JPH0640349B2 - Digital figure processing method - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a digital figure processing method, and more particularly, to an intersection of straight lines passing through two given two points in an image memory or the like. The present invention relates to a digital figure processing method capable of accurately extracting dots to be formed with a simple configuration.

(Prior Art) For example, digital figure reading / reading of a facsimile machine, etc.
In the reproducing apparatus, in various applications such as the object of highlighting or the boundary point of the graphic filling process, the data stored in the bit map memory, the image memory, or the like is stored.
It is often necessary to have dots that correspond to the intersections of two straight lines.

An example of a conventional method for extracting dots corresponding to the intersections of _two straight lines L ₁ and L ₂ is shown in FIG.

That is, the two dots that the straight line L ₁ passes through are P ₁₁ (x ₁₁ ,
y ₁₁ ), P ₁₂ (x ₁₂ , y ₁₂ ), and two dots that the straight line L ₂ passes through are P ₂₁ (x ₂₁ , y ₂₁ ),
When given by P ₂₂ (x ₂₂ , y ₂₂ ), x = (b ₂ c ₁ −b ₁ c ₂ ) × 1 / (a ₁ b ₂ −a ₂ b ₁ ), y = (a ₁ c ₂ −) _{a 2 c 1) × 1 /} (a 1 b 2 -a 2 b 1) ... (1) _{where, a 1 = x 12 -x 11} , a 2 = x 22 -x 21, b 1 = y 11 -y _{12, b 2 = y 21 -y} 22, c = a 1 x 11 + b 1 y 11, c 2 = a 2 x 22 + b 2 y 22 ... (2) is calculated.

The numerical values x ₁₁ , y ₁₁ , x ₁₂ , y ₁₂ , x ₂₁ , y
₂₁ , x ₂₂ , y ₂₂ are all integer values.

Then, the coordinate value (x, y) calculated by the above equation (1)
May not be an integer value, and if the coordinate value is not an integer value, the final dot position cannot be determined, so rounding, rounding up, or rounding down (x, y), etc. The dot closest to the coordinate value (dot represented by integer coordinate) is calculated, and this dot is very close to the intersection of the _two straight lines L ₁ and L ₂ , or the dot R (x _c , which corresponds to this intersection, y _c ).

(Problems to be Solved by the Invention) According to the conventional method as described above, the two straight lines L ₁ and L
To obtain the dot R corresponding to the intersection of ₂ ,
The function of executing the remainder division as expressed by equation (2) is required, and the hardware configuration becomes complicated accordingly, and the entire apparatus becomes complicated and expensive.

The present invention has been made in view of such a point, and an object thereof is to extract a dot corresponding to an intersection of a straight line passing through two sets of two given dots with a simple configuration and with high accuracy. It is to realize a possible digital figure processing method.

