JPH03223977A - Graphic processor - Google Patents

Abstract

PURPOSE:To accurately draw the graph of a high-order function in the small using frequency of a storage means by designating in fine pitches the characteristic parts of the high-order function like the extreme value, a flection point, etc., and then designating other parts in rough pitches respectively. CONSTITUTION:A temporary storage means 2 is provided to store a designated passing point together with a deciding means 1 which decides whether the passing point is equal to the prescribed periphery of each feature point or not, and a pitch deciding means 1 which designates a fine pitch as decided previously with the affirmative result of decision of decision of the deciding means 1 and then a rough pitch as decided previously with the negative result of decision respectively. Then such feature points of an input high-order function as the extreme value, the flection point, the drawing start/end points, etc., are calculated. Then it is decided whether the designated passion points is equal to the prescribed periphery of each feature point or not. If so, the prescribed fin pitch is designated. If not, the prescribed rough pitch is designated. Thus the graph of the high-order function can be accurately traced with the small number of passing points.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a graphic processing device that draws graphs of high-order functions such as quadratic functions and cubic functions, and more specifically, - This relates to a passing point designation method in which passing points in characteristic parts such as near inflection points are specified finely, and passing points in other parts are specified coarsely.

[Prior Art] Conventionally, this kind of graphic processing device that draws a graph of a high-order function calculates the passing points of the input high-order function at appropriate pitch intervals, and uses splines or the like to draw between each passing point. After interpolation, the interpolated points were connected with straight lines and drawn.

[Problems to be Solved by the Invention] By the way, when drawing a graph of a high-order function by interpolating it using splines, etc., as in the past, in the vicinity of extreme values, it is necessary to change the pitch between passing points, which is the basis for calculating interpolation points. The graph of a higher-order function cannot be accurately traced unless it is specified in detail. In addition, if you specify passing points at a fine pitch in order to accurately trace the graph of a higher-order function as described above, you will have to specify a large number of passing points, which will require a large amount of storage means (memory).
is required, and furthermore, the calculation takes an amount of time.

The present invention solves the above problems by specifying characteristic parts of high-order functions such as extreme values and inflection points with fine pitches, and specifying other relatively featureless linear parts with coarse pitches. To provide a graphic processing device capable of accurately tracing a graph of a higher-order function with a smaller number of passing points as a whole, using less memory, and specifying by pitch.

[Means for Solving the Problems] In order to achieve the above object, the present invention provides an input means for inputting a higher-order function to be drawn, and an input means for inputting an extremum, an inflection point, and a drawing start of the input higher-order function. a calculation means for calculating at least one feature point such as a point and a drawing end point, a storage means for storing the calculation result, a designation means for designating a passing point of a higher-order function, and each of the designated higher-order functions. A graphic input device comprising interpolation means for interpolating between passing points, temporary storage means for storing designated passing points, and determining whether the temporarily stored passing points are in the predetermined vicinity of each feature point. and a pitch determining means that specifies a predetermined fine pitch when the determination result is near a predetermined value of each feature point, and a predetermined coarse pitch in other cases, and determines the pitch. The specifying means specifies the pitch point determined by the means as the next passing point.

[Operation] According to the above configuration, when a high-order function to be drawn is input, feature points such as the extreme value, inflection point, drawing start point, and drawing end point of the input high-order function are calculated, Determine whether the specified passing point is in the predetermined vicinity of each feature point,
If the determination result is near a predetermined value for each feature point, a predetermined fine pitch is specified, and in other cases, a predetermined coarse pitch is specified. Then, the determined pitch point is designated as the next passing point, and when each passing point is designated, these points are interpolated to draw the input higher-order function.

[Example] Hereinafter, an example of the present invention will be described with reference to the drawings.

