JPH05250479A - Curve interpolation device - Google Patents

Abstract

PURPOSE:To prevent the increase of hardware and to reduce the calculation of mid point of less step and of one step in interpolating points on the curve while repeatedly obtaining the mid point based on four control points on the three-dimensional Bezier curve. CONSTITUTION:The mid points are calculated in small mid-point generators 31-33 based on the coordinate of the control point stored in small registers 11-14. The result is saved in the registers 11-14 or in small auxiliary registers 21-24. The processing is repeated three times to obtain the halved control points. The latter half of the control point is retrieved in a stack and the first half is divided into two again. When a discrimination section detects that the both ends of the control point are converged into two points, outputted as an interpolation point. Then, the latter half of the control point is restored from the stuck to the small registers 11-14 to repeat the same processing.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a device for interpolating points on a curve from a plurality of control points.

[0002]

2. Description of the Related Art When printing with a printer in a high-performance word processor and displaying text on a display, a so-called outline font is used.
The technology of deployment is widely used. This is because the outline of a character is stored at a plurality of points (referred to as “control points”) corresponding to the contour of the character, and for a request such as printing, the stored plurality of points are basically used as a space between them. The requested character is expressed by supplementing and displaying a line (which is also called "interpolation" in this specification because it is usually called "interpolation"), and then the printing or light on a CRT is followed according to this expression. It forms the locus of points.

In this case, the line interpolation is usually 3
Next, depending on the case, 2nd or 4th, and rarely 5th or higher
Bezier curves are used. The cubic Bezier curve is a curve represented by a cubic function of the parameter t (0 ≦ t ≦ 1),
It is defined by the following equation using four control points, and in this case, a plurality of points stored corresponding to each character, coordinates of A, B, C, and D.

P = A (1-t) ³ + 3Bt (1-t) ² + 3Ct ² (1-t) + Dt ³ (Equation 1) Here, the control point A is the starting point of the curve (t = 0. ) And D are the end points (t = 1) of the curve. The quadratic Bezier curve is P = A (1-
t) ² + 2Bt (1-t) + Ct ^2, which is defined according to this form even in the case of the fourth or higher order. In addition, because the information about the interpolation to the printing means is output, A is usually called the start point and D is the end point. When the curve is divided into two, the one closer to the start point A is closer to the front half and the end point D. It is said that the latter half is
This also applies to this specification. When the curve is divided into two at t = 0.5, the newly created control points A ₁ , B ₁ , C ₁ , D ₁ and the latter half of the curve of the first half (0 ≦ t ≦ 0.5) The newly created control points A ₂ , B ₂ , C ₂ and D ₂ of the curve of (0.5 ≦ t ≦ 1) are different from the original control points as shown in (Equation 2) to (Equation 8). It can be easily obtained by repeatedly calculating the midpoint.

A ₁ = A (Equation 2) B ₁ = (A + B) / 2 (Equation 3) C ₁ = (A + 2B + C) / 4 = {(A + B) / 2 + ( B + C) / 2} / 2 = {B ₁ + (B + C) / 2} / 2 (Equation 4) D ₁ = A ₂ = (A + 3B + 3C + D) / 8 = (C ₁ + B ₂ ) / 2 (Equation 5) B ₂ = (B + 2C + D) / 4 = {(B + C) / 2 + (C + D) / 2} / 2 = {(B + C) / 2 + C ₂ } / 2 (Equation 6) C ₂ = (C + D) / 2 (Equation 7) D ₂ = D (Equation 8) Further, by repeating this operation, A _i , B _i ,
C _i and D _i are as close as possible to a curve aiming at interpolation.

The conventional curve interpolating apparatus utilizes this property to decompose a curve into two parts one after another, and the starting point A _i and the end point D _{i of} the decomposed curve are the minimum display capability of the printing means or the display means. The method is to output two adjacent points defined by the above or when they converge within a predetermined section, as the interpolation points on the curve. Here, the starting point A _i and the ending point D
_{When i} and _i are adjacent to each other, the intermediate points B _i and C _i are also adjacent to each other, and the application such as printing is limited. Therefore, inconvenience does not occur in practice. The presence or absence of adjacency is not normally judged. Moreover, these are the same in the embodiments described later.

As a conventional Bezier curve interpolator, for example, "A High Speed Outline Font Rasterizing LSI" (P
roceedings of the IEEE Custom Integrated Circuits
Conference 1989). Figure 10
Shows the configuration thereof as an example of the Bezier curve interpolation device according to the prior art. In the figure, 1 is an X register that stores the X coordinates of four control points, 2 is a Y register that stores the Y coordinates of four control points, 3 is a selector that selects X register 1 and Y register 2, and 4 is A two-division circuit that divides the control point of the curve into two by calculating the midpoint of the X coordinate or the Y coordinate.
A stack stored by the (First In Last Out) method, and 6 is a determination unit that inputs the coordinates of the start point and the end point of the curve among the coordinates output by the selector 3 and determines whether or not they are adjacent.
Here, the two-divided circuit 4 is composed of six midpoint generators as shown in FIG.

In this figure, these devices are integrated to control the curve interpolation calculation and saving, transfer, output, etc. of the calculation results in the middle necessary for this, and a master which also has a clock signal generator built-in. A computer (host computer) and an input / output device are not shown because they are complicated. In the conventional curve interpolation device configured as described above,
First, X of four control points (A, B, C, D) of Bezier curve
Coordinates and Y coordinates are X register 1 and Y register 2, respectively.
Is set to. At this time, the minimum display interval (corresponding to the resolution in the photograph) of the printing means or the display means is usually adopted as 1 as the basic unit of the X coordinate and the Y coordinate.

This also applies to the embodiments described later. The selector 3 first selects the X register 1, and the 2-division circuit 4 divides the contents of the X register 1 into two sets of control points (A ₁ , B ₁ , C ₁ , D ₁ ) and (A ₂ , B).
₂ , X ₂ coordinates of C ₂ , D ₂ ) are obtained. The coordinates of the control points (A ₁ , B ₁ , C ₁ , D ₁ ) of the _first half of them are returned to the X register 1, and the control points of the latter half (A ₂ , B ₂ , C ₂ , D ₁ ) are returned.
The coordinates of ₂ ) are saved in the stack 5. In the following, including the examples of the present invention, the above A ₁ , B ₁ , A ₂ ,
The control points calculated during the interpolation calculation of B ₂ , A _i , B _i, etc. will be called “control points for interpolation” in principle. Next, the selector 3 selects the Y register 2 and executes the same processing for the Y coordinate.

The decision unit 6 decides whether or not to continue the division into two and outputs the interpolation points on the curve. The determination is whether or not the control points for interpolation (A _i , B _i , C _i , D _i ) have converged to two points where the curve start point (A _i ) and end point (D _i ) are adjacent to each other, that is, interpolation. X coordinate A of control points A _i , D _i for
The difference between the integer parts of x _i and Dx _i and the Y coordinates Ay _i and Dy _i
See if the difference between the integer parts of is less than or equal to 1. If 2
If the points are adjacent to each other, the amount of change in the X coordinate and the Y coordinate from the start point (A _i ) to the end point (D _i ) is not significant even if the division is further divided into two because it is meaningless in terms of printing ability. It is output as the final or regular information about the interpolation point on the curve. In the present specification, the interpolation point where the start point and the end point are adjacent to each other is, in principle, referred to as a “normal interpolation point”.

Here, four control points A of the Bezier curve,
The initial values of B, C and D are A₀, B₀, C ₀, D₀And this
After the control point is divided into two, the control points for the two sets of interpolation are A
₁, B ₁, C₁, D₁And A₂, B₂, C₂, D₂And before
Control point A for half interpolation₁, B₁, C₁, D₁2
The control point for the two sets of interpolation after division is A₁₁, B₁₁,
C₁₁, D₁₁And A₁₂, B₁₂, C₁₂, D₁₂Then, interpolation for the second half
Control point A for₂, B ₂, C₂, D₂After splitting into two
The control points for the two sets of_{twenty one}, B_{twenty one}, C_{twenty one}, D_{twenty one}
And A_{twenty two}, B_{twenty two}, C_{twenty two}, D_{twenty two}And A₁₁And D₁₁(=
A₁₂) And D₁₂(= A_{twenty one}) And D_{twenty one}(= A_{twenty two}) And D_{twenty two}Adjacent to
Consider the case where it converges to the point. The position of these control points
The relationship is illustrated in FIG.

