JPH02310783A - Curve interpolating system - Google Patents

Abstract

PURPOSE:To perform curve interpolation with high accuracy at high speed by finding the sum of the larger length of each neighboring control coordinate point in an axial direction, and deciding the number of developmental data points corresponding to the value. CONSTITUTION:The length of control coordinate data in the axial direction of each coordinate between the neighboring coordinate points, and the number of coordinate data points generated by attaching positive correlative relation with the sum of the larger length of the each neighboring coordinate point in a direction of coordinate axis is decided. In other words, distances x1 and y1 for an x<->axial direction and a y<->axial direction between control data C0 and C1 are calculated, respectively, and the y1 with a larger value is selected, and a distance x2 with the larger value between the control data C1 and C2 is selected similarly, and distance y3 with the large value between the control data C2 and C3 is selected similarly. Then, the number of developmental data points can be obtained from the range of the value of the sum ( y1 + x2 + y3) with a developmental data point number table for coordinate data P0 - Pn-1 on Bezier curve corresponding to the range. Thereby, it is possible to realize the acceleration of processing speed without lowering the accuracy of the curve interpolation.

Description

[Detailed Description of the Invention] [Industrial Application Field] Curve interpolation that generates a pseudo curve by generating coordinate data on a curve from control coordinate data that defines the curve and connecting the generated coordinate points with a straight line. The present invention relates to a curve interpolation method for extracting necessary coordinate data on a curve from generated coordinate data.

[Prior Art] Conventionally, a method for generating a cubic Bezier curve is described in the PostScript Language Reference Manual (PO5TSCRIPT Language Reference Manual).
eReference Ma, nual, (1985)
) pages 140 and 215, or Davi
Discussed in "Computer Graphics", co-authored by F., Rogsrs, J. and Alan Adams, translated by Fujio Yamaguchi, published by Nikkan Kogyo Shimbun, pp. 154-161.

To generate a cubic Bezier curve, data on one curve is calculated using a Bezier curve generation formula, and the calculated coordinate points are connected with straight lines, thereby generating a pseudo curve.

Therefore, the distance (flatnessparamet
er), and its value is the tolerance (toleran
Data on the curve is extracted so that it falls within an allowable error called ce).

[Problem M to be solved by the invention] The distance between the pseudo-curve connecting the generated coordinate points and the curve represented by the curve equation is used as a parameter, and its value is the tolerance number S.
In the aforementioned method of drawing a cubic Bezier curve, the coordinate data on the curve is calculated, and then the distance between the curve and the straight line connecting the generated coordinate data is calculated, In addition, various processes are performed, such as determining whether the value falls within an allowable error and determining final coordinate data on the curve based on the determination result, which makes the process complicated. Therefore, there was a problem that high-speed curve interpolation processing could not be performed. Particularly in processing using so-called outline fonts, in which high-quality characters are displayed or printed based on main coordinate data that defines the outline of a single character, the precision of curve interpolation and the processing speed are problems.

One object of the present invention is to provide a curve interpolation method that can draw pseudo curves with simple processing without reducing the accuracy of the generated pseudo curves.

Another object of the present invention is to provide a curve interpolation method that can draw Bezier curves at high speed.

[Means for Solving the Problems] In order to achieve the above object, the curve interpolation method according to the present invention generates coordinate data on the curve from control coordinate data defining the curve, and connects the generated coordinate points with a straight line. In the curve interpolation method that generates a pseudo curve by connecting, the length in each coordinate axis direction between each adjacent coordinate point of the above control coordinate data is determined, and the length in the longer coordinate axis direction for each adjacent coordinate point is calculated. The total sum is calculated, and the number of coordinate data points generated is determined by having a positive correlation with the total sum.

In this method, for example, the total length in the direction of the longer coordinate axis is classified in advance into a plurality of ranges, and the number of points of the coordinate data generated is determined for each of the plurality of ranges by referring to a table. Determine the number of coordinate data points.

