JPH0453318B2 - - Google Patents

Description

Detailed Description of the Invention (Field of Industrial Application) The present invention relates to a digital line segment generator, and more particularly to a digital line segment generator that can rapidly generate digital line segments whose starting points are not on a straight line. .

(Prior Art) In fields such as graphic display devices and numerically controlled machine tools (NC machines), it is necessary to generate line figures such as digital line segments and digital arcs at high speed and with high precision. For this reason, various graphic generation algorithms have been developed, and line graphic generators have been devised that incorporate these algorithms into hardware.

As one method for generating digital line segments, a displacement comparison method is used that can uniformly generate highly accurate quadratic curve figures including straight lines. In the displacement comparison method, when the equation of the straight line to be generated is f (x, y) = ax - by + c = 0 (1), the dot to be selected next to the already selected dot including the starting point is IF MIN | f (Pi)|=|f(Pj)|THEN TAKE Pj (2) (where i, j〓I, I=1, 2...8). Here, a, b, and c in equation (1) are constants.

FIG. 8 is a diagram for explaining the aforementioned direction selection of candidate dots. P ₀ to P ₈ indicate dot positions in the xy plane. P ₀ is the previously selected dot,
P ₁ to P ₈ respectively indicate candidate dots to be selected this time. Among candidate dots P ₀ to P ₈ , P ₁ to _{P 4}
is a candidate dot for 4-pixel connected display, P ₁ to _{P 8} is 8
These are candidate dots when displaying pixel connections. I in formula (2)
indicates the numbers of dots _P1 to _P8 , and f(Pi) indicates the displacement of dot Pi from the specific plane φ (details will be described later).

Equation (1) can be thought of as the line of intersection between the plane φ and the xy plane (z=0 plane), which is expressed by the following equation: φ:Z=f(x,y)=ax−by+c (3) . FIG. 9 is a diagram showing the intersection of the specific plane φ and the xy plane in the xyz three-dimensional space, and FIG. 10 is a sectional view of the specific plane φ. L in FIG. 9 is the intersection line between the plane φ and the xy plane. xy
When a perpendicular line extending perpendicularly from a point P ₀ on a plane (same as P ₀ in Figure 8) intersects a specific plane φ, the distance from P ₀ to the intersection A ₀ is |f(P ₀ )| or |Z ₀ |, and f(P ₀ ) is defined as the displacement at the dot P ₀ from the plane φ.

The displacement comparison method is used to select the next dot after the previously selected point _P0 , but only if its displacement f(Pi) (i = ₁ to 8) is the smallest among the candidate points shown in Figure 8, P1 to _P8 . The point is to choose the point that becomes . That is, the absolute values of displacements are compared using equation (2), and the candidate dot with the smallest displacement is selected as the next selected dot.

(Problem to be Solved by the Invention) In order to generate a digital line segment using only a simple addition and subtraction function using the displacement comparison method described above, the starting point P _s (x _s , y _s ) must be determined by formula (1). It is assumed that the displacement Z _s at the starting point is 0, that is, Z _s = f (P _s ) = ax _s −by _s + c = 0 (4). . however,
For the equation (1) of the straight line to be generated, use either the x or y coordinate as a parameter: x _s ≦x≦x _e (5) or y _s ≦y≦y _e (6) When generating a digital line segment within a range that satisfies the following, it is necessary to find the coordinates of the starting point P _s (x _s , y _s ) and the displacement Z _s at the starting point P _s . According to the conventional method, the coordinates of the starting point P _s (x _s , y _s ) and the displacement at P _s
Multiplication and division functions are required to find Z _s .

That is, when x _s is given, y = (ax _s + c)/
The digital value closest to the true value than b is y _s , while y _s
is given, find the digital value closest to the true value from x=(by _s - c)/a as x _s , and use the calculated value of x _s or y _s to find the starting point P _s (x _s , y _s ) had to be calculated: Z _s =ax _s −by _s +c.

The present invention has been made in view of these points, and its purpose is to solve the equation f(x,y)=ax−
Written by + c = 0, x _s ≦x≦x _e or y _s ≦y≦
The object of the present invention is to realize a digital line segment generator with a simple configuration that can generate digital line segments satisfying y _e at high speed and with high precision using only simple addition and subtraction functions using a displacement comparison method.

