JPH01152583A - Straight line approximating processor - Google Patents

Abstract

PURPOSE:To reduce the quantity of operation and to obtain an approximating straight line less in an approximating error by disposing a maximum error calculating part, and operating the error between a curve and the straight line approximating to the curve. CONSTITUTION:The data of the straight line to be approximated is stored in a memory 4 and the coordinate of the data corresponding to a parameter value is obtained in a Xm, Ym calculating part 6 through a parameter function calculating part 2. In a work memory 3, as an initial value, the coordinates x1, y1, x2, y2 of two points on the curve and pointer values t1, t2 are stored. Based on these coordinate values and the pointer values, the arithmetic mean value of the parameter values on the two arbitrary points on the curve is obtained in a tm calculating part 4 and the angle of inclination is calculated in the angle (a) of inclination a calculating part 5. Then, the maximum error calculating part 7 calculates a maximum error according to an equation I when the absolute value of (a) is large and according to an equation II when it is small, and compares with an allowable value in an error decision processing part 8. When the maximum error is situated within the allowable value, it is stored in a memory 9 and when it is outside the range of the allowable value, it is returned to the memory 3, so that the approximating straight line small in the approximating error is obtained.

Description

[Detailed Description of the Invention] [Summary] Regarding a linear approximation processing device used when expanding arbitrary vector data into bit data in an image processing system, etc., the present invention reduces the amount of calculations when obtaining an approximate straight line, The aim is to keep approximation errors relatively low and quickly obtain smooth approximate straight lines on the display. The inclination calculation unit for a straight line connecting two points calculates the distance between the coordinates of the curve corresponding to the average value of the parameter values and the straight line connecting the two points of the curve, and corrects the distance according to the inclination of the straight line to obtain an approximation. A maximum error calculation unit that calculates the maximum error, and a predetermined error tolerance value and the maximum error are compared, and if it is within the tolerance, it is used as approximate data, and if it is outside the tolerance, the number of divisions of the curve is increased, It is configured to include an error determination processing section that feeds back to the parameter average value calculation section.

[Industrial application field]

The present invention relates to a linear approximation processing device used when developing arbitrary vector data into bit data in an image processing system, etc., and particularly to a device that can approximate a curve to a straight line with simpler processing and relatively less error.

[Conventional technology]

In an output device such as a printer display, it is necessary to develop vector data, which is an arbitrary cubic curve, into bit data. For example, filling an area surrounded by straight lines and/or cubic curves, or clipping a similar area is difficult to realize. - In order to realize these for boat fishing, it is possible to approximate the curve to a straight line and perform polygon processing.

There are two methods of linear approximation that are problematic here. One of them is linear approximation, which divides the curve into n equal parts and replaces each divided part with a straight line. In this n-equal approximation, it is necessary to make n sufficiently large in order to maintain smoothness in all linear approximation parts of the curve.

Another type of straight line approximation is to accurately calculate the distance between the curve and the approximate straight line, divide the curve so that the distance is within a tolerance, and approximate it with straight lines.

[Problem that the invention seeks to solve]

As mentioned above, in linear approximation divided into n equal parts, it depends on the shape and size of the curve.
is difficult to determine. Linear approximation, which accurately calculates distances, has the problem that the calculations are complicated and the amount of calculations becomes extremely large.

An object of the present invention is to introduce a simpler process for calculating the distance between a curve and its approximate straight line, to reduce the amount of calculation when obtaining an approximate straight line, and to keep the approximation error relatively small. To quickly obtain a smooth approximate straight line on a display output device.

[Means for solving problems]

As shown in FIG. 1, the linear approximation processing device of the present invention has the following features:
parameter function calculation unit 2, parameter average value calculation unit 4,
It includes a coordinate value calculation section 6, an inclination calculation section 5, a maximum error calculation section 7, and an error determination processing section 8.

The parameter function calculation section 2 displays the curve to be approximated as a function using parameters, and the parameter average value calculation section 4 calculates the arithmetic mean of the parameter values for any two points of the curve to be approximated, and calculates the coordinates. The value calculation unit 6 calculates the coordinate value Xs+y+s corresponding to the parameter value tm, and the slope calculation unit 5 calculates the slope a of the approximate straight line connecting the arbitrary two points.

When the absolute value of the slope a is 1 or more, the maximum error calculation unit 7 calculates the following:
The maximum error is l (x+ xm) (y+
y−)/al, and when the absolute value of slope a is smaller than 1, the maximum error is l (y8 y+)+a (xm
-xm)1. Here, xm is the X coordinate of one of two arbitrary points on the curve to be approximated, and yl is the similar y coordinate.

The error determination processing unit 8 compares a predetermined error tolerance value, for example, the size of one dot of a display device, with the calculated maximum error, and if it is within the tolerance, the
is output to accumulate, and if it is out of tolerance, the above X++3
The parameter value and tm value corresponding to '+' are returned to the parameter average value calculation unit as two arbitrary points on the curve.