In this case, the coordinates of the points stored in the X register 1 and the Y register 2 for each operation step of the Bezier curve interpolating device, the register selected by the selector 3, and the control after the division output by the division circuit 4. FIG. 13 shows the coordinates of the points, the interpolation points (start point and end point) on the curve output by the determination unit 6, and the contents of the stack 5. However, in FIG. 13, Xi is the X coordinate of the control points A _i , B _i , C _i , D _i for interpolation,
Similarly to Y _i , control points A _i , B _i , C _i for interpolation,
It represents the set of Y coordinates of D _i , where X ₀ and Y ₀ correspond to the initial values A ₀ , B ₀ , C ₀ , D ₀ of the control points.

In step 1, X ₀ , Y is stored in the X register 1.
Y ₀ is set in the register 2, the selector 3 selects the X register 1, and the two-division circuit 4 sets X ₁ as the coordinate of the control point for the interpolation of the _first half and the coordinate of the control point for the interpolation of the second half. To output X ₂ . In step 2, X ₁ is set in the X register 1 and X ₂ is saved in the stack 5. Then, the selector 3 selects the Y register 2, and the two-division circuit 4 sets Y as the coordinate of the control point for the interpolation of the first half.
₁ , Y ₂ is output as the coordinate of the control point for interpolation of the second half.

Similarly, in step 3, X in the X register 1
₁ division, in step 4, division of Y ₂ in the Y register 2 is executed. In step 5, X ₁₁ in the X register 1 is divided, but in step 6, the determination unit 6 determines the control points A ₁₁ and D.
_Since it is determined that ₁₁ are adjacent and the interpolation point is output, the division result of step 5 is not saved in the stack 5. Also,
Since the division into two is completed in step 6, Y ₁₂ is returned from stack 5 to Y register 2 in step 7, and X ₁₂ is returned from stack 5 to X register 1 in step 8,
It is a new target of division and determination.

In the same manner as described above, in step 17, the judgment unit 6
Determines the end of the two divisions, outputs a normal interpolation point, and the division and the determination are repeated until there are no control points for interpolation stored in the stack 5. In this way, the conventional Bezier curve interpolating device can perform 17 steps in FIG.
The interpolation process shown in 2 is ended. However, depending on the initial value of the control point and the required coarseness (accuracy) of the interpolation point,
Furthermore, the number of steps increases. In addition, second-order, fourth-order, etc.
The Bezier curve interpolation has the same basic calculation method for the interpolation points.

[0016]

However, in the above-mentioned configuration, as shown in FIG. 11, the two-divided circuit connects three-stage midpoint generators in series, and the three-stage midpoint calculation is performed in one step. Need to run. Therefore, the frequency of the clock supplied to the Bezier curve interpolation device cannot be increased.

Further, since the X-coordinate and the Y-coordinate are alternately processed in another step, the judgment unit holds the judgment result of the X-coordinate completed one step before, and stores the judgment result of the Y-coordinate in the next step. It is necessary to determine whether or not it has really converged within a predetermined section, that is, the end of the two divisions together with the determination result, and the determination process becomes complicated. In view of the above problems, the present invention has been made for the purpose of providing an apparatus for interpolating a Bezier curve with a small number of steps without increasing the amount of hardware.

[0018]

In order to achieve the above object, in the invention of claim 1, an X register for storing a plurality of X coordinates given in order before and after, and stored in the X register. X midpoint generator for calculating midpoint coordinates between adjacent X coordinates, and an X auxiliary register for holding X coordinates stored in the X register or midpoint coordinates output by the X midpoint generator And X to the X auxiliary register
When the X coordinate of the control point for the new interpolation of the first half of the curve newly output by the midpoint generator is input, the control point for the interpolation held until now or the newly output curve The X stack for storing the X coordinates of the control points for the latter half of the interpolation is stored and stored, the Y register for storing a plurality of Y coordinates given in order before and after, and the Y register for storing the Y coordinates. Y midpoint generator for calculating midpoint coordinates between adjacent Y coordinates and a Y auxiliary register for holding the Y coordinate stored in the Y register or the midpoint coordinate output by the Y midpoint generator When the Y coordinate of the control point for the new interpolation of the second half of the curve newly output by the Y midpoint generator is input to the Y auxiliary register, the point previously held or the new output is output. The second half of the curve Of the Y coordinate of the control point for interpolating the Y coordinate stored therein, the difference between the X coordinate of the start point and the end point of the two-divided curve stored in the X register, and the 2 stored in the Y register. A determination unit that determines whether the start point and the end point are adjacent to each other depending on whether the difference between the Y coordinates of the start point and the end point of the divided curve is within a predetermined value, and the coordinate of the control point for interpolating the curve is the X-axis. When given to the register and the Y register, the X midpoint generator and the Y midpoint generator are made to repeatedly calculate the midpoint, and the calculation result is given to the X register, the X auxiliary register, and the Y register. An interpolation control point calculating means for obtaining a control point for interpolating the curve of the first half and a control point for interpolating the curve of the second half by holding the register and the Y auxiliary register, and the interpolation calculated by the interpolation control point calculating means. Nota Control points for the second half of the control points are saved in the X stack and the Y stack, and the control points in the first half are stored in the X register and the Y register for repeated division, and then the X register is stored. And the determination unit determines that the two points, which are the start point and the end point of the curve, of the first half control points stored in the Y register are adjacent to each other. Evacuation / recovery control means for outputting to the X register and the Y register the control points for the latter half of the interpolation, which are output as the interpolation points and saved in the X stack and the Y stack, are provided. And Bezier curve interpolator.

In a second aspect of the present invention, when h is a natural number of 2 or more and j is a natural number of 1 or more and h or less, the X register is composed of the first to (h + 1) th X small registers, and The j-th small-middle-point generator is the j-th small-middle-point generator, and is composed of first to h-th small-middle-point generators for calculating the middle point of the j-th small register and the (j + 1) X small register. The X auxiliary register includes first to hth X small auxiliary registers, and the Y register includes the first to (h) th auxiliary registers.
+1) Y small registers, the middle point generator is the j-th small middle point generator, and the first to the first to calculate the middle point of the jth Y small register and the (j + 1) Y small register. h
Up to Y-th small auxiliary point register, the Y auxiliary register is formed of first to h-th Y small auxiliary registers, and the determination unit is the first X small register and the (h +
1) It is configured to determine whether the difference between the X coordinate values stored in the X small register and the difference between the Y coordinate values stored in the first Y small register and the (h + 1) Y small register is within a predetermined value. The Bezier curve interpolating apparatus according to claim 1, wherein the Bethier curve interpolating apparatus calculates the h-th degree Bezier curve.

In the invention of claim 3, at least one of the hX register and the first X auxiliary register or the hY register and the first Y auxiliary register is the same 1
3. The small register is also used as one small register.
The described Bezier curve interpolation device is used. In the invention of claim 4, the X register for storing a plurality of X coordinates given in order before and after, the X auxiliary register for storing a plurality of X coordinates, and the X register or the X auxiliary register are stored. X to calculate the midpoint coordinate between adjacent X coordinates
When the midpoint generator and the X coordinate of the control point for interpolation of the first half of the curve newly output by the X midpoint generator are input to the X auxiliary register, the control point that has been held so far Alternatively, an X stack that stores the coordinates of control points for interpolation of the second half of the newly output curve, a Y register that stores a plurality of Y coordinates given in order before and after, and a plurality of Y coordinates And a Y midpoint generator for calculating the midpoint coordinates between the Y registers stored in the Y register or the Y auxiliary register, and a Y midpoint generator for the Y auxiliary register. When the Y coordinate of the control point for interpolation of the first half of the newly output curve is input, the control point that has been held so far or the control point for interpolation of the second half of the newly output curve is input. Memorize the coordinates of Wherein a tack, the difference between the start and end points X coordinate of the two divided curves stored in the X register Y
Y of the start point and end point of the curve divided into two stored in the register
A determination unit that determines whether the start point and the end point are adjacent to each other depending on whether the difference between the coordinates is within a predetermined value, and the coordinates of the control point for interpolating the curve are given to the X register and the Y register. To cause the X midpoint generator and the Y midpoint generator to repeatedly calculate the midpoint, and to calculate the calculation result by the X midpoint generator.
Interpolation control point calculation means for holding a register and the X auxiliary register, and a Y register and the Y auxiliary register to obtain a control point for interpolating the first half curve and a control point for interpolating the second half curve And the above X
If the determination section indicates that the two points indicating the start point and the end point of the control points for interpolation of the first half curve stored in the register and the Y register are adjacent to each other, the two points on the curve are normalized. Control points for interpolation of the latter half curve stored in the X auxiliary register and the Y auxiliary register and transferred to the X register and the Y register, and the start point of the curve in the first half. When the determination unit does not indicate that two points indicating the end point and the end point are adjacent to each other, the control point for interpolating the second half curve stored in the X auxiliary register and the Y auxiliary register is set to the X point.
A transfer save / hold means for saving in the stack and the Y stack and holding in the X register and the Y register the control point for interpolating the first half curve repeatedly in two, and the X auxiliary register or the X register. Of the control points for interpolation of the second half curve transferred from the stack and the Y auxiliary register or the Y stack to the X register and the Y register, it is determined that two points indicating the start point and the end point of the curve are adjacent to each other. When the section indicates, the two points are output as the normal interpolation points on the curve, and the control points for interpolation of the subsequent curves saved in the X stack and the Y stack are set to the X register and the above. The Bezier curve interpolating device is characterized in that it has an evacuation return control means for returning to the Y register.