(Means for Solving the Problems) The present invention for solving the above-mentioned problems uses an equation in which x and y are variables and a, b, and c are known constants f(x, y)=ax-by+c= 0 and satisfies the range of x _s ≦ x ≦ x _e or y _s ≦ y ≦ y _e , and when the parameters x _s and x _e are given, y,
If the equation f ₁ (y, u) = -by + c - u = 0 where u is a variable, -b is a coefficient, and c is a constant is given parameters y _s and y _e , then
Define the equation f ₂ (x, v) = ax + c - v = 0 where x and v are variables, a is a coefficient, and c is a constant, and from these equations, the neighboring points of f ₁ (y, u) = 0 are defined. The digital value y _e1 closest to the true value on the y-axis that satisfies u=0, or v= at a point near f ₂ (x, v)=0.
The digital value x _e2 that is closest to the true value on the x-axis that satisfies 0, and when the equation f ₁ (y, u) = 0, f ₁ (y, u) =
The point Q _s1 (0, c) that satisfies 0 is defined by the equation f ₂ (x,
When v)=0, the point that satisfies f ₂ (x, v)=0
Given Q _s2 (0, C) as the starting point, it is calculated simply by adding and subtracting functions by applying the displacement comparison method. Next, in the equation f(x, y) = 0, P _s1
(0, y _e1 ) or P _s2 (x _e2 , 0) as the starting point, these y _e1
Or _{the known f 1 (} y _e1 ,
0) or f ₂ (x _e2 , 0) as the initial displacement of the starting point in each case, and by using the displacement comparison method again based on these values, x _s ≦x≦x _e or y _s ≦ The present invention is characterized in that digital line segments in the range y≦y _e are generated simply by addition and subtraction functions.

(Example) Hereinafter, an example of the present invention will be described in detail with reference to the drawings.

FIG. 1 is a block diagram showing an embodiment of the present invention. The device shown in the figure adopts a microprogram control system, and includes an input control section 10 and an output section 2.
0, a register operation section 30, and a microprogram control section 40. The input control section 10 and the register calculation section 30 are interconnected by an internal bus UB. 10
1 is an input control section that inputs and decodes commands from a host computer or the like via the system bus SB and controls initial value setting, and is composed of an input register 11 and a bus control section 12. Reference numeral 20 denotes an output unit that outputs x and y coordinate values to an external display device (not shown) such as an image memory, and includes an x register 21 and a y register 22 that receive coordinate data sent via the internal bus UB. It consists of Respective values are set in these registers 21 and 22 via an internal bus UB.

Reference numeral 30 denotes a register operation section for performing numerical operations, which is mainly composed of a register and arithmetic logical unit (hereinafter abbreviated as RALU) 31. The RALU 31 has a register group 32 composed of a plurality of internal registers, and can perform arithmetic operations such as addition/subtraction, logical product, and logical sum operation between the internal registers. Further, various statuses in the calculation results in the RALU 31 are input to a multiplexer in the microprogram control unit 40. 40 is a microprogram control unit that executes the overall control and line segment generation algorithm;
1, an address sequencer 42, a microprogram memory 43, and a pipeline register 44. Pipeline register 44
holds the output from the microprogram memory 43 and supplies microinstructions to each part of the input control section 10, output section 20, and register operation section 30 described above. Conditional branching in a microprogram is performed by selecting one of the inputs including various statuses from the register calculation unit 30 in the multiplexer 41 and making a determination in the address sequencer 42. The operation of the circuit configured as described above will be explained as follows.

Here, it is described by the equation f(x,y)=ax-by+c=0, with a, b, and c as known constants, and satisfies the range of x _s ≦x≦x _e or y _s ≦y≦y _e . As an example of a digital line segment, a case where the line segment exists in the first quadrant of the xy plane as shown in FIG. 2 will be explained. In Figure 2, a is x _s ≦
B indicates the case where x≦x _e , and y _s ≦y≦y _e . A's P _s1 (0, y _e1 ), B's P _s2
(x _e2 , 0) indicates the starting point of each straight line, and L indicates a line segment.

