Digital vector generator

Claim 1

In a display system, a vector segment encoder for generating a sequence of vector segment words for describing a vector to be represented as a connected sequence of vector segments selected from a symbol set of 4n vector segments, each complete vector segment having orthogonal components of magnitude of n and m, where 0 < or = m < or = n, m and n being integers, comprising: an input storage register for receiving origin, length, and slope data describing the vector to be represented; said vector to be represented being oriented with the ordinate of its origin having a magnitude not less than the ordinate of its head; said slope data composed of an octant portion, a high order portion, and a low order portion; said octant portion describing which of the four octants having a negative ordinate, contains the vector to be represented; said high order slope portion describing the approximate value as m/n for the tangent of the angle between the vector to be represented and the abscissa or ordinate contained in the octant designated by said octant portion, where 0 < or = m < or = n, and m and n are integers; said low order slope portion describing the difference between the value m/n of a high order slope portion and the true value of the tangent of said angle; said length portion composed of a high order portion and a low order portion; said high order length portion describing the number of complete vector segments having orthogonal components of length n lying along th ordinate or abscissa contained in the octant specified by said octant portion, required to approximate without exceeding the true length of the vector to be represented; said low order length portion describing the length of the orthogonal component of a partial vector segment, said component lying along the ordinate or abscissa contained in the octant specified by said octant portion, said partial vector segment being the approximate vector difference between said plurality of complete vector segments and the vector to be represented, where 0 < or = l < or = n, and 1 is the outputted length; said origin portion describing the ordinate and abscissa coordinate values for the origin of the vector to be represented; an x abscissa register and a y ordinate register gateably connected to the origin portion of said input register for storing the value of the coordinate of the origin for a first vector segment and gateably outputting said values on a first output line; a vector length residue register gateably connected to the high order length portion of said input register, for storing the remaining number of complete vector segments to be encoded for the vector to be represented; a length residue decrementing means gateably connected to said length residue register for decrementing the contents thereof by unity after each vector segment word is encoded; a length residue compare means gateably connected to said length residue register for comparing the contents therein with the value zero; and gateably connecting the low order length portion of said input register with a second output line outputting the l, when the contents of said length residue register is zero, or when the contents of said length residue register is greater than zero, outputting on said second output line the value n, as the length of the orthogonal component of said vector segment being encoded, said component lying along the ordinate or abscissa contained in the ocTant specified by the octant portion of said input register; a slope residue adder gateably connected to said low order slope portion of said input register for adding the slope residue for a present vector segment to the accumulated slope residues for previously encoded vector segments of the vector to be represented; a cummulative slope residue register gateably connected to said slope residue adder, for storing the accumulated slope residues for said previously encoded vector segments, and outputting the cummulative slope residue to said slope residue adder; a cummulative slope residue comparison means connected to said slope residue adder for comparing the cummulative slope residue with the value 0.5, incrementing the contents of said cummulative slope residue register by the slope residue when the cummulative slope residue is less than 0.5 and decrementing the contents of the cummulative slope residue register by 1.0 when the cummulative slope residue is greater than 0.5; a modified slope adder gateably connected to said high order slope portion of said input register and connected to said cummulative slope residue comparison means, for selectively modifying the slope of a vector segment being encoded from m/n to (m+1)/n when said cummulative slope residue is greater than 0.5; a vector segment encoding matrix gateably connected to the output of said modified slope adder and gateably connected to the octant portion of said input register, for converting the octant data and modified slope data to one out of 4n vector segment symbol codes stored therein, to be outputted on a third output line; an arithmetic logic unit gateably connected to the output of said modified slope adder, gateably connected to the octant portion of said input register, and gateably connected to said x abscissa register and said y ordinate register, for calculating the value of the coordinates for the orgin for the next vector segment to be encoded by adding or subtracting the value of n to the contents of the x or the y register when x or y corresponds, respectively to the abscissa or ordinate contained in the octant designated by said octant register, and by adding or substracting the value of the modified slope to the contents of the x or the y register when x or y does not correspond, respectively to said abscissa or ordinate contained in the octant designated by said octant register; whereby the vector to be represented is decomposed into a connected sequence of vector segments and said segments are encoded into a sequence of data words describing their origin, length, and symbol code selected from a symbol set.