[Function] When the device of the present invention is used, as shown in FIG.
z.

yz) and the above 1. , the point on the curve corresponding to P.

(When X+e, y++u, the distance between Pl and the straight line PIP2 is found, and this value is compared with the distance between the curve and the straight line P+Pz and corrected so as to cancel out the different error according to the slope of the straight line.

〔Example〕

Prior to describing the embodiments, related technology will be described with reference to the drawings.

Parameter representation of the curve is performed using the parameter t as shown in Fig. 2, and the X and Y coordinate values are xmf, respectively.
x (t) , V=fy (t) .

Here, t is 0≦t≦1.

In FIG. 4, when the partial flow diagram of FIG. 7 is inserted into the broken line block part, the process flow diagram for calculating the accurate distance between the curve and the approximate straight line as a conventional example and comparing it with the error tolerance value. becomes.

Since FIG. 4 will be explained in detail in the embodiment, the flow chart of FIG. 7 will be explained here.

First, one end of the curve in Fig. 3 is Pl(xIny1),
The other end is Pz(Xz, )'2) and the curve and straight line P
+ Expressing the distance between Pz as a function of t, D(t)
= l αx(t)+βy(t)+r l /77
0TJgo・(1). By differentiating this function with respect to t and finding t that satisfies D'(t)=O, t at the point of maximum error is obtained.

Here, α=Yz)'I-β=xm-x2, γ=
3'I Lx X+ Vz-.

x(t) = a X t + b,
l t z + c x t + d X 1y
(t)=a, t3+b, t''+c, t+d.

Therefore aX+ bX+ CX+ d X+ aV+ b
Y+ CF+ dV has already been determined.

Therefore, in the processing step 371, the above α, β, and γ are defined, and also in the step S72, f, , f2 . f3 is defined. Step 373 is performed by adding r, , r2 .
The process of finding t is shown by substituting r. In step S74, t is determined within the range tm≦t≦t2, and in step S75, xmy for the determined t is determined. Step S76 is to substitute this xmy into equation (1) to find the distance.

A linear approximation processing device according to an embodiment of the present invention will be explained with reference to FIG.

This device includes a memory 1, a parameter function calculation unit 2, a work memory 3, a calculation unit 4, a slope a calculation unit 5,
It includes a yrh calculation section 6, a maximum error calculation section 7, an error determination section 8, and a memory 9.

The memory l stores data of a curve to be approximated and supplies the data to the parameter function calculation unit 2. The output of the parameter function calculation unit 2 is xl.

It is supplied to the ym calculating section 6. The t i calculation section 4 receives the output of the work memory 3 and supplies the output to the xM l )' II calculation section 6 . Work memory 3 contains xI as an initial value.
n)'l+xIn)'! , tIn tt are stored.

The slope a calculation unit 5 receives the output from the work memory 3 and supplies the output to the maximum error calculation unit 7. In addition, the maximum error calculation section 7 receives the output from the xm, ym calculation section 6 and supplies the output to the error determination processing section 8 . The error determination processing section 8 supplies the output to the work memory 3 or the memory 9.

The operation of the above-mentioned apparatus will be explained using the flowcharts of FIGS. 4 and 5. The flowchart in FIG. 5 is inserted into the broken line block in FIG.

First, in the initial setting step 341, jl+t2, etc. are set in the data area 1 of the work memory 3, the value of t2 indicated by the pointer (abbreviated as "po" in the figure) 2 of the data area 1 is read, and t2 is set to Xs, y. Input to calculation section 6 x
t and 'It are determined (S42). Next, xm and yl are similarly calculated from the value of tl indicated by pointer 1 of data area 1 (S43).

In step S51, 1. The arithmetic mean value tm of and t2 is determined by the t1 calculation unit 4. The xm, yms calculation unit 6 calculates the corresponding X and Y coordinates xm and 71% from tl.
is calculated (S52). Next, the slope a is calculated by receiving the initial data from the work memory 3 (S5
3). In step S54, the process branches into two processes depending on whether the absolute value of a is 1 or more.

When lal≧1, the maximum error calculation unit 7 calculates d=l (xt
-xm)-(y+-yma)/a l is calculated (S55)
, when l a l<1, d=l(ym y+)+
Find a (xt x1%) l (356),
Each is the maximum error.

Next, the error determination processing unit 8 determines whether the maximum error d is within the tolerance (for example, within the size of one pixel of the display device) (544), and if it is within the tolerance, the data of x1, yI is stored as the data in the memory 9. The data is stored in area 2 and used as linear approximation data, and the pointer is moved (S45). If the value is outside the allowable value, the contents of pointer 1 are placed in the address next to pointer 1, t=(tm +t2)/2 is stored in pointer 1, and the pointer is moved (S46).