According to the fifth aspect of the invention, when h is a natural number of 2 or more, an X consisting of (h + 2) X small registers from the first X small register to the (h + 2) X small register.
Register and the 1st X small auxiliary register to (h + 2) X
X auxiliary registers consisting of (h + 2) X small auxiliary registers up to the small auxiliary registers, and the first to (h +)
2) The X-small register or the midpoint coordinate of the X-coordinate stored in two of the first to (h + 2) X small auxiliary registers is calculated to calculate the first to (h + 2) X small registers or the first to (h + 2) X small registers. An X midpoint generator consisting of h pieces of X small midpoint generators from 1 to h to be output to any one of the 1st to (h + 2) X small registers, and a first Y small register to h + 2) up to Y small register (h + 2)
Y register consisting of Y small registers and (h + 2) th Y small auxiliary register (h
+2) a Y auxiliary register consisting of Y small auxiliary registers, and a Y coordinate stored in two registers of the first to (h + 2) Y small registers or the first to (h + 2) Y small auxiliary registers. The midpoint coordinates are calculated to calculate the first
To (h + 2) Y small registers or any one of the first to (h + 2) Y small auxiliary registers to output the Y midpoint consisting of h first to hth Y small midpoint generators A generator, the first X register, and the (h +)
2) The difference between the X coordinate value stored in the X small register and the first
The i-th Be register has a Y-register and a determiner that determines whether two Y-coordinates stored in the (h + 2) th Y-small register are equal to or less than a predetermined value so as to determine the adjacency of two corresponding points.
The Bezier curve interpolating device according to claim 4, wherein interpolation calculation of a zier curve is performed.

In the invention of claim 6, the (h +) th
2) At least one of the X small register and the first X small auxiliary register or the (h + 2) Y small register and the first Y small auxiliary register is shared by the same small register. The described Bezier curve interpolation device is used.

[0023]

With the above construction, in the invention of claim 1, X
The midpoint coordinates of the X coordinates of the points adjacent to the four control points input in order in the register are calculated by the X midpoint generator.
Thereafter, among the midpoint coordinates calculated by the X midpoint generator by the instruction of the interpolation control point calculation means and the coordinates stored in the X register, those relating to the control point for the interpolation of the curve of the first half are the X register. The control points for interpolation of the second half curve are transferred to the X auxiliary register. When this process is repeated for three steps, control points for interpolation of the first half of the divided curve are set in the X register, and control points for interpolation of the second half are set in the X auxiliary register.

By performing the same processing for the Y coordinate of the control point, two sets of control points divided at the same time as the X coordinate can be obtained. Thereafter, under the control of the save / restore control means, the coordinates of the control points for the interpolation of the second half curve stored in the X auxiliary register and the Y auxiliary register are saved in the X stack and the Y stack, and the determination unit Of the coordinates of the control points for interpolation of the first half curve stored in the X register and the Y register, both points are determined by whether the difference between the X coordinate and the Y coordinate of the start point and the end point of the curve is within a predetermined value. Is converged to two adjacent points.

If the two adjacent points are not converged, the contents of the X register and the Y register are subject to the next two divisions. When converged to two adjacent points, the information of these two points is output as information on the regular interpolation point, and the coordinates stored in the X stack and the Y stack and stored are stored in the X register and the Y register. Then, it becomes the target of the next two divisions.

When the above-mentioned processing is repeated and the judging section finishes the judgment of the control point division into two and outputs the information of the regular interpolation points, and there are no coordinates to be restored in the X stack and the Y stack. , Bezier curve interpolation processing ends. In the invention of claim 2, in the X midpoint generator, the jX small midpoint generator calculates the midpoint of the X coordinate stored in the jth small register and the (j + 1) X small register. Further, in the Y midpoint generator, the jY small midpoint generator calculates the midpoint of the Y coordinate stored in the jY small register and the (j + 1) Y small register, and the judging section further determines the first X. The difference between the X-coordinates stored in the small register and the (h + 1) th small register and the first Y small register and the (h) th register.
+1) It is determined that the difference between the Y coordinates stored in the Y small register is less than or equal to a predetermined value.

In the invention of claim 3, at least one of the hX small auxiliary register and the first X small auxiliary register or the hY small auxiliary register and the first Y small auxiliary register is used in common. In the invention of claim 4, the midpoint coordinates of the X coordinates of the points adjacent to the control points input in order to the X register are calculated by the X midpoint generator. After that, among the midpoint coordinates calculated by the X midpoint generator by the interpolation control point calculation means and the coordinates stored in the X register, those relating to the control point for the interpolation of the curve of the first half are set in the X register. The control points for interpolation of the second half curve are transferred to the X auxiliary register. When this process is repeated three steps, control points for interpolation of the first half of the divided curve are set in the X register, and control points for interpolation of the second half of the curve are set in the X auxiliary register.

With respect to the Y-coordinate of the control point, the same processing is executed on the two sets divided at the same time as the X-coordinate to obtain the control point for the curve interpolation. After that, under the control of the save / restore control means, the coordinates of the control points for the interpolation of the second half curve stored in the X auxiliary register and the Y auxiliary register are saved in the X stack and the Y stack. Of the coordinates of the control points for the interpolation of the first half curve stored in the Y register, the coordinates of the start point and the end point of the curve are determined by the determination unit whether or not they have converged to two adjacent points.

If the two adjacent points are not converged, the contents of the X register and the Y register are subject to the next two divisions. When converged to two adjacent points, the information of these two points is output as information on the regular interpolation point, and the coordinates stored in the X stack and the Y stack and stored are stored in the X register and the Y register. Then, it becomes the target of the next two divisions.

In addition, the determination unit determines that the transfer saving and holding means has two control points for interpolation of the first half curve stored in the X register and the Y register, which are adjacent to each other, which indicate a start point and an end point. In the case shown, the two points are output as the normal interpolation points on the curve, and the control points for the latter half of the interpolation stored in the X auxiliary register and the Y auxiliary register are output to the X register and the Y register. If the determination unit does not indicate that the two points indicating the start point and the end point of the first half curve are adjacent to each other, the second half curve for interpolation is stored in the X auxiliary register and the Y auxiliary register. The control points are saved in the X stack and the Y stack, and the control points for interpolating the curve of the first half are repeatedly divided into two, so that the X register and the Y register are repeatedly divided. To be held in the register.

Further, the save / restore control means includes the X auxiliary register or the X stack and the Y auxiliary register or the Y stack to the X register and the Y stack.
Of the control points transferred to the register, if two points indicating the start point and the end point of the curve are adjacent to each other, the two points are output as regular interpolation points on the curve and the X stack and the above The control points for interpolation saved in the Y stack are returned to the X register and the Y register.

By repeating the above processing, when the determination unit finishes the determination of the control point division into two, outputs the information of the regular interpolation point, and there is no coordinate to be returned to the X stack and the Y stack. Then, the Bezier curve interpolation processing ends. In a fifth aspect of the present invention, when j is a natural number of 1 or more and h or less, the jth X small midpoint generator is the first to the (h + 2) X small register or the first to the (h).
+2) The midpoint coordinate of the X coordinate stored in two registers of the X small auxiliary registers is calculated, and the first to (h +) th coordinates are calculated.
2) Output to the X small register or any one of the first to (h + 2) X small auxiliary registers.

The jYth small-midpoint generator is arranged from the first to the (h)
+2) Y small register or the first to (h + 2) Y
The midpoint coordinate of the Y coordinate stored in two of the small auxiliary registers is calculated to be one of the first to (h + 2) Y small registers or the first to (h + 2) Y small auxiliary registers. Output to. Further, the determination unit is configured such that the X coordinate stored in the first X small register and the (h + 2) X small register, the first Y small register, and the (h +) th register.
2) It is determined whether the difference between the Y coordinates stored in the Y small register is less than or equal to a predetermined value.