(Means for Solving Problems) According to the present invention for solving the problems described above, an input control unit which decodes a command from a host device via a system bus and controls initial value setting, and the input control. Register arithmetic unit that performs numerical operations based on various constants given by
A method of performing graphic processing by dots, comprising: a micro program control unit that receives various statuses obtained from the calculation result of the register calculation unit and controls the whole, which is a method of performing dot graphic processing using dots P ₁₁ (x ₁₁ , y ₁₁ ) and Dot P ₁₂ (x
Straight line L ₁ passing through ₁₂ , ₁₂ and dot P
₂₁ (x ₂₁ , y ₂₁ ) and the dot P ₂₂ (x ₂₂ , y ₂₁ ).
₂₂ ) through a straight line L ₂ (however, x ₁₁ , y ₁₁ , x ₁₂ , y ₁₂ , x ₂₁ , y
_In the digital figure processing method for extracting the dot R (x _c , y _c ) corresponding to the intersection with ₂₁ , x ₂₂ , y ₂₂ is an integer value, (a) the straight lines L ₁ and L ₂ are converted into the function L ₁ : f _{1 (x, y) = a} 1 x + b 1 y-c 1, L 2: f 2 (x, y) = a 2 x + b 2 y-c 2 ( _{where, a 1 = x 12 -x 11} , b 1 = y ₁₁ −
_{y 12, a 2 = x 22} -x 21, b 2 = y 21 -y 22, c 1, c 2 is _{optionally, f 1 (x 11, y} 11) = f 1 (x 12, y 12) =
0, f ₂ (x ₂₁ , y ₂₁ ) = f ₂ (x ₂₂ , y ₂₂ ) =
0) was defined as _an error generating step of an error when _a 1 ₌ a 2 ₌ 0 or _b 1 _{= b} 2 ₌ 0, the plane including the (b) said linear _{L 1 1: z = f 1} (x, y) = a ₁ x + b ₁ y−c ₁ is defined, and x ₂₁ −x ₁₁ → xd ₁ , y ₂₁ −y ₁₁ → yd ₁ , x ₁₁ → x, 0 → f ₁ (x) is stored in the register calculation unit. When xd ₁ ≧ 0, x is sequentially incremented by 1 from x ₁₁ to x ₂₁ and a ₁ is added to f ₁ (x) to obtain xd ₁ <0.
In the case of x, x is sequentially decremented by 1 from x ₁₁ to x _21, f ₁ (x) = 0 to a ₁ is subtracted, and f ₁ (x) = f ₁
(X ₂₁ ) is calculated and stored as f ₁ (x ₂₁ ) = f ₁ (y) in the register in the register operation unit, and yd ₁ ≧ 0
In the case of, y is sequentially incremented by 1 from y ₁₁ to y ₂₁ and b ₁ is added to f ₁ (y). When yd ₁ <0, y is sequentially decremented by 1 from y ₁₁ to y ₂₁ and f
B ₁ is subtracted from ₁ (y), and f ₁ (y) = f
₁ (y ₂₁ ) from the dot P ₂₁ to the plane ₁
Up to the displacement f _11, and subsequently store x ₂₂ −x ₁₁ → xd ₂ , y ₂₂ −y ₁₁ → yd ₂ x ₁₁ → x, 0 → f ₁ (x) in the register in the register operation unit, When xd ₂ ≧ 0, x is sequentially incremented by 1 from x ₁₁ to x _22, and a ₁ is added to f ₁ (x) to obtain xd ₂ <0.
In the case, x is sequentially decremented by 1 from x ₁₁ to x ₂₂ and a ₁ is subtracted from f ₁ (x) = 0 to obtain f ₁ (x) = f ₁
(X ₂₂ ) is calculated and stored as f ₁ (x ₂₁ ) = f ₁ (y) in the register in the register operation unit, and yd ₂ ≧ 0
In the case of, y is sequentially incremented by 1 from y ₁₁ to y ₂₂ and b ₁ is added to f ₁ (y). When yd ₂ <0, y is sequentially decremented by 1 from y ₁₁ to y ₂₂ and f
B ₁ is subtracted from ₁ (y) to obtain f ₁ (y) = f
₁ (y ₂₂ ) from the dot P ₂₂ to the plane ₁
A displacement _{f 12 up, | f 11 | ≦ | f} 12 | of when a start point of the dot _{P 21 | f 11 |> |} f 12
In the case of |, the starting point selection step of selecting the dot P ₂₂ as a starting point, (c) the straight line L ₂ from the starting point P ₂₁ or P ₂₂ obtained in the step (b) using the displacement comparison method Select the best dot to draw, and the plane of this best dot
_A dot generating step of sequentially generating optimum dots in a direction in which the absolute value of the displacement from ₁ becomes smaller than | f ₁₁ | or | f ₁₂ |, and (d) the step (c) and the step (c) in parallel. In the step 1), the optimum dot sequentially generated in the step (c) is formed on the xy plane toward the plane ₁ : z = f ₁ (x, y) = a ₁ x + b ₁ y-c ₁ . The vertical length of the vertical line is the distance F
₁ (x, y), and F ₁ (x, y) = f ₁ (x + Δx, y + Δy) = f
_{1 (x, y) + a} 1 Δx + b 1 Δy ( _where, f 1 _(x, initial value of y) is _{f 1 (x 21, y 21} ) = f 11 or _{f 1 (x 22, y 22} ) = f 12 Δx, Δy = −1, 0, +1) is calculated every time the optimum dot is selected in the step (c) by using the values of Δx and Δy selected at that time.
A distance calculation step of calculating ₁ (x, y), (e) a step performed in parallel with the step (d), wherein the code of the distance F ₁ (x, y) is sequentially monitored, , The distance F ₁ immediately before the sign is reversed.
The distance F immediately after the absolute value of (x, y) and the sign are inverted
₁ (x, y) is compared with the absolute value, and the smaller distance F ₁
The dot (x, y) corresponding to (x, y) is defined by the straight line L ₁
And the dot R (x _c , y corresponding to the intersection of the line L ₂ and the straight line L _2.
The digital figure processing method is characterized by comprising an intersection point extraction step of extracting as _c ).

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

FIG. 1 is a configuration block diagram showing a hardware configuration example for implementing the method of the present invention.

The device shown in the figure adopts a micro program control system, and is composed of three main parts: an input control unit 10, a register operation unit 20, and a micro program control unit 30. The input control unit 10 and the register calculation unit 20 are interconnected by an internal bus UB.

Reference numeral 10 denotes an input control unit for inputting / decoding a dot extraction command corresponding to an intersection of a straight line from a high-order computer or the like via the system bus SB, and controlling initial value setting. It consists of

Reference numeral 20 is a register arithmetic unit that performs numerical arithmetic.
It is mainly composed of an AND ARISTIC Logical Unit (hereinafter abbreviated as “RALU”) 21.

The RALU 21 has a register group 22 composed of a plurality of internal registers, and performs logical arithmetic operations such as addition and subtraction, logical product, and logical sum between these internal registers.
Further, various statuses in the calculation result of the RALU 21 are input to the multiplexer 31 in the micro program control unit 30.

