Method of and means for printing a multilevel representation of an image

Claim 3

A method according to claim 1 wherein the computing step utilizes a threshold screen value function that is an analytical function of the modular coordinates.

Claim 4

A method according to claim 2 wherein said threshold screen value is based on an analytical function of the form: u=(t) cos (kt), v=(t) sin (kt) where u and v are the transformed coordinates of the exposure point, k is a constant, and t is the threshold screen value.

Claim 5

A method according to claim 3 wherein k is greater than 2π.

Claim 6

A method according to claim 3 wherein k is in the range of about 2.5π to 2.8π.

Claim 7

A method according to claim 3 wherein k is about 2.65π.

Claim 8

A method according to claim 3 wherein the threshold screen value for an exposure point having coordinates u',v' not lying on the curve represented by u=(t) cos (kt), v=(t) sin (kt) is determined by the point on the curve at which the distance of the exposure point u, v to the curve is a minimum.

Claim 9

A method according to claim 2 wherein Val(u,v) is the threshold screen value at an exposure point u, v where Val(u,v)=(S)floor{(u.sup.2 +v.sup.2).sup.1/2 /S}+(S){a tan (u,v)/2π} where S is a constant, "floor" is the next lowest integer below the value of the argument, and a tan (u,v) is an angle associated with (u,v).

Claim 10

A method according to claim 7 wherein S is less than about 1.

Claim 11

A method according to claim 7 wherein S is in the range 0.7 to 0.8.

Claim 12

A method according to claim 7 wherein S is about 0.73.

Claim 13

The method according to claim 2 wherein Val(u,v) is the threshold screen value at an exposure point u,v where Val(u,v)=(S)round{(u.sup.2 +v.sup.2).sup.1/2 /S}+(S){a tan (u,v)/2π} where S is a constant, "round" means to round the argument to the nearest integer, and a tan (u,v) is an angle associated with (u,v).

Claim 14

The method of claim 12 wherein S is less than about 1.

Claim 15

A method according to claim 12 wherein S is in the range 0.7 to 0.8.

Claim 16

A method according to claim 12 wherein S is about 0.73.

Claim 17

A method according to claim 2 wherein Val(u,v) is the threshold screen value and exposure point u,v where Val(u,v)=(S)round{[abs(u)+abs(v)]/S}+(S){a tan (u,v)/2π} where S is a constant, "round" means to round the argument to the nearest integer, abs(u) is the absolute value of u, abs(v) is the absolute value of v, and a tan (u,v) is an angle associated with (u,v).

Claim 18

Apparatus for producing a half-tone reproduction of an image on a recording medium using gray level values associated with object points having object coordinates related to the image, said apparatus comprising: (a) an actuatable marking device operatively associated with and displaceable relative to said medium for marking a spot on the medium at an exposure point determined by the coordinates of the marking device at which the latter is actuated; (b) means for displacing said marking device relative to said medium; (c) means responsive to the location of said marking device relative to said medium for producing a representation of the coordinates of the marking device; (d) means for converting the representation of the coordinates of the marking device to modular coordinates representative of the coordinates of the exposure point on a mesh of a fictitious half-tone screen having a predetermined angular orientation relative to said object; (e) means for computing a threshold screen value from the modular coordinates; (f) means for obtaining the gray level value of an object point whose coordinates are related to said exposure point; (g) a comparator for comparing the obtained gray level value with said threshold screen value and producing an actuating signal depending upon the results of the comparison; and (h) means for applying said actuating signal to said marking device for selectively actuating the same.

Claim 19

Apparatus for producing a half-tone reproduction of an image on a recording medium using gray level values associated with object points having object coordinates related to the image, said apparatus comprising: (a) an actuatable marking device operatively associated with and displaceable relative to said medium for marking a spot on the medium at an exposure point determined by the coordinates of the marking device at which the latter is actuated; (b) means for displacing said marking device relative to said medium; (c) means responsive to the location of said marking device relative to said medium for producing a representation of the coordinates of the marking device; (d) means for converting the representation of the coordinates of the marking device to modular coordinates representative of the coordinates of the exposure point on a mesh of a fictitious half-tone screen having a predetermined angular orientation relative to said object; (e) means for computing a threshold screen value from the modular coordinates; (f) means for obtaining the gray level value of an object point whose coordinates are related to said exposure point; (g) a comparator for comparing the obtained gray level value with said threshold screen value and producing an actuating signal depending upon the results of the comparison; and (h) means for applying said actuating signal to said marking device for selectively actuating the same.

Claim 20

Apparatus according to claim 17 wherein said threshold screen value is computed from an analytical function of the modular coordinates.

Claim 21

Apparatus according to claim 18 wherein said threshold screen value is based on a function: u=(t) cos (kt), v=(t) sin (kt) where u and v are the modular coordinates of the exposure point, k is a constant, and t is the threshold screen value.

Claim 22

Apparatus according to claim 19 wherein k is greater than about 2π.

Claim 23

Apparatus according to claim 19 wherein k is in the range of about 2.5π to 2.9π.

Claim 24

Apparatus according to claim 19 wherein k is about 2.65π.

Claim 25

Apparatus according to claim 19 wherein the threshold screen value for an exposure point having coordinates u', v' not lying on the curve represented by u=(t) cos (kt), v=(t) sin (kt) is determined by the point on the curve at which the distance of the exposure point u, v to the curve is a minimum.

Claim 26

Apparatus according to claim 16 wherein Val (u,v) is the threshold screen value at an exposure point (u,v) where Val(u,v)=(S)floor{(u.sup.2 +v.sup.2).sup.1/2 /S}+(S){a tan (u,v)/2π} where S is a constant, "floor" is the next lowest integer below the value of the argument, and a tan (u,v) is an angle associated with (u,v).

Claim 27

Apparatus according to claim 23 wherein S is less than about 1.

Claim 28

Apparatus according to claim 23 wherein S is in the range of about 0.7 to 0.8.

Claim 29

Apparatus according to claim 23 wherein S is about 0.73.

Claim 30

Apparatus according to claim 18 wherein Val(u,v) is the threshold screen value at an exposure point u, v where Val(u,v)=(S)floor{(u.sup.2 +v.sup.2).sup.1/2 /S}+(S){a tan (u,v)/2π} where S is a constant, "floor" is the next lowest integer below the value of the argument, and a tan (u,v) is an angle associated with (u,v).

Claim 31

Apparatus according to claim 28 wherein S is less than about 1.

Claim 32

Apparatus according to claim 28 wherein S is in the range 0.7 to 0.8.

Claim 33

Apparatus according to claim 28 wherein S is about 0.73.

Claim 34

A method according to claim 3 wherein the exposure points are spaced a distance apart, and wherein the threshold screen value for an exposure point having coordinates (u',v') not lying on the curve represented by u=(t) cos (kt), v=(t) sin (kt) is determined by the value of a point on the curve which is less than half the spacing between said exposure points.