Claim 3

A method for generating a sequence of vector segment words for describing a vector to be represented as a connected sequence a vector segments selected from a symbol set of 4n vector segments, each complete vector segment having orthogonal components of magnitude of n and m, where 0 < or = m < or = n, m and n being integers, comprising: orienting a vector to be represented with the ordinate of its origin having a magnitude not less than the the ordinate of its head; calculating the origin, length, and slope describing the vector to be represented; said slope composed of an octant portion, a high order portion, and a low order portion; said octant portion describing which of the four octants having a negative ordinate, contains the vector to be represented; said high order slope portion describing the approximate value as m/n for the tangent of the angle between the vector to be represented and the abscissa or ordinate contained in the octant designated by said octant portion, where 0 < or = m < or = n, and m and n are integers; said low order slop portion called the slope residue, describing the difference between the value m/n of saId high order slope portion and the true value of the tangent of said angle; said length portion composed of a high order portion and a low order portion; said high order length portion describing the number of complete vector segments having orthogonal components of length n lying along the ordinate or abscissa contained in the octant specified by said octant portion, required to approximate without exceeding the true length of the vector to be represented; said low order length portion describing the length of the orthogonal component of a partial vector segment, said component lying along the ordinate or abscissa contained in the octant specified by said octant portion, said partial vector segment being the approximate vector difference between said plurality of complete vector segments and the vector to be represented, were 0 < or = l < or = n, and 1 is the outputted length said origin describing the y- ordinate and x- abscissa coordinate values for the origin of the vector to be represented; storing the value of the coordinates of the origin for a first vector segment and gateably outputting said values on a first output line; storing the remaining number of complete vector segments to be encoded for the vector to be represented as the vector length residue; decrementing said vector length residue by unity after each vector segment word is encoded; comparing the vector length residue with the value zero; and outputting the value l on the second output line when said length residue is zero, or when said length residue is greater than zero, outputting on said second output line the value n, as the length of the orthogonal component of said vector segment being encoded, said component lying along the ordinate or abscissa contained in the octant specified by said octant portion; adding the slope residue for a present vector segment to the accumulated slope residues for previously encoded vector segments of the vector to be represented; storing the accumulated slope residues for said previously encoded vector segments; comparing the cummulative slope residue with the value 0.5, incrementing said cummulative slope residue by said slope residue when the cummulative slope residue is less than 0.5 and decrementing the cummulative slope residue by 1.0 the cummulative slope residue is greater than 0.5; selectively modifying the slope of a vector segment being encoded from m/n to (m+1)/n when said cummulative slope residue is greater than 0.5; encoding the octant data and modified slope data as one out of 4n stored vector segment symbol codes to be outputted on a third output line; calculating the value of the coordinates for the origin for the next vector segment to be encoded by adding or substracting the value of n to the value of the x abscissa or y ordinate of the origin of the present vector segment encoded when x or y corresponds, respectively to the abscissa or ordinate contained in the octant designated by said octant portion, and by adding or subtracting the value of the modified slope to the value of the x abscissa or y ordinate of the origin of the present vector segment encoded when x or y does not correspond, respectively to said abscissa or ordinate contained in the octant designated by said octant portion; whereby the vector to be represented is decomposed into a connected sequence of vector segments and said segments are encoded into a sequence of data words describing their origin, length, and symbol code selected from a symbol set.

Claim 4

A method for generating a sequence of vector segment words for describing a vector to be represented as a connected sequence a vector segments selected from a symbol set of 4n vector segments, each complete vector segment having orthogonal components of magnitude of n and m, where 0 < or = m < or = n, m and n being integers, comprising: orienting a vector to be represented with the ordinate of its origin having a magnitude not less than the the ordinate of its head; calculating the origin, length, and slope describing the vector to be represented; said slope composed of an octant portion, a high order portion, and a low order portion; said octant portion describing which of the four octants having a negative ordinate, contains the vector to be represented; said high order slope portion describing the approximate value as m/n for the tangent of the angle between the vector to be represented and the abscissa or ordinate contained in the octant designated by said octant portion, where 0 < or = m < or = n, and m and n are integers; said low order slop portion called the slope residue, describing the difference between the value m/n of saId high order slope portion and the true value of the tangent of said angle; said length portion composed of a high order portion and a low order portion; said high order length portion describing the number of complete vector segments having orthogonal components of length n lying along the ordinate or abscissa contained in the octant specified by said octant portion, required to approximate without exceeding the true length of the vector to be represented; said low order length portion describing the length of the orthogonal component of a partial vector segment, said component lying along the ordinate or abscissa contained in the octant specified by said octant portion, said partial vector segment being the approximate vector difference between said plurality of complete vector segments and the vector to be represented, were 0 < or = l < or = n, and 1 is the outputted length said origin describing the y- ordinate and x- abscissa coordinate values for the origin of the vector to be represented; storing the value of the coordinates of the origin for a first vector segment and gateably outputting said values on a first output line; storing the remaining number of complete vector segments to be encoded for the vector to be represented as the vector length residue; decrementing said vector length residue by unity after each vector segment word is encoded; comparing the vector length residue with the value zero; and outputting the value l on the second output line when said length residue is zero, or when said length residue is greater than zero, outputting on said second output line the value n, as the length of the orthogonal component of said vector segment being encoded, said component lying along the ordinate or abscissa contained in the octant specified by said octant portion; adding the slope residue for a present vector segment to the accumulated slope residues for previously encoded vector segments of the vector to be represented; storing the accumulated slope residues for said previously encoded vector segments; comparing the cummulative slope residue with the value 0.5, incrementing said cummulative slope residue by said slope residue when the cummulative slope residue is less than 0.5 and decrementing the cummulative slope residue by 1.0 the cummulative slope residue is greater than 0.5; selectively modifying the slope of a vector segment being encoded from m/n to (m+1)/n when said cummulative slope residue is greater than 0.5; encoding the octant data and modified slope data as one out of 4n stored vector segment symbol codes to be outputted on a third output line; calculating the value of the coordinates for the origin for the next vector segment to be encoded by adding or substracting the value of n to the value of the x abscissa or y ordinate of the origin of the present vector segment encoded when x or y corresponds, respectively to the abscissa or ordinate contained in the octant designated by said octant portion, and by adding or subtracting the value of the modified slope to the value of the x abscissa or y ordinate of the origin of the present vector segment encoded when x or y does not correspond, respectively to said abscissa or ordinate contained in the octant designated by said octant portion; whereby the vector to be represented is decomposed into a connected sequence of vector segments and said segments are encoded into a sequence of data words describing their origin, length, and symbol code selected from a symbol set.