Reference numeral 30 denotes a microprogram control unit that executes the overall control and dot calculation process corresponding to the intersections, and includes a multiplexer 31, an address sequencer 32, a microprogram memory 33, and a pipeline register 34.

The pipeline register 34 holds the output from the micro program memory 33 and supplies a micro instruction to each part of the input control unit 10 and the register operation unit 20 described above.

In the conditional branching in the microprogram, the multiplexer 31 selects one of the inputs including various statuses from the register operation unit 20 and selects the address sequencer 3
The determination is made in 2.

The present invention is a method realized by using the circuit thus configured, and its detailed operation is as follows.

In the present invention, as shown in FIG. 2, two dots P ₁₁ (x ₁₁ , y ₁₁ ), P ₁₂ (x ₁₂ , y ₁₂ ).
Straight line L ₁ that passes through and two dots P ₂₁ (x ₂₁ , y
₂₁ ) P ₂₂ (x ₂₂ , y ₂₂ ) is very close to an intersection with a straight line L ₂ passing through, and R is a dot corresponding to the intersection.
The operation will be described by taking the case of extracting (x _c , y _c ) as an example.

In the method of the present invention, the displacement comparison method conventionally proposed in the process of extracting the dots R (x _c , y _c ) is used. The displacement comparison method is one of line segment generation methods and is used when generating a straight line, a quadratic curve, or the like.

Such displacement comparison methods include, for example, "Dot display of figures", Theory of theory, vol.56-A, No.7, p.401 (July1973), "An improved algorithm for the generation of no.
nparametric curves ”: BWJordan.Jr., WJLennon, BDHolm: IEEETrans.C-22 No.12, p.1052 (Dec.1973) and the like.

The outline is as follows.

When the equation of the straight line L to be generated is L: f (x, y) = ax−by + c = 0 (3), the dot to be selected next to the already selected dot including the start point is IF MIN | f ( P _i ) | = | f (P _j ) | THEN TAKE P _j (where i, jεI, I = 1,2, ..., 8) (4) is a method of generating.

Here, a, b, and c are constants.

FIG. 3 is an explanatory diagram when selecting a candidate dot in such a displacement comparison method.

_{P 0, P 1, ...,} P 8 represents the dot position in the xy plane, _{P 0} is a dot previously _selected, P 1, ..., _{P 8} represents a candidate dot to be selected this time, respectively. Candidate dots _P 1, ..., _P 1 of the _{P 8,} ..., _{P 4} candidate dots at four pixels connected _{display, P 1, ...,} P ₈ is a candidate dots at 8 pixel connected display.

Further, I in the equation (4) represents the subscript number of the dots P ₁ , ..., P ₈ , and f (P _i ) represents the displacement from the specific plane to the position of the dot P _i (details will be described later). is there.

That is, the straight line L represented by the equation (3) is the intersection of the plane represented by the following equation: z = f (x, y) = ax−by + c (5) and the xy plane (the surface of z = 0). It can be thought of as a line and is represented in FIGS. 4 and 5.

FIG. 4 is a diagram showing the intersection of the specific plane and the xy plane in the xyz three-dimensional space, and FIG. 5 is a sectional view of the specific plane.

In FIGS. 4 and 5, the line of intersection between the specific plane and the xy plane is represented by L. Then, the dot P ₀ on the xy plane
(As shown in FIG. 3, if the point where the perpendicular line from the previously selected previous dot P ₀ ) intersects with the specific plane is A ₀ , the dot P ₀ (x ₀ , y ₀ ) to the intersection A ₀ Is represented by | f (P ₀ ) | or | z ₀ |, and f (P ₀ )
Is defined as the displacement with respect to the dot P ₀ from the specific plane.

That is, it is represented by f (P ₀ ) = z ₀ = ax ₀ −by ₀ + c (51).

As described above, the displacement comparison method refers to the previously selected dot P ₀
From the candidate dots P ₁ , ..., P ₈ as shown in FIG. 3, the displacement f (P _i ) (i = 1, ..., 8) is determined to be the minimum in determining the dot to be selected this time. This is a method in which the dot is selected to generate a line segment, and this operation is sequentially repeated to generate the line segment.

That is, the absolute value of the displacement f (P _i ) corresponding to each candidate dot P ₁ is compared by the equation (4), and the candidate dot P _i having the smallest displacement is selected as the next dot to be selected. .

Here, in order to generate a straight line or a curved line only by a simple addition / subtraction function using the displacement comparison method, the starting point P _{s of the} line figure to be generated must exist on the line figure, that is, the starting point P
it is assumed displacement in _s f _{(P S)} is "0".

As described above, when the optimum dot is selected by the displacement comparison method, the displacement f (P _i ) (i = 1, 2, ..., 8) is calculated based on the equations (5) and (51). Then, it is represented by f (P _i ) = f (x ₀ + Δx, y ₀ + Δy) = f (x ₀ , y ₀ ) + aΔx−bΔy = f (P ₀ ) + aΔx−bΔy.