In the sixth aspect of the invention, the above-mentioned (h +
2) At least one of the X small register and the first X small auxiliary register or the (h + 2) Y small register and the first Y small auxiliary register is shared by the same small register.

[0035]

【Example】

(First Embodiment) FIG. 1 is a block diagram of an embodiment of a curve interpolation device according to the invention of claim 1.

In the figure, 1 is an X register for storing X coordinates, 2 is an X auxiliary register for storing X coordinates, and 3 is an X register.
X for calculating the midpoint of the X coordinate stored in register 1
The midpoint generator, 4 is the X stored in the X auxiliary register 2.
X stack for saving coordinates, 5 Y register for storing Y coordinates, 6 Y auxiliary register for storing Y coordinates, 7 Y
Y for calculating the midpoint of the Y coordinate stored in register 5
Midpoint generator, 8 is Y stored in Y auxiliary register 6.
A Y stack that saves the coordinates, and 9 is a determination unit that determines the end of the two-division processing and outputs information on the regular interpolation point.

Further, FIG. 2 is a block diagram of the second embodiment.
X-register 1 dedicated to the cubic Bezier curve calculation according to the invention of
The internal configurations of the X auxiliary register 2 and the X midpoint generator 3 are shown. In the figure, 11 to 14 are X small registers for storing one X coordinate respectively, and 15 to 18 are X small selectors for selecting inputs to the X small registers 11 to 14, respectively.
21 to 24 are X small auxiliary registers for storing one X coordinate each, and 25 to 28 are X small auxiliary registers 2 respectively.
X small selectors 31 to 33 for selecting inputs to 1 to 24
Is an X small midpoint generator that inputs two X coordinates and calculates the midpoint.

However, because the figure becomes complicated, the characters "small" such as "X small register" are omitted. And
This also applies to FIG. 6 described later. Also, the internal configuration of the Y register 5, the Y auxiliary register 6, and the Y midpoint generator 7 is
The configurations of the X register 1, the X auxiliary register 2, and the X midpoint generator 3 shown in this figure are exactly the same. Therefore, in principle, only the X coordinate will be described below, and the Y coordinate will be described in parentheses as necessary. It should be noted that these devices are integrated to control Bezier curve interpolation calculation and saving, transfer, output, etc. of intermediate calculation results necessary for this, and by extension, interpolation control point calculating means and save / restore control described in the claims. The circuit configuration that plays the role of the means, the master computer (host computer) that controls the entire interpolation calculation after generating the necessary clock signal, etc. are complicated because the figure is complicated as with the small letters. Bezier on technology
Like the block diagram of the curve interpolation device, it is not shown. Also, this operating principle, programming method, etc. are not limited to the current Bezier curve interpolating device, but are widely known techniques widely used in computer systems, and are also the main part of the present invention or the part directly connected to the creation. Therefore, the explanation is omitted in principle.

Bezier of the present embodiment configured as described above
The curve interpolator has four modes S, T, and
It has U, V, that is, an operating state, and the processing is started from the mode S, and the interpolation processing is performed while changing the four states at each step. It should be noted that the operation of the selector and the like is different in each mode, and in mode S, a new coordinate is added from the X stack 4 to the X coordinate.
It is the mode to return to the register 1, and the modes T, U, V
Is a mode for instructing the operation of three steps necessary for dividing the curve into two and obtaining control points for interpolating the first half and the second half of the curve. The determination unit 9 in mode S and mode T
The difference in the integer part of the X coordinate stored in the X small register 11 and the register X small 14 is 1 or less as described in the prior art (and the difference in the integer part of the Y coordinate is the same as described in the prior art. If the X coordinate (and naturally also the Y coordinate) is 1 or less, the X coordinate itself from the small register 11 (curve start point) to the small register 14 (curve end point) is determined. Or the amount of change (and Y
Output the information of the regular interpolation points on the curve.

The detailed operation in each mode will be described below.
The third-order example shown in FIG.
The Bezier curve interpolation control point will be described with reference to FIG. This
In the case of, each X small which is the X register 1 at each operation step
Registers 11 to 14 and X auxiliary registers 2 each X small
The X coordinate stored in the auxiliary registers 21 to 24 is shown in FIG.
And the seat of the midpoint output by each X small midpoint generator 31-33.
The standard interpolation points (starting point and
And the end point), and the contents of the X stack 4 are shown in FIG. However
Then, in FIGS. 3 and 4, Ax_i, Bx_i, Cx_i,
Dx_iAre control points A_i, B_i, C_i, D_iX seat
Represents the mark, X_iIs control point A_i, B _i, C_i, D_iX
Represents a set of coordinates. Also, Ax₀, Bx₀, Cx₀,
Dx ₀Is the X value of the initial value of control points A, B, C, D respectively
It shall represent the mark.

In the curve interpolating apparatus according to the present embodiment, the host computer (ultimately, operator's operation) preliminarily sets the X coordinates Ax ₀ , Bx ₀ , Cx ₀ of the initial values of the control points A, B, C, D. , Dx ₀ are stored in the X stack 4, and then the curve interpolation processing is started from the mode S. (As mentioned above, Y register 5, Y
The operation of the auxiliary register 6, the Y midpoint generator 7, and the Y stack 8 and the storage of the Y coordinates of the initial values of A, B, C, and D are basically X register 1, X auxiliary register 2, and X midpoint generation. Bowl 3,
The operation and the like of the X stack 4 are the same. ) Step 1 is the first step, and the state of this curve interpolator is mode S
Is. In mode S, X-coordinate Ax ₀ from X-stack 4
Bx ₀ , Cx ₀ and Dx ₀ are read out. The X small selectors 15 to 18 select the X stack, and the X small registers 11 to 11 are selected.
Ax ₀ , Bx ₀ , Cx ₀ , Dx ₀ are stored in 14. At this stage, the X small selectors 25 to 28 do not select anything, and no value is stored in the X small auxiliary registers 21 to 24. The X small and medium point generator 31 is the middle point of the X small register 11 and the X small register 12, and the X small and medium point generator 32 is the middle point of the X small register 12 and the X small register 13. 33
Calculates the midpoint of X small register 13 and X small register 14. The determination unit 9 determines the X coordinate Ax stored in the X small register 11.
_It is determined whether _{0 and} the X coordinate Dx ₀ stored in the X small register 14 are adjacent to each other. At this stage, since Ax ₀ and Dx ₀ are not adjacent to each other, nothing is output. If the determination unit 9 outputs nothing in the mode S, the mode transitions to the mode U in the next step. If the determination unit 9 outputs a regular interpolation point on the curve, the mode S is continuously set.

Step 2 is mode U. In mode U, since the X small selector 15 selects the X small register 11, the contents of the X small register 11 do not change. The X small selectors 16 to 18 respectively select the X small midpoint generators 31 to 33, and the X small registers 12 to 14 store the results of the midpoint calculation in step 1. The X small selectors 25 to 27 do not select anything, and the values are not stored in the X small auxiliary registers 21 to 23. However, since the X small selector 28 selects the X small register 14, the X small auxiliary register 24 is stepped. X at 1
The content Dx ₂ (= Dx ₀ ) of the small register 14 is stored. Regardless of the mode, the X small and midpoint generator 31 is always X
The midpoint of the small register 11 and the X small register 12, the X small midpoint generator 32 is the midpoint of the X small register 12 and the X small register 13, and the X small midpoint generator 33 is the X small register 13 and the X small register. Although the midpoint of the register 14 is calculated, the calculation result of the X small midpoint generator 31 is not used anywhere and is omitted in FIG. Then, the mode U surely transits to the mode V.

Step 3 is mode V. In mode V, the X small selector 15 selects the X small register 11 and the X small selector 16 selects the X small register 12, so that the contents of the X small registers 11 and 12 do not change. X small selector 1
7 and 18 respectively select the X small midpoint generators 32 and 33, and the results of the midpoint calculation in step 2 are stored in the X small registers 13 and 14. The X small selectors 25 and 26 do not select anything, and no value is stored in the X small auxiliary registers 21 and 22. However, since the X small selector 27 selects the X small register 14, the X small auxiliary register 23 is stepped. X at 2
The content Cx ₂ of the small register 14 is stored. The small X selector 28 selects the small X auxiliary register 24, and the content of the small X auxiliary register 24 does not change. X small and medium point generator 33 is X
Although the midpoint of the small register 13 and the X small register 14 is calculated, the calculation results of the X small and midpoint generators 31 and 32 are not used anywhere and are therefore omitted in FIG. When the processing of mode V is executed, one division of the curve is completed, and in the next step, control points for interpolating the first half curve are set in the X small registers 11 to 14, and the X small auxiliary registers 21 to In 24, a control point for interpolation of the latter half curve is set. The control point for interpolation of the latter half curve is the X small auxiliary register 21.
At the same time as being set to .about.24, it is saved in the X stack 4. Mode V always transits to mode T.