Input variable parameters x s , x e of line segment parameters a, b, c, and x or variable parameters y _s , _{y e of y} from a host computer, etc. via system bus SB into the control unit 10 It is set in the register 11, and a start activation is applied to the input control unit 10 from a host computer or the like. When the start starts,
The microprogram control unit 40 sets the parameters a, b, c, x _s , x _e in the input register 11 when the variable parameter is x, and sets the parameters a, b, c, x e when the variable parameter is y. y _s and y _e are stored in the register group 32 in the register calculation unit 30 via the internal bus UB.

The following procedure is the same regardless of whether the variable parameter is x or y, so here we will explain the procedure for generating a digital line segment in the range where the variable parameter is x, that is, x satisfies x _s ≦ x ≦ x _e . do. In this case, as shown in FIG.
Parameters a, b, c, x _s , and x _e are stored in the register group 32 in order from the top register.

First, as shown in FIG. 2A, the dot P _s1 (0, y _e1 ) closest to the straight line L (L: ax-by+c=0) at the point on the y-axis and the displacement of P _s1 Z _s1 = f (0,y _e1 )
seek. For that purpose, y and u are variables, -b is a coefficient,
The equation f ₁ (y, u)=-by+c-u=0 (7) where c is a constant is newly defined. Then, starting from the point Q _s1 (0, c) that satisfies f ₁ (y, u) = 0, by using the displacement comparison method, the optimal dot is converted into a line segment one dot at a time from the starting point Q _s1 until u = 0. L ₁ (L ₁ :-by+c-u
=0).

FIG. 3A is a diagram showing the generation of line segment _L1 .
The horizontal axis shows y, and the vertical axis shows u. L ₁
is the line segment defined by equation (7), Q _s1 is the starting point, and Q _s1
Then, dots are sequentially generated using the displacement comparison method, and a line segment _L1 is generated. When u=0, the generation of line segment L ₁ is stopped, and the y coordinate at that time is y _e1 ,
The displacement Z _e1 =f ₁ (y _e1 , 0) of the end point Q _e1 (y _e1 , 0) is stored in the register group 32 again.

When y _e1 is determined by the operation explained in Figure 3 A, the starting point P _s1 (0, y _e1 ) and
The displacement Z _s1 = f (0, y _e1 ) of P _s1 is found. Therefore,
y _e1 , the displacement Z _e1 , the starting point is P _s1 (0, y _e1 ), the displacement of the starting point P _s1 Z _s1 = f (0, y _e1 ) = Z _e1 , and here again,
Using the displacement comparison method, optimal dots are generated one dot at a time from the starting point _Ps1 until x= _xs .

From the time when x= _xs , optimal dots are continuously generated and, at the same time, the x, y coordinate values of the optimal dots are set in the x, y registers 21, 22 of the output section 20 via the internal bus UB. As a result, the digital line segment L is displayed on, for example, a CRT. The above operation is based on the x-coordinate upper limit value (final arrival point) of line segment L x _e
is repeated until . FIG. 4 is a flowchart showing the above-described operation.

As described above, according to the present invention, a digital line segment described by the equation f(x,y)=ax−by+c=0 and satisfying x _s ≦x≦x _e can be generated at high speed and with high efficiency using only simple addition and subtraction functions. Can be generated with precision. The above description has been made taking the case where the variable parameter is x as an example, but the situation is exactly the same when the variable parameter is y.

_That is, as _shown in _{FIG .} (x _e2 ,0)
seek. For this purpose, a new equation f ₂ (x, v)=ax+c−v=0 (8) is defined in which x and v are variables, a is a coefficient, and c is a constant. Then, starting from the point Q _s2 (0, c) that satisfies f ₂ (x, v) = 0, by using the displacement comparison method, the optimal dot is converted into a line segment one dot at a time from the starting point Q _s2 until v = 0. L ₂ (L ₂ :ax+c−v=
0) is generated.

FIG. 3B is a diagram showing the generation of line segment _L2 .
The horizontal axis shows y, and the vertical axis shows v.
_L2 is a line segment defined by equation (8), _Qs2 is a starting point, and dots are sequentially generated from _Qs2 by the displacement comparison method to generate line segment _L2 . The following operation is the same as in the case where x is a variable parameter, so the explanation will be omitted.

Figure 6 shows a=2, b=3, c=5, x _s =3,
FIG. 7 is a diagram showing an example of digital line segment generation in the case of x _e =9. A shows the occurrence of a line segment when calculating Q _s1 and its displacement Z _e1 , and B shows an example of the actual occurrence of the intended line segment. Both shapes A and B are
The value in parentheses indicates the displacement at that point.