Preferably, when the longer coordinate axis direction lengths of the adjacent coordinate points all belong to the same axial direction, the number of generated coordinate data points is determined to be a smaller value than when they do not belong to the same axial direction.

Another curve interpolation method according to the present invention is a curve interpolation method in which coordinate data on a curve is generated from control coordinate data that defines a curve, and a curve is generated in a pseudo manner by connecting the generated coordinate points with a straight line. Among the coordinate data points generated above, find the angle formed by two straight lines connecting the end points of the three adjacent coordinate points and the other two points, and if the angle is within a predetermined tolerance range, the three The coordinate data of other end points in the coordinate points are deleted.

In this case, preferably, the length in each coordinate axis direction between the end points of the three adjacent coordinate points is determined, and if one of them exceeds a predetermined tolerance range, the angle formed by the two straight lines is within the tolerance range. The coordinate data of the other end point should not be deleted even if the coordinate data is in the other end point.

[Function] In a curve interpolation method that generates a pseudo curve by generating coordinate data on a curve from control coordinate data that defines the curve and connecting one generation coordinate point with a straight line, the accuracy and processing speed of curve interpolation are improved. In order to improve
We focused on In other words, we realized that there is a correlation between the sum of the longer axial lengths between adjacent control coordinate points and the length or complexity of one curve. We came up with the idea of finding the sum of the longer axial lengths between them and determining the number of generated data points according to this value. That is, for a long curve, the number of generated data points is increased, and for a short curve, the number of generated data points is decreased. This makes it possible to increase the processing speed without reducing the accuracy of curve interpolation.

Also, even if the sum of the longer axial lengths is the same, the X-axis and Y#! It is expected that the curve in the case where all the coordinates belong to the same coordinate axis direction will be a relatively smooth curve compared to the case where there are a mixture of rivers. Therefore, in such a case, the number of generated data points can be reduced in principle.

However, even in this case, it is considered that the curvature of the curve changes depending on the size of the sum of the smaller axial lengths, so the number of generated data points is determined based on this value. This allows for smooth curves.

The processing speed can be increased by further reducing the number of generated data points without reducing the accuracy of curve interpolation.

Further, according to the present invention, among the coordinate data points generated by any method, if the angle formed by two straight lines connecting the end points of three adjacent coordinate points and the other two points is within the allowable range, the corresponding By deleting the coordinate data of the other end point among the three coordinate points and connecting the remaining coordinate data with a straight line, the final number of coordinate points can be reduced while maintaining the accuracy of one-curve interpolation.

Furthermore, even if the angle formed by the two straight lines is within the allowable range, if the maximum value of the length in each coordinate axis direction between the end points of the three adjacent coordinate points exceeds the allowable range, the other end point without deleting coordinate data.

By connecting the remaining coordinate data with straight lines, it is possible to improve the accuracy of curve interpolation even for curves consisting of 5 small and large curvature parts.

[Example] Embodiments of the present invention will be described below with reference to the drawings.

Control coordinate data c, , c1 defining a cubic Bezier curve
．． Based on c,,c,, the cubic (k=3) Bezier curve equation is expressed as follows.

P(t) = ΣctJ, 1(t) (o≦t≦1
) Here, J h, I(t) is a coefficient that is predetermined by the value of t when the value of k is determined, and the sought locus sP can be obtained by giving the value of t. Therefore, the number of values of t to be given corresponds to the number of generated data points. In addition,
For details on Bezier curves, please refer to the above-mentioned known documents.

FIG. 1 shows the control coordinate data C using this Bezier curve equation.
,,C-work,c,,C,The coordinate data P on curve 2 generated based on,,P-work,P2. ... is a diagram in which pfi-□ is plotted.

In the curve interpolation in this embodiment, first, the distances ΔX and Δy1 are calculated in the y-axis direction and the y-axis direction between the control data C, , C, respectively.