Step 4 is mode T. In mode T
X small selectors 15 to 17 are respectively X small registers 1
Contents of X small registers 11 to 13 to select 1 to 13
Does not change. The X small selector 18 is an X small midpoint generator 33.
Is selected, and the midpoint meter in step 3 is set in the X small register 14.
The result of the calculation is stored. X small selector 25 starts from X small middle point
X small auxiliary register for selecting the calculation result of the genitals 33
21 stores the result of the midpoint calculation in step 3.
Since the X small selector 26 selects the X small register 14,
The X small auxiliary register 23 has the X small register in step 3
Contents of 14 Bx ₂Is memorized. X small selector 27,2
8 selects the X small auxiliary registers 23 and 24, respectively.
Therefore, the contents of the X small auxiliary registers 23 and 24 do not change.
The X small and medium point generator 31 includes an X small register 11 and an X small register.
12 midpoint, the X small midpoint generator 32 uses the X small register 12
And X small register 13 midpoint, X small midpoint generator 33 X
The midpoint of the small register 13 and the X small register 14 is calculated.
The determination unit 9 determines the X coordinate Ax stored in the X small register 11.₁When
X coordinate Dx stored in the X small register 14₁Are adjacent
Ax is judged, but Ax₁And Dx₁Because they are not adjacent
Is not output. When the determination unit 9 outputs nothing in mode T
In the next step, the mode is changed to the mode B. if,
When the determination unit 9 outputs a regular interpolation point on the curve,
It becomes the mode S.

Thereafter, similarly, the processing is executed in the mode U in step 5 and in the mode V in step 6. 1 in step 6
Since the curve is divided into two, the control point X ₁₂ for interpolating the latter half of the curve is saved in the X stack 4 in the next step 7. Step 7 executes the processing in mode T. Then, the determination unit 9 causes the X small register 11 to store the X
It is determined whether or not the coordinate Ax ₁₁ and the X coordinate Dx ₁₁ stored in the X small register 14 are adjacent to each other (of course, at the same time, it is also determined whether or not the Y coordinate is also adjacent), the X coordinate (and the Y coordinate). Since the difference between the integer parts of the coordinates is 1 or less and the two are adjacent to each other, the determination unit 9 outputs information about the coordinates of A ₁₁ and D ₁₁ as information about the regular interpolation points on the curve. Then, since the determination unit 9 has output the information of the regular interpolation point in the mode T, the mode is changed to the mode S in the next step.

In step 8, the process is executed in mode S.
The determination unit 9 is stored in the X small register 11
X coordinate Ax₁₂And the X seat stored in the X small register 14.
Mark Dx₁₂Determine whether they are adjacent to each other (of course, at the same time, the Y seat
Also determines whether or not the marks are adjacent to each other.)
(And of course the Y coordinate too) the difference in the integer part is less than or equal to 1
Since they are adjacent to each other, the determination unit 9 relates to the regular interpolation points on the curve.
As information₁₂, D ₁₂Output information about the coordinates of
It Then, in mode A, the determination unit 9 obtains information on the regular interpolation points.
Since it has been output, the next step is the mode S.

Thereafter, the same processing is continued, and finally, in step 13, the judgment section 9 outputs information on the regular interpolation point, and when there is no data to be read from the X stack 4 in the next step (mode S), the data is read. The Bezier curve interpolation calculation process ends. In this way, the curve interpolating apparatus of this embodiment completes the interpolation of the cubic Bezier curve shown in FIG. 12 in 13 steps.

As described above, according to this embodiment, the hardware for calculating the midpoint of the control points required for Bezier curve interpolation is divided into the X coordinate and the Y coordinate, and the same processing is performed at the same time. High-speed processing can be performed without increasing the hardware required for midpoint calculation. Further, since the X coordinate and the Y coordinate are calculated at the same time, it is possible to determine whether the start point and the end point of the curve are adjacent to each other without holding the calculation result of the X coordinate for one step.

The midpoint generator used in the present embodiment for calculating the midpoint of two coordinates is an adder for calculating the sum of two coordinates represented by a binary number, and the addition result is 1 bit. It can be easily realized by shifting shifters. Next, claim 3
The technical contents of the invention will be described. In the above-described embodiment, the X small register 14 and the X small auxiliary register 21 are different small registers, but the X small auxiliary register 21 does not hold values other than the same coordinates as the X small register 14, so both are used in common. Good. Further, the X small selector 25 may be omitted since it has no input other than the X small register 14 (and this also applies to the Y side).

FIG. 5 is a block diagram of an embodiment of the Bezier curve interpolation device according to the invention of claim 4. In FIG. In this figure, 1 is an X register that stores the X coordinate, and 2 is an X register that stores the X coordinate.
Auxiliary register, 3 is an X midpoint generator that calculates the midpoint of the X coordinate stored in X register 1 or X auxiliary register 2, and 4 is an X stack that saves the X coordinate stored in X auxiliary register 2. 5 is a Y register for storing the Y coordinate,
6 is a Y auxiliary register for storing the Y coordinate, 7 is a Y midpoint generator for calculating the midpoint of the Y coordinate stored in the Y register 5 or Y auxiliary register 6, and 8 is stored in the Y auxiliary register 6. A Y stack for saving the existing Y coordinate, and 9 is a determination unit for determining the end of the two-division processing and outputting information on the regular interpolation point.

FIG. 6 corresponds to FIG. 2 in the first embodiment, and the X register 1, the X auxiliary register 2 and the X midpoint generator 3 according to the invention of claim 5 adopted in this embodiment. 2 shows the internal configuration of the. 10 to 1 in this figure
4 is an X small register that stores one X coordinate each,
15 to 19 are X small selectors for selecting inputs to the X small registers 10 to 14, 20 to 24 are X small auxiliary registers for storing one X coordinate respectively, and 25 to 29 are X small auxiliary registers 20 to respectively. X small selectors 31 to 33 for selecting the input to 24, X small and medium point generators for inputting two X coordinates to calculate the middle point, and 34 and 35 for the input to the X small and medium point generator 31. X small selector to select, 36, 37
Is an X small selector for selecting the input to the X small and medium point generator 32, and 38 and 39 are small X selectors for selecting the input to the X small and medium point generator 33. Further, as in the first embodiment, the transfer save / hold means, the host computer, etc. are not shown, and the internal configuration of the Y register 5, Y auxiliary register 6, and Y midpoint generator 7 is calculated for interpolation. Processing etc. X shown in FIG.
Since the configuration and the like of the register 1, the X auxiliary register 2, and the X midpoint generator 3 are the same, the following description will be described only for the X coordinate in principle.

The curve interpolating apparatus of this embodiment constructed as described above has five states (modes S, W, T, U and V), and the processing is started from the mode S and five states are provided for each step. Interpolation processing is performed while transitioning. The operation of the selector and the like is different in each mode. Mode S is a mode for returning new coordinates from the X stack 4 to the X register 1, mode W is a mode for copying the X coordinates stored in the X auxiliary register 2 to the X register 1, and modes T, U and V are curves. This is a mode for instructing the operation of three steps necessary for obtaining the control points for interpolating the curves in the first half and the second half by dividing into two.
In mode S, mode W, and mode V, the determination unit 9 determines that the difference between the integer parts of the X coordinates stored in the register 10 and the register 14 is 1 or less (and the difference between the integer parts of the Y coordinate is also 1 or less). It is determined whether or not there is, and if it is 1 or less, the register 10 (curve start point) to the register 14
The X coordinate itself to (the end point of the curve) or its change amount (and that of the Y coordinate) is output as information on the regular interpolation point on the curve.

The detailed operation in each mode will be described below with reference to the figure of the control points for interpolation of the cubic Bezier curve shown in FIG. In this case, each X small register 1 which is the X register 1 for each operation step
The X coordinates stored in 0 to 14 are shown in FIG. 7, the X coordinates stored in each X small auxiliary register 20 to 24, which is the X auxiliary register 2, are shown in FIG. 8, and each X small midpoint generator 31 to 33 is shown. FIG. 9 shows the coordinates of the middle point output by the X stack 4, the normal interpolation points (start point and end point) on the curve output by the determination unit 9, and the contents of the X stack 4.
Shown in. Incidentally, Ax _i, Bx _i in FIGS. 7 to 9, C
The meanings of x _i , Dx _i, etc. are the same as in the first embodiment.