However, the candidate dot to be selected this time is the dot P _i (x ₀ +
Δx, y ₀ + Δy), and the previously selected dot is dot P ₀ (x ₀ , y ₀ ). Further, since Δx and Δy are intended for the coordinates of the display dot, depending on the value of i, 0,
It takes either a value of +1 or -1.

Further, since the starting point P _{s of the} line figure to be generated exists on the line L and the displacement f (P _S ) is “0”, the initial value of f (P ₀ ) is “0”.

As described above, according to the displacement comparison method, even if the multiplication / division function is not installed, it is possible to realize the line segment generation only by having the addition / subtraction function.

The above is a brief description of the conventional displacement comparison method. In the method of the present invention, this displacement comparison method is used in the procedure.

Next, the steps involved in the method of the present invention will be described with reference to FIGS.
This will be described with reference to the flowcharts of FIGS.

First, the description will be started from the flowchart of FIG.

The x-coordinates and y of the two dots P ₁₁ and P ₁₂ through which the straight line L ₁ passes and the two dots P ₂₁ and P ₂₂ through which the straight line L ₂ pass from the host computer or the like via the system bus SB.
Coordinates (x ₁₁ , y ₁₁ , x ₁₂ , y ₁₂ , x ₂₁ , y
₂₁ , x ₂₂ , y ₂₂ ) are set in the input register 11 in the input control unit 10, and then a start-up (START) is applied to the input control unit from the host computer or the like.

When the start-up (START) is applied, the micro program control unit 30 causes the parameters x ₁₁ , y ₁₁ , x
₁₂ , ₁₂ , y ₂₁ , x ₂₁ , y ₂₁ , x ₂₂ , y ₂₂ are stored in the register group 22 in the register arithmetic unit 20 via the internal bus UB. Thus, from the register of top to bottom in the register group 22, as shown in FIG. 1, x _11, x
Data of ₁₂ , x ₂₁ , x ₂₂ , ... Are stored.

Then register arithmetic unit 20, based on these _{data, x 12 -x 11, y 11} -y 12, x 22 -x 21, y 21 -x 22, calculates a, _x 12 _{-x 11} → a _The values a ₁ , a ₂ , b ₁ , b ₂ are stored in the respective registers 22 as ₁ , y ₁₁ −y ₁₂ → b ₁ , x ₂₂ −x ₂₁ → a ₂ , y ₂₁ −y ₂₂ → b ₂ .

At this point, when a ₁ = a ₂ = 0 or b ₁ = b ₂ = 0 (YES), the straight line L ₁ and the straight line L ₂ have the same x coordinate or y coordinate in two different dots, respectively. , X-axis or y-axis, and as is apparent from FIG. 2, the straight line L ₁ and the straight line L ₂ are parallel, and there is no intersection. Therefore, in this case, an error (ERROR) is set, and the register calculation unit 20 stops the processing.

On the other hand, when at least one of a ₁ and a ₂ is not “0” or when at least one of b ₁ and b ₂ is not “0” (NO), the straight line L ₁ and the straight line L ₂ are parallel to each other. However, since there is a dot corresponding to the intersection, the processing is continued.

Here, the function expressing the straight line L ₁ is L ₁ : f ₁ (x, y) = a ₁ x + b ₁ y−c ₁ (where f ₁ (x ₁₁ , y ₁₁ ) = f ₁ (x ₁₂ , y
₁₂ ). Since the value c ₁ is not used in the calculation formula described later, it does not need to be particularly calculated and is an arbitrary constant.

Then, a plane ₁ in a three-dimensional space including the straight line L ₁ : z = f ₁ (x, y) = a ₁ x + b ₁ y-c ₁ and a displacement f ₁₁ between the dot P ₂₁ on the straight line L ₂ and This plane
_The process of obtaining the displacement f ₁₂ between ₁ and the dot P ₂₂ on the straight line L ₂ is started.

The process of obtaining the displacements f ₁₁ and f ₁₂ will be described later in detail, but is for selecting a point to be a starting point when the straight line L ₂ is generated by the displacement comparison method.

The process of obtaining the displacement f ₁₁ and the displacement f ₁₂ is simply performed by using the formula of ₁ : z = f ₁ (x, y) = a ₁ x + b ₁ y-c ₁ to calculate the dot P ₂₁ (x ₂₁ , y ₂₁ ) Or dot P ₂₂
It can be obtained by substituting (x ₂₂ , y ₂₂ ), but in order to perform this calculation, processing cannot be performed unless a multiplier is set as a hardware resource. According to the present invention, the displacement f ₁₁ and the displacement f ₁₂ are obtained by a calculation process that does not include multiplication by the process described below on the assumption that the multiplication / division function is not set.

The concept of obtaining these displacements f ₁₁ and f ₁₂ is shown in FIG. 6, and the process of obtaining the displacements f ₁₁ and f ₁₂ will be described below with reference to this figure.

Now, returning to the flowchart of FIG. 8, first, the displacement f
A procedure for obtaining ₁₁ will be described.