The process returns to step S42 and repeats each of the above steps until there is no more data, and linear approximation data is obtained in data area 2.

The calculations in the above processing process will be explained. In FIG. 3, first, the coordinates (Xa++3'a) of P are determined. P,
As mentioned above, the parameter value is t.

is the function value of the curve when . Similarly, the parameter values of PI and Pg are each tI+t2. Here t* =
(tm + tz)/z. This P, and the straight line P, p
Find the distance #d from g. As shown in Figure 3, draw a straight line from P parallel to the Draw a straight line, find the intersection with the straight lines P and P, and let the distance from the intersection to P be Δy. This ΔX or Δ
If d is expressed using y, then d=Δx//TT 7-cho "or d=Δy / , /' 1 + al-. a is the straight line P, the slope of P2, that is, a"' Dz y+)
/ (xi xt)=Δy/ΔX, and Δx=l (y+a −y+)/a+ (xt−xe
)lΔy=1 (xt X+*)a+ (y+*
)'+)l.

Here, when lal≧1, d=Δ as jTTiTla
y/a, and when lal<1, jTTT7111- is approximated as d=aΔX.

This d, that is, P. FIG. 5 is a flowchart showing a process in which the value d calculated by approximating the distance from PlP2 to the straight line PlP2 according to the slope a as described above is regarded as the maximum error. These two approximations, the first approximation are the curve and the straight line P+P
Considering the distance between z as the distance between Pl and straight lines P and P, the second approximation is that when lal≧1, 7″TTir is a, and when lal<1, /”1-1= 711-1/
a is in the direction of canceling out the errors from each other. 1st
The approximation of is estimated to be smaller than the actual error, and the second approximation is estimated to be larger than the actual error.

A block diagram of a drawing system using the apparatus of the embodiment as a linear approximation processing section is shown in FIG.

In the case of straight line data, the data is directly input to the RAM of the work memory 65, and the graphic control unit 63 executes processes such as straight line drawing and polygon inner painting, and then the data is transferred to the image memory (VRAM).
) 62 as bit data and displayed on the display device 66 or 67 via the mechanism control section 64. The curve data is approximated to a straight line by a straight line approximation processing unit 61 using the apparatus of this embodiment, and the data is added to the work memory 65 and thereafter processed in the same manner as the straight line data. Furthermore, in the linear approximation processing section 61, by setting the resolution of an arbitrary device (display device) as an error tolerance value, linear approximation processing suitable for an arbitrary device is executed.

〔Effect of the invention〕

According to the present invention, a simpler processing process for calculating the error between a curve and a straight line that approximates the curve is introduced, thereby reducing the amount of calculation when obtaining an approximate straight line, and reducing the approximation error relatively. As a result, a smooth approximate straight line can be quickly obtained on the display device.

[Brief explanation of the drawing]

Figure 1 is a block diagram explaining the present invention in detail, Figure 2 is a diagram explaining the parameter display of a function curve, Figure 3 is a diagram explaining the error between the curve and the approximate straight line, and Figure 4 is a diagram of the embodiment. Flowchart of approximation processing, FIG. 5 is a partial flowchart of approximation processing in the embodiment, FIG. 6 is a block diagram of a drawing system using the apparatus of the embodiment, and FIG. 7 is a partial flowchart of approximation processing in the conventional example. be. In the figure, 1... Memory, 2... Parameter function calculation section, 3... Work memory, 4... tm calculation section, 5
... Slope a calculation section, 6 ... Xn, ys calculation section, 7. Maximum error calculation section, 8. , 62... image memory, 6
3... Graphic control unit, 64... Mechanism control unit, 65... Work memory,
66, 67...Display device. $1 Parameter display of graphical function Diagram explaining the error between the curve and the approximate straight line 1
Figure 2 Figure 3 Partial flowchart of approximation processing in the embodiment Figure 5 Block diagram of drawing system using I2i 'IJθ limb) Figure 6

Claims (1)

[Claims] A parameter function calculation unit (2) that displays a curve to be approximated as a function using parameters, a parameter average value (t_m) calculation that calculates the arithmetic average of parameter values at arbitrary two points of the curve. Part (4) Coordinate values (x_m, y_
m) a calculation unit (6), a slope calculation unit (5) that calculates the slope (a) of a straight line connecting two points of the curve; when the absolute value of the slope a is 1 or more, any two points of the curve; If the coordinates of one of the points are x_1, y_1 and the corresponding coordinate values of the parameter average values are x_m, y_m, then the maximum error is |(x_1-x_m)-(y_1-y_
m)/a|, and when the absolute value of the gradient a is smaller than 1, the maximum error is calculated as |(y_m-y_1)+a(x_1
-x_m) , an error determination processing unit (8) that returns the parameter values corresponding to x_1, y_1 and the t_m value as arbitrary two points of the curve to the parameter average value calculation unit (4) if the values are outside the tolerance. Processing equipment.