FIG. 1 shows the circuit configuration of a graphic processing device. This device is a central processing unit (central processing unit) that executes calculations and other processes for drawing figures.
CPU) 1, random access memory (RAM > 2 as a temporary storage means for storing data to be processed), and read-only memory (ROM) that stores the processing procedure.
3, a display device 4 as input/output means, and a keyboard 5 as input means. Inside the RAM 2, there are provided a program area 2a for storing processing programs, a work area 2b for processing data, and a designated buffer 2C for storing data to be processed. And C
Together with the ROM 3 and the RAM 2, the PUI constitutes the above-described calculation means, specification means, interpolation means, determination means, and pitch determination means.

FIG. 2 is a flowchart showing the procedure for drawing a higher order function using the above device.

The user selects the higher-order function to draw, and then
Each coefficient of the higher-order function f (x) is input as data using the keyboard 5 (step 1, hereinafter referred to as Sl). When the data is input, the CPUI calculates the coordinates (drawing start point and drawing end point) of the intersection of the input higher-order function f (x) and the display frame of the display device 4 (32), and Starting point (xi, yl), drawing end point (x2.y2
), initial setting of each variable is performed (S3). That is, the drawing start point (xi, yl), the drawing end point (X2,
The width of one section is determined by dividing the difference in the X-axis direction of the coordinates of y2) (<x2-xi) by an appropriate constant (an integer of about 10, experimental value). Also, the width of one section obtained is set as a coarse pitch p1,
The fine pitch p2 is determined by dividing the width of one section by a constant of about 5 (experimental value).

Next, the CPU differentiates the input higher-order function f (x) to obtain the derivative f' (x), and then calculates f' (X) -
Calculate the extremum by solving the equation marked with 〇, and then calculate the second derivative f′ (x) by dividing the higher-order function f (x) into two equal machines, and obtain f″ (X)−〇 The inflection point is calculated by solving a large equation (34.85).

After completing the above processing, the CPUI next specifies a passing point between the drawing start point (xi, yl) and the drawing end point (x2y2). At this time, one section from the drawing start point, one section before the drawing end point, one section before and after the extreme value, and one section before and after the inflection point are defined as characteristic parts.

First, the coordinates of the drawing start point are stored in the designated buffer 2c of RAM2.
is stored as the coordinates of the passing point, and below, each time the pitch is determined,
Sequentially store the coordinates of the designated passing points (S6, S7
). The CPU checks whether the specified passing point is a characteristic part of the curve (S8), and if the specified point is a characteristic part, the pitch in the X-axis direction to the next passing point is set to a fine pitch. If the pitch is not a characteristic part, a rough pitch p1 is adopted (S9).

The X coordinate of the next specified point is the value obtained by adding the adopted pitch to the X coordinate of the last specified passing point, and the Y coordinate of the next specified point is the value of the X coordinate of the next specified point. The next function f (
It is calculated by substituting it into the equation of x) (S i 1 ).

In this way, until the X coordinate of the next passing point or the drawing end point is reached (YES in S12), the process returns to step 7, specifies the passing point, and repeats the above operation. Then, when the X coordinate of the next passing point or the drawing end point is passed, the drawing end point is stored in the designated buffer 2c as the last passing point (813).
.

Next, interpolation is performed between each passing point stored in the designated buffer 2c (514), and CP is calculated from the data of each passing point and the interpolation point.
The UI displays the high-order function f(x) on the display device 451.
5) End the operation.

Taking the above procedure as an example of a cubic function, as shown in Figure 3, the pitch is fine at the extreme value, and the other points are taken as passing points with a coarse pitch, and the number of data stored in the specified buffer 2c. Based on the adopted pitch, a desired cubic function can be drawn as shown in FIG. 4.

Next, a method of omitting passing points in a straight line portion of a high-order function will be explained using FIG. 5.

This method checks whether three consecutive points are on the same straight line, and if they are on the same straight line, the point that is meaningless to specify is deleted by deleting the middle point. . If it is also used when drawing the cubic function mentioned above,
Furthermore, the number of passing points stored in the designated buffer 2c can be reduced.

First, it is checked whether point B exists on straight line AC.