First, the dot P ₂₁ (x ₂₁ , y ₂₁ ) and the dot P _21
11 (x ₁₁ , y ₁₁ ) x-coordinate and y-coordinate difference are respectively calculated, and x ₂₁ −x ₁₁ → xd ₁ , y ₂₁ −y ₁₁ → yd ₁ (8) are stored in registers in the register group 22. To do.

Next, the process proceeds to the flowchart of FIG.

Here, it can be expressed as f ₁ (x ₁₁ + Δx, y ₁₁ ) = f ₁ (x ₁₁ , y ₁₁ ) + a ₁ Δx (9) (however, for the increase / decrease Δx of the x coordinate, the xy plane Since the display dots above are targeted, Δx = −1,0, + 1), f ₁ (x ₁₁ , y ₁₁ ).
= 0 ((x ₁₁ , y ₁₁ ) is a point on the straight line L ₁ ), the formula (9) is as follows: f ₁ (x, y ₁₁ ) = f ₁ (x) (where f ₁ (x ₁₁ ) = 0) ... (10)

Then, y = y ₁₁ is fixed and x ₁₁ → x, 0 → f ₁
(X) is stored in the register in the register group 22.

Then, when xd ₁ ≧ 0, the value of x is sequentially incremented by 1 from x = x ₁₁ and at the same time, a ₁ is added to f ₁ (x) = 0 each time x is incremented. This operation is repeated until x = x ₂₁ .

On the other hand, when xd ₁ <0, the value of x is sequentially decremented from x = x ₁₁ by 1, and at the same time, a ₁ is subtracted from f ₁ (x) = 0 each time x is decremented. x =
repeat until the x _21.

Thus, the value of f ₁ (x) when x = x ₂₁ is represented by f ₁ (x ₂₁ ).

Next, x = x ₂₁ is fixed.

In this case, it can be expressed as f ₁ (x ₂₁ , y ₁₁ + Δy) = f ₁ (x ₂₁ , y ₁₁ ) + b ₁ Δy (11) (however, for the increase / decrease Δy of the y coordinate, the xy plane Since the display dots above are targeted, Δy = −1, 0, +1), from equation (10), f ₁ (x
₂₁ , y ₁₁ ) = f ₁ (x ₂₁ ).

Therefore, the equation (11) can be expressed as f ₁ (x ₂₁ , y) = f ₁ (y) (where f ₁ (y ₁₁ ) = f ₁ (x ₂₁ )) (12).

Then, y ₁₁ → y, f ₁ (x ₂₁ ) → f ₁ (y) are stored in the registers in the register group 22.

Here, when yd ₁ ≧ 0, the value of y is sequentially incremented by 1 from y = y ₁₁ and at the same time, b ₁ is set to f ₁ (y) = f ₁ (x ₂₁ ) each time y is incremented. Addition is performed, and this operation is repeated until y = y ₂₁ .

On the other hand, when yd ₁ <0, the value of y is sequentially decremented from y = y ₁₁ by 1, and at the same time, b ₁ is subtracted from f ₁ (y) = f ₁ (x ₂₁ ) each time y is decremented. Then, this operation is repeated until y = y ₂₁ .

The above operation of adding or subtracting b ₁ to f ₁ (y) = 0 is repeated until y = y ₂₁ is reached.

The value of f ₁ (y ₂₁ ) when y = y ₂₁ is reached is the displacement f ₁₁ . This displacement f ₁₁ corresponds to the displacement of the dot P _{21 from} the plane ₁ .

Next, the displacement f ₁₂ is calculated.

Dot P ₂₂ (x ₂₂ , y ₂₂ ) and dot P ₁₁ (x
The difference between the x-coordinate and the y-coordinate of ( ₁₁ , y ₁₁ ) is obtained, and x ₂₂ −x ₁₁ → xd ₂ , y ₂₂ −y ₁₁ → yd ₂ (13) are stored in the registers in the register group 22.

Hereinafter, as shown in the flowchart of FIG. 10, f ₁ (y ₂₂ ) is processed according to the same steps as those of the flowchart of FIG.
Is calculated, and this value is defined as the displacement f ₁₂ between the dot P ₂₂ (x ₂₂ , y ₂₂ ) and the plane ₁ .

Next, the absolute values of the displacements f ₁₁ and f ₁₂ | f
₁₁ |, | f ₁₂ | are calculated, and the magnitude relationship is calculated as | f
_It is investigated as ₁₁ | ≦ | f ₁₂ |.

If | f ₁₁ | ≦ | f ₁₂ | is satisfied (YES), the process from M _{1 in} FIG.
₂₁ (x ₂₁ , y ₂₁ ) is the starting point.

On the other hand, when | f ₁₁ | ≦ | f ₁₂ | is not satisfied (N
O) starts the process from M _{2 in} FIG.
₂₂ (x ₂₂ , y ₂₂ ) is the starting point.