In the Bezier curve interpolating apparatus in this embodiment, a host computer (ultimately an operator's operation) is used.
In advance, the midpoints (Ax ₀ + Bx ₀ ) / 2, (Bx ₀ + Cx) of the adjacent points from the X-coordinates Ax ₀ , Bx ₀ , Cx ₀ , Dx ₀ of the initial values of the control points A, B, C, D are set in advance. ₀ ) /
2, (Cx ₀ + Dx ₀ ) / 2 is calculated, and Ax ₀ ,
(Ax ₀ + Bx ₀ ) / 2, (Bx ₀ + Cx ₀ ) / 2,
(Cx ₀ + Dx ₀ ) / 2, Dx ₀ are stored in the X stack 4 (of course, the Y coordinate is also similarly calculated and the middle point is stored in the Y stack 8). Then, the curve interpolation processing is performed from the mode S. Shall start.

Step 1 is the first step, and the mode of the present curve interpolator is S. In this state, from the X stack 4, the X coordinates Ax ₀ , (Ax ₀ + Bx ₀ ) / 2, (Bx
₀ + Cx ₀ ) / 2, (Cx ₀ + Dx ₀ ) / 2, Dx ₀ are read out. The X small selectors 15 to 19 select the X stack, and the X small registers 10 to 14 respectively store Ax ₀ and (A
x ₀ + Bx ₀ ) / 2, (Bx ₀ + Cx ₀ ) / 2, (Cx
₀ + Dx ₀ ) / 2, Dx ₀ are stored. At this stage, the X small selectors 25 to 29 do not select anything, and no value is stored in the X small auxiliary registers 20 to 24. Since the X small selector 34 selects the X small register 10 and the X small selector 35 selects the X small register 11, the X small midpoint generator 31 calculates the midpoint of the X small register 10 and the X small register 11. .. Since the X small selector 36 selects the X small register 11 and the X small selector 37 selects the X small register 12, the X small midpoint generator 32 calculates the midpoint of the X small register 11 and the X small register 12. .. Since the X small selector 38 selects the X small register 12 and the X small selector 39 selects the X small register 13, the X small midpoint generator 33 calculates the midpoint of the X small register 12 and the X small register 13. .. Judgment unit 9
Determines whether the X coordinate Ax ₀ stored in the X small register 10 and the X coordinate Dx ₀ stored in the X small register 14 are adjacent to each other. At this stage, since Ax ₀ and Dx ₀ are not adjacent to each other, nothing is output. do not do. If the determination unit 9 outputs nothing in the mode S, the mode is changed to the mode U in the next step. If the determination unit 9 outputs a regular interpolation point on the curve, the mode S is continuously set.

In step 2, mode U is set. In mode U
The X small selector 15 selects the X small register 10.
Therefore, the contents of the X small register 10 do not change. X small selector
16 selects the X small midpoint generator 31, so the X small register
The result of the midpoint calculation in step 1 is stored in the controller 11.
Since the X small selector 17 selects the X small register 11,
The X small register 12 has the X small register 11 in step 1.
X coordinate Bx stored in ₁Is memorized. X small selector 1
8 selects the X small-midpoint generator 32, so the X small register
In 13, the midpoint calculation result in step 1 is stored. X
Since the small selector 19 selects the X small midpoint generator 33,
The result of the midpoint calculation in step 1 is recorded in the X small register 14.
Remembered The X small selector 27 selects the X small register 13.
Therefore, the X small auxiliary register 22 stores the X
X coordinate Cx stored in the small register 13₂Is memorized.
Since the X small selector 29 selects the X small register 14,
The X small auxiliary register 24 has the X small register in step 1.
X coordinate DX stored in 14 ₂Is memorized. X small selection
25, 26, 28 do not select anything, X small auxiliary register
Nothing is stored in 20, 21, and 23. X small selector
34 selects the X small register 12, and the X small selector 35
In order to select the X small register 13, the X small midpoint generator 31
Calculates the midpoint of X small register 12 and X small register 13
It The X small selector 36 selects the X small register 13 and X
Since the small selector 37 selects the X small register 14, X small register 37
The small / middle point generator 32 includes an X small register 13 and an X small register 1.
Calculate the midpoint of 4. X small selector 38 is an X small auxiliary cash register
Select the star 22 and select the X small selector 39 with the X small auxiliary register.
X-midpoint generator 33 is used to select
Calculate the midpoint of register 22 and X small auxiliary register 24
It Then, the mode U surely transits to the mode V.

Step 3 goes to mode V. In mode V, the X small selector 15 selects the X small register 10, so the contents of the X small register 10 do not change. Since the X small selector 16 selects the X small register 11, the contents of the X small register 11 do not change. Since the X small selector 17 selects the midpoint generator 31, the X small register 12 stores the midpoint calculation result in step 2. Since the X small selector 18 selects the X small register 13, the contents of the X small register 13 do not change. Since the X small selector 19 selects the X small midpoint generator 32, the X small register 14 stores the step 2
The midpoint calculation result of is stored. The X small selector 25 does not select anything, and nothing is particularly stored in the X small auxiliary register 20. Since the X small selector 26 selects the X small register 14, the X small auxiliary register 21 stores the X coordinate Bx ₂ stored in the X small register 14 in step 2. X
Since the small selector 27 selects the X small auxiliary register 22, the content of the X small auxiliary register 22 does not change. Since the X small selector 28 selects the X small midpoint generator 33, the midpoint calculation result in step 2 is stored in the X small auxiliary register 23. Since the X small selector 29 selects the X small auxiliary register 24, the content of the X small auxiliary register 24 does not change. The X small selector 34 selects the X small register 13 and
Since the small selector 35 selects the X small register 14, the X selector
The small / middle point generator 31 includes an X small register 13 and an X small register 1.
Calculate the midpoint of 4. The X small selector 36 selects the X small register 14, and the X small selector 37 selects the X small auxiliary register 2.
In order to select 1, the X small midpoint generator 32 calculates the midpoint of the X small register 14 and the X small auxiliary register 21. Since the X small selector 38 selects the X small auxiliary register 21 and the X small selector 39 selects the X small auxiliary register 22, the X small midpoint generator 33 selects the X small auxiliary register 21 and the X small auxiliary register 22. Calculate the points. The determination unit 9 determines whether or not the X coordinates of the X small register 10 and the X coordinate of the X small register 14 are adjacent to each other as in the case of the mode S, but outputs nothing because they are not adjacent. When the determination unit 9 outputs nothing in the mode V, the mode transitions to the mode T in the next step. If the determination unit 9 determines that the two points are adjacent and outputs a regular interpolation point on the curve, the mode W is set. When the processing of the mode V is executed, one division of the curve is completed, and if the determination unit 9 outputs nothing and the mode becomes the mode T in the next step, the first half of the curves are stored in the X small registers 10 to 14. Control point for interpolation and its middle point are set, and X small auxiliary register 20 to
In 24, a control point for interpolating the latter half curve and its middle point are set. Then, the control point and the middle point for interpolating the latter half curve are set in the X small auxiliary registers 20 to 24 and simultaneously saved in the X stack 4. If the determination unit 9
Outputs the information of regular interpolation points, and in the next step, mode P
In the case of, the control point and the middle point for interpolating the latter half curve are not saved in the X stack 4.

Step 4 is mode T. In mode T, the X small selector 15 selects the X small register 10, so the contents of the X small register 10 do not change. Since the X small selector 16 selects the X small register 11, the contents of the X small register 11 do not change. Since the X small selector 17 selects the X small register 12, the contents of the X small register 12 do not change. Since the X small selector 18 selects the X small midpoint generator 31, the midpoint calculation result in step 3 is stored in the X small register 13. Since the X small selector 19 selects the X small register 14, the contents of the X small register 14 do not change. Since the X small selector 25 selects the X small register 14, the X small auxiliary register 20 stores the X coordinate Ax ₂ stored in the X small register 14 in step 3. X
Since the small selector 26 selects the X small midpoint generator 32,
The X small auxiliary register 21 stores the midpoint calculation result in step 3. Since the X small selector 27 selects the midpoint generator 33, the X small auxiliary register 22 stores the midpoint calculation result in step 3. Since the X small selector 28 selects the X small auxiliary register 23, the X small auxiliary register 23
The content of does not change. Since the X small selector 29 selects the X small auxiliary register 24, the content of the X small auxiliary register 24 does not change. Since the X small selector 34 selects the X small register 10 and the X small selector 35 selects the X small register 11, the X small midpoint generator 31 calculates the midpoint of the X small register 10 and the X small register 11. .. X small selector 36 is X
Since the small register 11 is selected and the X small selector 37 selects the X small register 12, the X small midpoint generator 32 calculates the midpoint of the X small register 11 and the X small register 12. Since the X small selector 38 selects the X small register 12 and the X small selector 39 selects the X small register 13, the X small midpoint generator 33 calculates the midpoint of the X small register 12 and the X small register 13. .. Then, the mode T always transits to the mode U.