Then, if point B exists, the coordinates of point C are (x2.y
In 2), substitute the coordinates of the point into (x3.V3) and delete point B. Next, check whether point C is on the shoulder of the straight line. On the other hand, if point B does not exist in the above, the coordinates of point A are stored in the designated buffer 2c as designated points, and the coordinates of point B are set to (xi, yl) and the coordinates of point C are set to (X2.y2). , substitute the coordinates of the point into (x3.y3), and then draw the straight line B
Check whether point C is on D. In this way,
By going through all the points, we can remove the points that are collinear, so the specified buffer 2
It is possible to reduce the number of data stored in c.

Further, the case of drawing a fractional function will be explained using FIG. 6. Generally, after spline interpolation, a high-order function is drawn such that each interpolation point is connected by a straight line and connected by a broken line. Fractional functions are also drawn using broken lines, and the interval between each specified point on the broken line is determined by the curvature of the curve at each specified point. is set small. Therefore, by setting each designated point according to the size of this radius of curvature, the number of data stored in the designated buffer 2c can be reduced.

The specified point -a on y-+c (Tap, b key 0) is the next specified point (Xn+1+n'
To find n yn +-1), first, the absolute value n of the slope at the point < x, y)
Find n y′.

n When the slope is y′　　〉1, take the reciprocal.

n Here, the point with the smallest radius of curvature is the straight line y=x+
It is near the intersection with (a-c), and at this time y′
becomes 1. On the other hand, the largest radius of curvature n is near the start or end point of the graph, and y at this time has an n value near 0. Therefore, the interval X between designated points can be obtained using the following formula.

X5tep=l'Og <y'/α)1+β(ta
(where α and β are constants to set the interval to appropriate values) xn+1-X 10 Where the radius is large, the pitch becomes coarse, and where the radius of curvature is small, the pitch becomes fine.

In the manner described above, it is possible to draw a higher-order function by reducing the number of data stored in the designated buffer 2C.

Also, if we focus on the slope of the curve and assume that the pitch between passing points is proportional to the slope of the tangent passing through the passing points, we can create a spline by setting an appropriate proportionality constant and connecting each designated point with a broken line. It is possible to draw without necessarily using interpolation means.

[Effects of the Invention] As described above, according to the present invention, when specifying passing points of a high-order function, characteristic parts of the high-order function such as extreme values and inflection points are specified at fine pitches, Since high-order functions are drawn by specifying other relatively featureless linear parts at a coarse pitch, there is no need to specify a large number of passing points as in the conventional method, and by specifying a small number of passing points, there are fewer It is possible to accurately draw graphs of higher-order functions with less memory usage and less calculation time.

[Brief explanation of drawings]

FIG. 1 is a hardware configuration diagram of an embodiment of the graphic processing apparatus of the present invention, FIG. 2 is a flowchart showing its processing procedure, and FIG.
The figure shows an example of plotting passing points using this device.
Fig. 4 shows an example of drawing a higher-order function on a display device using this device, Fig. 5 shows coordinates on a curve, and Fig. 6 shows an example of drawing a fractional function using this device. It is a figure which shows the plot of the passage point of . 1... Central processing unit ff (CPU), 2... Random access memory (RAM), 2c... Designated buffer,
3... Read only memory <ROM), 5... Keyboard.

Claims (1)

[Claims] (1) An input means for inputting a high-order function to be drawn, and a calculation means for calculating at least one characteristic point such as an extremum, an inflection point, a drawing start point, and a drawing end point of the input high-order function. and a graphic input device comprising a storage means for storing the calculation result, a specifying means for specifying passing points of the higher-order function, and an interpolating means for interpolating between each passing point of the specified higher-order function. a temporary storage means for storing the designated passing point; a determining means for determining whether the temporarily stored passing point is in the predetermined vicinity of each feature point; pitch determining means for specifying a predetermined fine pitch in some cases and a predetermined coarse pitch in other cases, and specifying the pitch point determined by the pitch determining means as the next passing point. A graphic processing device characterized by specifying means.