Here, the function representing the straight line L ₂ is L ₂ : f ₂ (x, y) = a ₂ x + b ₂ y−c ₂ = 0 (however, f ₂ (x ₂₁ , y ₂₁ ) = f ₂ (x ₂₂ , Y ₂₂ ) = 0) (14). The value c ₂ is not used in the calculation formula to be described later and thus need not be calculated and may be arbitrary.

Then, from the determined starting point P ₂₁ or P ₂₂ , using the displacement comparison method described above, optimal dots are sequentially generated this time so as to draw the straight line L _{2 in a} direction approaching the straight line L ₁ .

That is, from the starting point P ₂₁ or P ₂₂ , the straight line L ₂ : f ₂ (x, y) = a ₂ x + b is obtained by the displacement comparison method f ₂ (x + Δx, y + Δy) = f ₂ (x, y) + a ₂ Δx + b ₂ Δy. The dot display of ₂ y−c ₂ = 0 is represented by a straight line L ₁ : f ₁ (x, y) = a ₁ x + b ₁ y−c ₁ = 0 (however, f ₁ (x ₁₁ , y ₁₁ ) = f ₁ ( x ₁₂ , y
₁₂ ) = 0) is executed sequentially.

At this time, together with the optimum dots on the straight line L ₂ that are sequentially generated, the plane ₁ including the straight line L ₁ is: z = f ₁ (x, y) = a ₁ x + b ₁ y−c ₁ toward the xy plane. A perpendicular line perpendicular to is drawn, and the length of the perpendicular line is defined as the distance F ₁ (x, y), and this value is calculated.

The distance _{F 1} to the optimum dot and plane ₁ on the straight line _{L 2}
(X, y) (however, the distance perpendicular to the xy plane) is simply ₁ : z = f ₁ (x, y) = a ₁ x + b ₁ y-c ₁ It can be obtained by successively substituting the coordinate values (x, y) of the above. However, in order to perform this calculation, processing cannot be performed unless a multiplier is set as a hardware resource. According to the present invention, on the assumption that the multiplication function is not set, the distance F ₁ (x, y) is obtained by a calculation process that does not include multiplication by the process described below.

More specifically, the optimum dot is selected by the displacement comparison method according to f ₂ (x + Δx, y + Δy) = f ₂ (x, y) + a ₂ Δx + b ₂ Δy. At the same time, however, the distance F ₁ is calculated. (x, y) the initial value of the _{F 1 (x, y) =} f 1 (x + Δx, y + Δy) = f 1 (x, y) + a 1 Δx + b 1 Δy ( _where, f 1 (x, y) is f ₁ (X ₂₁ , y ₂₁ ) = f ₁₁ or f ₁ (x ₂₂ , y ₂₂ ) = f ₁₂ , and Δx and Δy are any values of 0, +1 and −1.

That is, as the initial value f (x, y) of the distance F ₁ (x, y), the value of f ₁₁ is adopted when the dot P ₂₁ is selected as the starting point, and f is selected when the dot P ₂₂ is selected as the starting point. A value of ₁₂ is adopted. Then, every time a dot for drawing the straight line L ₂ is selected, Δx and Δy selected at that time are selected.
The distance F ₁ (x, y) is calculated using the value of (−1, 0, +1).

Here, the distance F ₀ at the time of the previous dot selection is set to f ₁ (x,
y), and the distance F ₁ at the time of dot selection this time is f ₁ (x +
Δx, y + Δy).

In order to generate the optimum dot in the direction approaching the straight line L ₁ , the absolute value of the displacement from the plane _{1 of the} optimum dot to be selected next to the start point P ₂₁ or P ₂₂ is that of the start point (from the plane ₁ It is sufficient to select the drawing direction of the straight line L _{2 in} a direction that becomes smaller than the drawing direction.

Then, when the code is inverted distance _F 1 (x, y), i.e., when the plane ₁ hangs xy plane, the distance _F 1 (x,
the distance F ₀ from the plane ₁ of the optimal dot straight line L ₂ immediately before the sign of y) is reversed, comparing the absolute value of the distance F ₁ from the plane ₁ of the optimal dot straight line L ₂ immediately after inversion.

In the case of | F ₀ | ≦ | F ₁ |, the optimum dot immediately before the sign inversion is set as a dot extremely close to the intersection of the straight line L ₁ and the straight line L ₂ , and this dot is extracted as a dot corresponding to the intersection.

In the case of | F ₀ |> | F ₁ |, the optimum dot immediately after sign reversal is set as a dot extremely close to the intersection of the straight lines L ₁ and L ₂ , and this dot is extracted as a dot corresponding to the intersection.

A point corresponding to this intersection, that is, a dot R (x _c , y _c )
Is shown in FIG.

As described above, according to the present invention, since the dot R corresponding to the intersection of the straight lines L ₁ and L ₂ is mainly added and subtracted without using the multiplication / division function, it is possible to accurately obtain the dot R with a simple hardware configuration. It is possible.