Thereafter, similarly, the processing is executed in the mode U in step 5 and in the mode V in step 6. In step 6,
The determination unit 9 determines the X coordinate A stored in the X small register 10.
x ₁₁ and the X coordinate Dx ₁₁ stored in the X small register 14.
Are adjacent to each other (of course, the Y coordinate is also determined at the same time), and since the difference in the integer part of the X coordinate (and also the Y coordinate) is 1 or less, they are adjacent to each other. As the information regarding, the information regarding the coordinates of A ₁₁ and D ₁₁ is output. Then, since the determination unit 9 has output the information of the regular interpolation point in the mode V, the mode W is transited to in the next step. In addition, in mode V, one division of the curve into two ends, but since the determination unit 9 outputs the information of the regular interpolation point, the control point for the interpolation of the latter half curve is the X stack in the next step 7. Not saved to 4.

Step 7 becomes the mode W. In mode W, since the X small selector 15 and the X small selector 25 select the X small register 14, the X small register 10 and the X small auxiliary register 20 store the X coordinate Ax ₁₂ stored in the X small register 14 in step 6. Is memorized. X small selector 16 and X
Since the small selector 26 selects the X small midpoint generator 32,
The X-small register 11 and the X-small auxiliary register 21 store the midpoint calculation result in step 6. Since the X small selector 17 and the X small selector 27 select the X small midpoint generator 33, the midpoint calculation result in step 6 is stored in the X small register 12 and the X small auxiliary register 22. X small selector 1
8 and the X small selector 28 select the X small auxiliary register 23, the contents of the X small auxiliary register 23 do not change, and the contents of the X small auxiliary register 23 are stored in the X small register 13. Since the X small selector 19 and the X small selector 29 select the X small auxiliary register 24, the contents of the X small auxiliary register 24 do not change, and the contents of the X small auxiliary register 24 are stored in the X small register 14. Since the X small selector 34 selects the X small register 10 and the X small selector 35 selects the X small register 11, the X small midpoint generator 31 calculates the midpoint of the X small register 10 and the X small register 11. .. The X small selector 36 selects the X small register 11, and the X small selector 3
Since 7 selects the X small register 12, the X small midpoint generator 32 calculates the midpoint of the X small register 11 and the X small register 12. Since the X small selector 38 selects the X small register 12 and the X small selector 39 selects the X small register 13, the X small midpoint generator 33 calculates the midpoint of the X small register 12 and the X small register 13. .. Judgment unit 9 is X small register 1
X coordinate Ax ₁₂ stored in 0 and X stored in register 14
It is determined whether the coordinates Dx ₁₂ are adjacent to each other (of course, the Y coordinate is also determined at the same time), and the difference between the integer parts of the X coordinates (also the Y coordinates) is 1 or less, and the coordinates are adjacent to each other. As the information about the interpolation point of, the information about the coordinates of A ₁₂ and D ₁₂ is output. If the determination unit 9 outputs the information about the regular interpolation point in the mode W, the mode changes to the mode S in the next step, but if the determination unit 9 outputs nothing, the mode changes to the mode U. To do.

Thereafter, similarly, the process is executed in the mode S in step 8, the mode U in step 9, the mode V in step 10, and the mode W in step 11, and finally, in step 11, the determination unit 9 determines the normal interpolation point. The information is output, and when there is no more data to be read from the X stack 4 in the next step (mode S), the interpolation process of the Bezier curve is finished. In this way, the Bezier curve interpolating apparatus of this embodiment completes the interpolation calculation of the cubic Bezier curve shown in FIG. 12 in 11 steps.

As described above, according to the present embodiment, only by adding two X small registers for storing X coordinates, Bezi can be operated at high speed without increasing the hardware required for the midpoint calculation.
It is possible to perform interpolation processing of the er curve. Further, by providing a path for directly inputting the coordinates of the control points for interpolation in the latter half of the curve to the X register, the number of times the coordinates of the control points for interpolation are stored in the stack is reduced, and the number of stack stages can be reduced. Become. Further, since the X coordinate and the Y coordinate are calculated at the same time as in the first embodiment, the calculation result of the X coordinate is 1
It is possible to easily determine whether the start point and the end point of the curve are adjacent to each other without holding the step.

Next, the technical contents of the invention of claim 6 will be described. Similar to the first embodiment, the X small register 14
The X small auxiliary register 20 uses another small register, but since the X small auxiliary register 20 does not hold values other than the same coordinates as the X small register 14, both can be used in common. Further, the X small selector 25 uses the X small register 14
It may be omitted because it has no other input (and this also applies to the Y side). In this embodiment, the midpoint coordinates of the initial values of the control points A, B, C, and D are calculated in advance. However, this may be calculated by using another device separately according to the end use of the Bezier curve interpolation device, or the small X midpoint calculator 3 of the present embodiment.
You may build the program calculated by 1-33.

Although the present invention has been described above based on the two embodiments, it goes without saying that the present invention is not limited to the above embodiments. That is, specifically, the Bezier curve used for the interpolation calculation is not quadratic, but quadratic, quartic, or higher. Since the precision of the initial values of the X coordinate and the Y coordinate or the precision required for convenience of other devices such as a display device is different, the calculation of one is continued even if the calculation of the other is completed.

Similarly, the predetermined value used when determining the adjacency of two points differs between the X coordinate and the Y coordinate. Similarly, the initial value of each control point is not strictly equidistant. It also has the ability to interpolate curves by other methods, so it stores a large number of control points, and after selecting those control points at equal intervals according to the application (for example, from control points at equal intervals). A predetermined value used as an initial value for Bezier curve interpolation processing (used every other one) and used for determining the presence / absence of adjacency has an additional capability such as being selectable.

Since the required interpolation accuracy is high, the number of repeated calculations is large. Therefore, the storage capacity of the X stack and the Y stack is also sufficiently large. 2 for convenience of other devices and applications that use the calculation results
The predetermined value used when determining the adjacency of dots is set separately from the identification and printing ability when the display means displays.

A linear interpolation capability in a three-dimensional space (Z coordinate) is added for application to architectural design. Therefore, it also has a Z coordinate register, an auxiliary register, a stack, a midpoint generator, and the like. In this case,
The present invention is used between any two coordinates of the X, Y, and Z coordinates. It goes without saying that the above is also included in the present invention. In addition, I
Needless to say, the material, circuit configuration, and other hardware aspects do not matter, such as C and semiconductor memory.

[0068]

As described above, according to the present invention,
Increase the hardware required for midpoint calculation by dividing the hardware for midpoint calculation of control points required for Bezier curve interpolation into X coordinate and Y coordinate and then performing the same processing at the same time. It is possible to realize high-speed interpolation processing without performing the above. Furthermore, since only one midpoint calculation is performed in one step, it becomes easy to increase the clock frequency supplied to the Bezier curve interpolating device, and the processing speed can be further increased.

Further, since the X coordinate and the Y coordinate are calculated at the same time, it is possible to easily determine the adjacency between the start point and the end point of the curve without holding the calculation result of the X coordinate for one step. Therefore, its practical effect is great.

[Brief description of drawings]

FIG. 1 is a configuration diagram of an embodiment of a Bezier curve interpolation device according to the invention of claim 1.

FIG. 2 is a block diagram showing an internal configuration of the above embodiment and an embodiment of the invention of claim 2;

FIG. 3 is an operation explanatory diagram of the above embodiment.

FIG. 4 is a diagram illustrating the operation of the above embodiment.

FIG. 5 is a block diagram of an embodiment of a Bezier curve interpolation device according to the invention of claim 4;

FIG. 6 is a diagram showing the internal configuration of the above embodiment and the configuration of an embodiment of the invention of claim 5;

FIG. 7 is an operation explanatory diagram of the above embodiment.

FIG. 8 is an operation explanatory diagram of the above embodiment.

FIG. 9 is a diagram illustrating the operation of the above embodiment.

FIG. 10 is a configuration diagram of a Bezier curve interpolation device according to a conventional technique.

