x ⁢ L y ] 2 ⁢ dxdy L x ⁢ L y ( 2 ) and S 1 given by formula (3) is equal to or less than 0.7: S 1 ⁡ ( r 1 , r 2 ) = ∫ r 1 r 2 ⁢ ⅆ r | g 1 ⁡ ( r ; r 1 , r 2 ) - g av | , ( 3 ) wherein g 1 in formula (3) is a value obtained from dividing an average radius distribution function g(r) by an integral value ranging from r 1 to r 2 and g av is a mean value of g 1 ranging from r 1 to r 2 , when dots are disposed in a shape of a tetragonal lattice to satisfy a given filling factor, r 1 and r 2 are specified to an equal value and a quadruple value of a lattice constant Dr, respectively. A filling factor of dots is the value in the condition that a square of a maximum diameter of a dot is multiplied by a number of dots, then thus calculated value is divided by an area of said region); setting said predetermined position coordinates as initial positions; changing said dot position coordinates so that dots of which said position coordinates have been determined do not overlap with each other; and employing a plurality of predetermined boundary conditions to adjoin said predetermined blocks to generate discrete patterns of predetermined sizes.

Claim 35

The program according to claim 25 , wherein said step of changing position coordinates comprises the steps of: calculating repulsion regarding a predetermined dot from another dot existing in the vicinity of said dot; displacing said predetermined dot according to a magnitude of said repulsion; calculating repulsion regarding said displaced dot; and summing up repulsion regarding dots within a predetermined range.

Claim 36

The program according to claim 25 , wherein said step of changing position coordinates employs repulsion which remains steady as against said distance between dots at a wavelength equal to or less than a principal wavelength, and which decreases according to increase of said distance between dots exceeding a predetermined value.

Claim 37

A computer readable storage medium storing a program for making a computer execute a generating method for binarized patterns of a variable-density image formed of discrete dots disposed two dimensionally, said program making said computer execute the steps of: providing a predetermined block; determining a number of dots disposed in said predetermined block; determining said dot position coordinates so that said dots contained in a rectangular block having a lateral size of Lx and a longitudinal size of Ly satisfy formula (1): D≦0.13N −1.15 (1) (wherein N in formula (1) denotes a number of dots contained in said block and D is given by formula (2) in the condition that a number of dots contained in a rectangular region having a diagonal line extending from a reference coordinate ( 0 , 0 ) to an arbitrary coordinate (x, y) is A (x, y): D ⁡ ( L x , L y ; N ) = ∫ ∫ L x ⁢ xL y ⁢ [ A ⁡ ( x , y ) N - xy L x ⁢ L y ] 2 ⁢ dxdy L x ⁢ L y ( 2 ) and S 1 given by formula (3) is equal to or less than 0.7: S 1 ⁡ ( r 1 , r 2 ) = ∫ r 1 r 2 ⁢ ⅆ r | g 1 ⁡ ( r ; r 1 , r 2 ) - g av | , ( 3 ) wherein g 1 in formula (3) is a value obtained from dividing an average radius distribution function g(r) by an integral value ranging from r 1 to r 2 and g av is a mean value of g 1 ranging from r 1 to r 2 , when dots are disposed in a shape of a tetragonal lattice to satisfy a given filling factor, r 1 and r 2 are specified to an equal value and a quadruple value of a lattice constant Dr, respectively. A filling factor of dots is the value defined in that a square of a maximum diameter of a dot is multiplied by a number of dots, then thus calculated value is divided by an area of said region); setting said predetermined position coordinates as initial positions; changing said dot position coordinates so that dots of which said position coordinates have been determined do not overlap with each other; and employing a plurality of predetermined boundary conditions to adjoin said predetermined blocks to generate discrete patterns of predetermined sizes.

Claim 38

A computer readable storage medium storing a program for making a computer execute a generating method for binarized patterns of a variable-density image formed of discrete dots disposed two dimensionally, said program making said computer execute the steps of: providing a predetermined block; determining a number of dots disposed in said predetermined block; determining said dot position coordinates so that said dots contained in a rectangular block having a lateral size of Lx and a longitudinal size of Ly satisfy formula (1): D≦0.13N −1.15 (1) (wherein N in formula (1) denotes a number of dots contained in said block and D is given by formula (2) in the condition that a number of dots contained in a rectangular region having a diagonal line extending from a reference coordinate ( 0 , 0 ) to an arbitrary coordinate (x, y) is A (x, y): D ⁡ ( L x , L y ; N ) = ∫ ∫ L x ⁢ xL y ⁢ [ A ⁡ ( x , y ) N - xy L x ⁢ L y ] 2 ⁢ dxdy L x ⁢ L y ( 2 ) and S 1 given by formula (3) is equal to or less than 0.7: S 1 ⁡ ( r 1 , r 2 ) = ∫ r 1 r 2 ⁢ ⅆ r | g 1 ⁡ ( r ; r 1 , r 2 ) - g av | , ( 3 ) wherein g 1 in formula (3) is a value obtained from dividing an average radius distribution function g(r) by an integral value ranging from r 1 to r 2 and g av is a mean value of g 1 ranging from r 1 to r 2 , when dots are disposed in a shape of a tetragonal lattice to satisfy a given filling factor, r 1 and r 2 are specified to an equal value and a quadruple value of a lattice constant Dr, respectively. A filling factor of dots is the value defined in that a square of a maximum diameter of a dot is multiplied by a number of dots, then thus calculated value is divided by an area of said region); setting said predetermined position coordinates as initial positions; changing said dot position coordinates so that dots of which said position coordinates have been determined do not overlap with each other; and employing a plurality of predetermined boundary conditions to adjoin said predetermined blocks to generate discrete patterns of predetermined sizes.

Claim 39

The program according to claim 28 , wherein said step of changing said position coordinates comprises: calculating repulsion regarding a predetermined dot from another dot existing in the vicinity of said dot; displacing said predetermined dots according to a size of said repulsion; calculating repulsion regarding said displaced predetermined dots; and summing up said repulsion regarding dots within a predetermined range.

Claim 40

The program according to claim 28 , wherein said step of changing position coordinates employs repulsion which remains steady as against said distance between dots at a wavelength equal to or less than a principal wavelength, and which decreases according to increase of said distance between dots exceeding a predetermined value.

Claim 41

A generation system of binarized patterns including discrete patterns comprising: an execution means to execute the method according to claim 22 ; a storage means to store position coordinates of dots forming said generated binarized patterns; a printer means to output position coordinates stored in said storage means; and a pattern acceptance element to discrete pattern is formed by said printer means.