It should be noted that if any _{one of the} values a ₁ , b ₁ , a ₂ , b ₂ expressed by the equation (4) is not 0 and a ₁ b ₂ = a ₂ b ₁ , that is, the straight lines L ₁ and L _{When 2} is parallel, the distance F
The sign of ₁ (x, y) does not invert. In order to prevent such an inconvenience from occurring, a time monitoring timer provided by software or hardware is provided, and if the operation does not end even after a certain period of time, an error is generated and the operation is aborted.

(Effects of the Invention) As described in detail above, the present invention operates as follows.

First, two dots P ₁₁ (x ₁₁ , y ₁₁ ) and P ₁₂
A straight line L ₁ passing through (x ₁₂ , y ₁₂ ) and two dots P
_The function f ₁ (x, y) = a ₁ x + b ₁ y-c ₁ , f ₂ (for each of the straight lines L ₂ passing through ₂₁ (x ₂₁ , y ₂₁ ) and P ₂₂ (x ₂₂ , y ₂₂ ). _{x, y) = a 2 x} + b 2 y-c 2 _{where, a 1 = x 12 -x 11} , b 1 = y 11 -y 12, a 2 = x 22 -x 21, b 2 = y 21 -y 22 , C ₁ , c ₂ are arbitrary, f ₁ (x ₁₁ , y ₁₁ ) = f ₁ (x ₁₂ , y ₁₂ ) = f ₂ (x ₂₁ , y ₂₁ ) = f ₂ (x ₂₂ , y ₂₂ ) =
Define 0.

Then, multiply select one of the dot P ₂₁ or dot P ₂₂ on the straight line L ₂ as a starting point without using division, while generating a linear L ₂ by the optimum dot selected using a displacement comparison method from the start point, At the same time, the distance F ₁ (x, y) from the plane ₁ : z = f ₁ (x, y) including the straight line L ₁ of the selected optimum dot is sequentially calculated, and this distance F ₁
Determine when the sign of (x, y) is inverted.

When the sign reversal of the distance F ₁ (x, y) is detected, the respective distances F from the plane ₁ of the optimum dots before and after the sign reversal
The absolute values of ₁ (x, y) are compared, and the smaller optimum dot is extracted as a dot corresponding to the intersection of the straight line L ₁ and the straight line L ₂ .

Therefore, according to the present invention, the dot corresponding to the intersection of two straight lines can be accurately obtained only by the simple addition / subtraction function.

Further, according to the present invention, when generating the straight line L ₂ , the distance f ₁₁ from the plane ₁ : z = f ₁ (x, y) to the dot P ₂₁ and the plane ₁ : z = f ₁ (x, y) from the dot P ₂₂ to the distance f ₁₂ and if | f ₁₁ | ≦ | f ₁₂ |, the dot P ₂₁ is the starting point, and if | f ₁₁ |> | f ₁₂ | , Dot P
_{Since 22} is selected as the starting point, compared to a method in which the starting point is fixed to either dot P ₂₁ or dot P ₂₂ when the drawing of the straight line L ₂ is started, the dot corresponding to the intersection of the two straight lines is obtained at higher speed. be able to.

[Brief description of drawings]

FIG. 1 is a configuration block diagram showing an embodiment for realizing the method of the present invention, FIG. 2 is a diagram showing dots corresponding to intersections of straight lines, FIG. 3 is a diagram showing directions of candidate dots, and FIG. Four
5 and 5 are diagrams for explaining the displacement comparison method, FIG. 6 is a diagram for explaining calculation of the displacements f ₁₁ and f ₁₂ , and FIG. 7 is for calculating dots corresponding to intersections of straight lines. FIGS. 8 to 11 are flow charts showing the processing steps of the present invention. 10 ... Input control unit, 11 ... Input register 12 ... Bus control unit, 20 ... Register operation unit 21 ... RALU, 22 ... Register group 30 ... Micro program control unit 31 ... Multiplexer 32 ... Address Sequencer 33 ... Micro program memory 34 ... Pipeline register SB ... System bus, UB ... Internal bus

Claims (1)