FIG. 11 is an internal configuration diagram of a two-divided circuit of a Bezier curve interpolation device according to a conventional technique.

FIG. 12 is an explanatory diagram of control points that interpolate a cubic Bezier curve.

FIG. 13 is an operation explanatory diagram of a Bezier curve interpolation device according to a conventional technique.

[Explanation of symbols]

 1 X register 2 X auxiliary register 3 X midpoint generator 4 X stack 5 Y register 6 Y auxiliary register 7 Y midpoint generator 8 Y stack 9 Judgment unit

Claims (6)

[Claims] 1. An X register for storing a plurality of X coordinates given in order before and after, and an X midpoint generator for calculating a midpoint coordinate between adjacent X coordinates stored in the X register. And an X auxiliary register that holds the X coordinate stored in the X register or the midpoint coordinate output by the X midpoint generator, and a curve newly output by the X midpoint generator to the X auxiliary register When the X coordinate of the control point for the new interpolation of the first half of the is input, the control point for the interpolation that was held so far or the X of the control point for the interpolation of the second half of the newly output curve X to save the coordinates and then store
A stack and a Y that stores a plurality of Y coordinates given in order before and after
A register, a Y midpoint generator for calculating midpoint coordinates between adjacent Y coordinates stored in the Y register, and a Y coordinate stored in the Y register or output from the Y midpoint generator. A Y auxiliary register that holds the midpoint coordinates, and the Y auxiliary register that holds the Y coordinates of the control points for the new interpolation of the latter half of the curve newly output by the Y midpoint generator The Y coordinate of the control point for interpolation that has been performed or the control point for interpolation of the rear half of the newly output curve is saved and then stored.
Whether the stack and the difference between the X coordinates of the start point and the end point of the divided curve stored in the X register and the difference between the Y coordinates of the start point and the end point of the divided curve stored in the Y register are within a predetermined value. A determination unit that determines whether the start point and the end point are adjacent to each other, and, if the coordinates of the control point for interpolating the curve are given to the X register and the Y register, the X midpoint generator And the Y midpoint generator to repeatedly calculate the midpoint, and hold the calculation results in the X register and the X auxiliary register and the Y register and the Y auxiliary register to interpolate the curve of the first half. Point and the control point calculating means for obtaining a control point for interpolating the curve of the latter half, and the control point for the latter half of the control points for interpolation calculated by the interpolation control point calculating means are the X stack and the front. Is retreated in the Y-stack, the first half of the control points for the interpolation to be stored in the X register and the Y register to repeatedly divide the X register and the Y thereon
Of the control points for interpolation of the first half stored in the register, the determination unit determines that two points that are the start point and the end point of the curve are adjacent to each other. And a save / restore control unit that restores the control points for the latter half of the interpolation saved in the X stack and the Y stack to the X register and the Y register. Features Bezier curve interpolator. 2. When h is a natural number of 2 or more and j is a natural number of 1 or more and h or less, the X register is composed of first to (h + 1) th X small registers, and the X midpoint generator. Is the j-th X small and mid-point generator
An X small register and first to hth X small midpoint generators for calculating the midpoint of the (j + 1) X small register, wherein the X auxiliary register is a first to hth X small auxiliary register. And the Y register is composed of first to (h + 1) th small Y registers, and the Y middle point generator is the jth Y small middle point generator.
A Y small register and first to hth Y small midpoint generators for calculating the midpoint of the (j + 1) th Y small register, wherein the Y auxiliary register is a first to hth Y small auxiliary register. And the difference between the X coordinate values stored in the first X small register and the (h + 1) X small register and the first Y small register and the (h + 1) th register.
The Bezier curve interpolating device according to claim 1, wherein the Bezier curve interpolating device is configured to determine whether or not a difference between Y coordinate values stored in the Y small register is within a predetermined value. 3. The hX small register and the first X small auxiliary register or the hY small register and the first Y
3. The Bezier curve interpolation device according to claim 2, wherein at least one of the small auxiliary registers is also used as the same small register. 4. An X register for storing a plurality of X coordinates given in order before and after, an X auxiliary register for storing a plurality of X coordinates, and a neighbor stored in the X register or the X auxiliary register. An X midpoint generator for calculating a midpoint coordinate between the matching X coordinates, and an X coordinate of a control point for interpolation of the first half of the curve newly output by the X midpoint generator are input to the X auxiliary register. When it is done, the X stack that stores the coordinates of the control point that has been held so far or the control point for the interpolation of the second half of the newly output curve, and the Y stacks that are given in order before and after Y to store coordinates
A register, a Y auxiliary register for storing a plurality of Y coordinates, a Y midpoint generator for calculating midpoint coordinates between adjacent Y coordinates stored in the Y register or the Y auxiliary register, and the Y auxiliary register When the Y coordinate of the control point for interpolation of the front half of the curve newly output by the Y midpoint generator is input to, the control point that has been held so far or the rear half of the newly output curve is input. And a Y stack storing the coordinates of the control points for the interpolation, and the difference between the X coordinates of the starting point and the ending point of the divided curve stored in the X register and the starting point of the divided curve stored in the Y register. A determination unit that determines whether the start point and the end point are adjacent to each other based on whether the difference between the Y coordinate of the end point and the Y coordinate of the end point is within a predetermined value, and the coordinates of the control point for interpolating the curve are stored in the X register and the Y register. Given In this case, the X midpoint generator and the Y midpoint generator are made to repeatedly calculate the midpoint, and the calculation results are held in the X register and the X auxiliary register, and the Y register and the Y auxiliary register. Interpolation control point calculation means for performing calculation to obtain a control point for interpolating the curve of the first half and a control point for interpolating the curve of the second half, and the curve of the first half stored in the X register and the Y register If the determination unit indicates that two points indicating the start point and the end point are adjacent to each other among the control points for interpolation of
The point is output as a normal interpolation point on the curve, and the control points for the interpolation of the second half curve stored in the X auxiliary register and the Y auxiliary register are transferred to the X register and the Y register. If the determination unit does not indicate that the two points indicating the start point and the end point of the first half curve are adjacent to each other, control points for interpolation of the second half curve stored in the X auxiliary register and the Y auxiliary register are set. Transfer save holding means for saving in the X stack and the Y stack and holding in the X register and the Y register for repeatedly dividing the control point for interpolation of the first half curve into two; The X stack and the Y
The determination unit indicates that two control points for interpolating the second half of the curve transferred from the auxiliary register or the Y stack to the X register and the Y register are adjacent to each other, which indicate the start point and the end point of the curve. In that case, the two points are output as the normal interpolation points on the curve, and the control points for interpolation of the subsequent curves that are saved in the X stack and the Y stack are stored in the X register and the Y register. A Bezier curve interpolating device, characterized in that it has a retracting and returning control means for returning. 5. When h is a natural number of 2 or more, an X register composed of (h + 2) X small registers from a first X small register to a (h + 2) small X register and a first X small auxiliary register to a first X small auxiliary register. An X auxiliary register comprising (h + 2) small X auxiliary registers up to (h + 2) small X auxiliary registers, and the first to (h + 2) X small registers or the first
To the (h + 2) X small auxiliary registers, the midpoint coordinates of the X coordinates stored in two registers are calculated to calculate the first to (h + 2) X small registers or the first to (h +) th small registers.
2) An X midpoint generator consisting of h number of X small midpoint generators from 1st to hth output to any one of the X small auxiliary registers, and a (h + 2) Yth small number from the 1st Y small register. A Y register consisting of (h + 2) Y small auxiliary registers up to a register, and a Y auxiliary register consisting of (h + 2) Y small auxiliary registers from a first Y small auxiliary register to a (h + 2) Y small auxiliary register 1st to (h + 2) Y small registers or the first
From the (h + 2) Y small auxiliary registers, the midpoint coordinates of the Y coordinates stored in two registers are calculated to calculate the first to (h + 2) Y small registers or the first to (h +) th small registers.
2) A Y midpoint generator comprising h small Y midpoint generators 1 to h for outputting to any of the Y small auxiliary registers; the first X register and the (h + 2) X If the difference between the X coordinate values stored in the small register and the difference between the Y coordinate values stored in the first Y register and the (h + 2) Y small register is less than a predetermined value, it is determined whether two corresponding points are adjacent to each other. The Bezier curve interpolating device according to claim 4, further comprising: 6. The same small register is used for at least one of the (h + 2) X small register and the first X small auxiliary register or the (h + 2) Y small register and the first Y small auxiliary register. The Bezier curve interpolating device according to claim 5, wherein