In the above explanation, the digital line segment is xy
The case where it exists in the first quadrant of the plane has been explained. However, the present invention is not limited to the first quadrant, and as shown in FIG.
Digital line segments can be generated using the same procedure even when the line segments exist in the third and fourth quadrants. However, if x _s , x _e <0 or y _s , y _e <0, the fourth
In the flowchart of Fig. 5, x _s and x _e ,
The relationship between y _s and y _e is swapped, and a line segment is generated from x = x _e in the direction of x = x _s or from y = y _e in the direction of y = y _s .

In addition, if the line segment exists across two or more quadrants as shown in Figure 7B, x=0 or y
=0 as the center in the horizontal or vertical direction, that is, in the direction from x = 0 to x = x _s , and from x = 0 in the direction of x = x _e ,
It is sufficient to generate line segments by dividing into two, one in the direction from y=0 to y= _ys , and the other in the direction from y=0 to y= _ye . Incidentally, in FIG. 7, the direction in which the line segment is generated is indicated by an arrow.

(Effects of the Invention) As explained in detail above, according to the present invention, f(x, y)=ax−by+c=0, where x _s ≦x≦x _e or y _s ≦y≦y _e When generating a digital line _{segment that} satisfies the range of y coordinate y _e1 or x
By calculating the coordinates x _e2 and finding the starting point, and then generating line segments using the displacement comparison method, digital line segments can be generated quickly and with high accuracy using only the simple addition function.

[Brief explanation of drawings]

FIG. 1 is a configuration block diagram showing one embodiment of the present invention, FIG. 2 is a diagram showing an example of the generation of digital line segments,
Fig. 3 is an explanatory diagram of calculation of y _e1 or x _e2 , Figs. 4 and 5 are flowcharts showing the operation of the present invention, and Fig. 6
The figure shows a specific example of the generation of digital line segments.
FIG. 7 is a diagram showing an example of digital line segment generation, FIG. 8 is a diagram showing the direction of candidate dots, and FIGS. 9 and 10 are diagrams explaining the displacement comparison method. 10...Input control unit, 11...Input register,
12... Bus control section, 20... Output section, 21...
x register, 22...y register, 30...register operation unit, 31...RALU, 32...register group, 40...microprogram control unit, 41
...Multiplexer, 42...Address sequencer, 43...Micro program memory, 44...
...pipeline register, SB...system bus,
UB...Internal bus.

Claims (1)

[Claims] 1. Described by the equation f(x, y)=ax-by+c=0, where x, y are variables and a, b, c are known constants, and x _s ≦x≦x _e or y When generating a Daisy line segment that satisfies the range _s ≦y≦y _e , if the parameters x _s and x _e are given, then y,
If the equation f ₁ (y, u) = -by + c - u = 0 where u is a variable, -b is a coefficient, and c is a constant is given parameters y _s and y _e , then
Define the equation f ₂ (x, v) = ax + c - v = 0 where x and v are variables, a is a coefficient, and c is a constant, and from these equations, the neighboring points of f ₁ (y, u) = 0 are defined. The digital value y _e1 closest to the true value on the y-axis that satisfies u=0, or v= at a point near f ₂ (x, v)=0.
The digital value x _e2 that is closest to the true value on the x-axis that satisfies 0, and when the equation f ₁ (y, u) = 0, f ₁ (y, u) =
The point Q _s1 (0, c) that satisfies 0 is defined by the equation f ₂ (x,
When v)=0, the point that satisfies f ₂ (x, v)=0
Given Q _s2 (0, C) as the starting point, it is calculated simply by adding and subtracting functions by applying the displacement comparison method. Next, in the equation f(x, y) = 0, P _s1
(0, y _e1 ) or P _s2 (x _e2 , 0) as the starting point, these y _e1
Or _{the known f 1 (} y _e1 ,
0) or f ₂ (x _e2 , 0) as the initial displacement of the starting point in each case, and by using the displacement comparison method again based on these values, x _s ≦x≦x _e or y _s ≦ A digital line segment generator characterized in that digital line segments in the range y≦y _e are generated simply by addition and subtraction functions.