[Claims] 1. An input control unit which decodes a command from a host device via a system bus and controls initial value setting, and a register which performs a numerical operation based on various constants given from the input control unit. A method for performing graphic processing by dots, which comprises a calculation unit and a microprogram control unit for controlling the whole by receiving various statuses obtained from the calculation result of the register calculation unit.
₁₁ (x ₁₁ , y ₁₁ ) and the dot P ₁₂ (x ₁₂ , y
₁₂ ) and a straight line L ₁ and a dot P ₂₁ (x ₂₁ ,
y ₂₁ ) and a straight line L ₂ (however, x ₁₁ , y ₁₁ , x ₁₂ , y ₁₂ , x) passing through the dot P ₂₂ (x ₂₂ , y ₂₂ ).
_In the digital figure processing method for extracting the dot R (x _c , y _c ) corresponding to the intersection point with ₂₁ , y ₂₁ , x ₂₂ , y ₂₂ is an integer value, (a) the straight lines L ₁ and L ₂ are converted into the function L _{1: f 1 (x, y} ) = a 1 x + b 1 y-c 1, L 2: f 2 (x, y) = a 2 x + b 2 y-c 2 ( _{where, a 1 = x 12 -x 11} , b ₁ = y ₁₁ −
_{y 12, a 2 = x 22} -x 21, b 2 = y 21 -y 22, c 1, c 2 is _{optionally, f 1 (x 11, y} 11) = f 1 (x 12, y 12) =
0, f ₂ (x ₂₁ , y ₂₁ ) = f ₂ (x ₂₂ , y ₂₂ ) =
0) was defined as _an error generating step of an error when _a 1 ₌ a 2 ₌ 0 or _b 1 _{= b} 2 ₌ 0, the plane including the (b) said linear _{L 1 1: z = f 1} (x, y) = a ₁ x + b ₁ y−c ₁ is defined, and x ₂₁ −x ₁₁ → xd ₁ , y ₂₁ −y ₁₁ → yd ₁ , x ₁₁ → x, 0 → f ₁ (x) is stored in the register calculation unit. When xd ₁ ≧ 0, x is sequentially incremented by 1 from x ₁₁ to x ₂₁ and a ₁ is added to f ₁ (x) to obtain xd ₁ <0.
In the case of x, x is sequentially decremented by 1 from x ₁₁ to x _21, f ₁ (x) = 0 to a ₁ is subtracted, and f ₁ (x) = f ₁
(X ₂₁ ) is calculated and stored as f ₁ (x ₂₁ ) = f ₁ (y) in the register in the register operation unit, and yd ₁ ≧ 0
In the case of, y is sequentially incremented by 1 from y ₁₁ to y ₂₁ and b ₁ is added to f ₁ (y). When yd ₁ <0, y is sequentially decremented by 1 from y ₁₁ to y ₂₁ and f
B ₁ is subtracted from ₁ (y), and f ₁ (y) = f
₁ (y ₂₁ ) from the dot P ₂₁ to the plane ₁
Up to the displacement f _11, and subsequently store x ₂₂ −x ₁₁ → xd ₂ , y ₂₂ −y ₁₁ → yd ₂ x ₁₁ → x, 0 → f ₁ (x) in the register in the register operation unit, When xd ₂ ≧ 0, x is sequentially incremented by 1 from x ₁₁ to x _22, and a ₁ is added to f ₁ (x) to obtain xd ₂ <0.
In the case, x is sequentially decremented by 1 from x ₁₁ to x ₂₂ and a ₁ is subtracted from f ₁ (x) = 0 to obtain f ₁ (x) = f ₁
(X ₂₂ ) is calculated and stored as f ₁ (x ₂₁ ) = f ₁ (y) in the register in the register operation unit, and yd ₂ ≧ 0
In the case of, y is sequentially incremented by 1 from y ₁₁ to y ₂₂ and b ₁ is added to f ₁ (y). When yd ₂ <0, y is sequentially decremented by 1 from y ₁₁ to y ₂₂ and f
B ₁ is subtracted from ₁ (y) to obtain f ₁ (y) = f
₁ (y ₂₂ ) from the dot P ₂₂ to the plane ₁
A displacement _{f 12 up, | f 11 | ≦ | f} 12 | of when a start point of the dot _{P 21 | f 11 |> |} f 12
In the case of |, the starting point selection step of selecting the dot P ₂₂ as a starting point, (c) the straight line L ₂ from the starting point P ₂₁ or P ₂₂ obtained in the step (b) using the displacement comparison method Select the best dot to draw, and the plane of this best dot
_A dot generating step of sequentially generating optimum dots in a direction in which the absolute value of the displacement from ₁ becomes smaller than | f ₁₁ | or | f ₁₂ |, and (d) the step (c) and the step (c) in parallel. In the step 1), the optimum dot sequentially generated in the step (c) is formed on the xy plane toward the plane ₁ : z = f ₁ (x, y) = a ₁ x + b ₁ y-c ₁ . The vertical length of the vertical line is the distance F
₁ (x, y), F ₁ (x, y) = f ₁ (x + Δx, y + Δy) = f ₁ (x, y) + a ₁ Δx + b ₁ Δy (however, the initial of f ₁ (x, y) The value is f ₁ (x ₂₁ , y ₂₁ ) = f ₁₁ or f ₁ (x ₂₂ , y ₂₂ ) = f ₁₂ , and Δx, Δy = −1, 0, +1) in step (c) above. Each time the optimum dot is selected,
The distance F is calculated using the values of Δx and Δy selected at that time.
₁ (x, y) to calculate a distance, (e) a step performed in parallel with the step (d), wherein the code of the distance F ₁ (x, y) is sequentially monitored, and the code is calculated. , The distance F ₁ immediately before the sign is reversed.
The distance F immediately after the absolute value of (x, y) and the sign are inverted
₁ (x, y) is compared with the absolute value, and the smaller distance F ₁
The dot (x, y) corresponding to (x, y) is defined by the straight line L ₁
And the dot R (x _c , y corresponding to the intersection of the line L ₂ and the straight line L _2.
(c ) A digital figure processing method comprising an intersection extraction step of extracting as _c ).