Compare the two, and as a result, in the example of Figure 1, Δy1>Δx
Since it is L, Δy□ with a large value is selected. Next, in the same way between the control data C1 and C2, the distance Δ
Calculate X 2 wΔy2 and compare the two. ΔX, )
Since Δy2, the larger one ΔX2 is selected. Furthermore, similarly for the control data C, , C3,
Calculate the distance X3tΔy3 and compare the two. Δy
Since s > ΔX, the larger one Δy8 is selected.

As shown in FIG. 5, within a range of values of the sum of all selected larger axial distances (Δy1+Δx2+Δyz)12, that is, a distance range 15, the occurrence data of coordinate data P on the Bezier curve corresponding to that range Score table 16
Thus, the number n of generated data points is obtained. For example, when the distance cylinder g115 is "Q2"', the corresponding number of generated data points n is 114 II. In this case, 1 (0≦t≦1) of the Bezier curve equation, for example, t=1/4.2/4
．． 3/4.4/4 (excluding the starting point of t=o), calculate the coordinate data P on the Bezier curve, and connect them with straight lines to generate a pseudo curve.

With this curve interpolation method, the accuracy of the generated approximate curve can be increased because the number of generated coordinate data P is increased in the case of a long or complicated curve. Conversely, for a short curve, the number of generated coordinate data P is reduced to eliminate data that degrades the approximation accuracy, and a Bezier curve can be generated at high speed. In addition, control data C0~
Determine the number of generated data points of the generated coordinate data P from C3,
Since the generated data P is calculated, an improvement in the drawing speed of Bezier curves can be expected.

Next, a case where the curve shape is gentle will be explained using FIG. 2. FIG. 2 shows control coordinate data C,,C, which defines a cubic Bezier curve, from C2°C1 to coordinate data P0°pl, p2...P□ on the cubic Bezier curve 2.
-1 is calculated and plotted.

Similarly to what was explained in FIG. 1, first the control data C,
, C, in the X-axis direction and the y-axis direction, respectively.
Calculate X engineering and Δy1. Compare the two, and the result is ΔX
Since 1>Δy, select ΔX□. Next, similar processing is performed for the control data C and 02. As a result, since ΔX2>Δy2, Δx2 is selected. Similarly, for control data C, ,C, ΔX1
is selected.

The selected values are all distances between control coordinate data in the X-axis direction. That is, it can be estimated from only the control coordinate data C6-C5 that the shape of this third-order Bezier curve is a gentle curve extending in the X-axis direction. Therefore, in this case, there is no problem even if curve interpolation is performed using fewer points than the number of generated data points corresponding to the length of the curve as explained in FIG. Therefore, the distances ΔX and Δy are calculated and compared in the X-axis direction and the y-axis direction of the control data C0 to C3, respectively, and if the results are all values on the same axis (ΔX>Δy), as shown in FIG. As shown in the selector 14
Δy with the smaller value is selected, and from the range 15 of values of all the selected sums (Δy + Δy, +Δys) 13, a table 16 of the number of generated data points of coordinate data P on the Bezier curve corresponding to that range is created. As a result, the number of generated data points can be reduced to m points (m<n: n is the number of generated data points corresponding to the sum of ΔX), and it is expected that the drawing speed of Bezier curves will be further improved.

Note that the distance range 15 and generated data point number table 16 shown in FIG. 5 can be easily constructed using a memory or a combinational logic circuit. In this example, the sum of the maximum values is 12
Although the same distance range 15 and generated data point number table 16 are used for the sum of minimum values 13 and 13, they may be prepared separately for both.

FIG. 3 is a diagram for explaining another embodiment of the present invention. Figure 3 (a) shows the final result obtained from the coordinate data P on the cubic Bezier curve calculated in advance, using the angle formed by two straight lines connecting the end points of the adjacent three coordinate data and the other two points as parameters. Coordinate data on the curve to be extracted P (P,
, Pl, P,, P,.

...) is plotted.

First, t of the Bezier curve equation is changed according to the length of the Bezier curve, and the coordinate data P Or pxl PZ+ ”'PHt+ax− of the maximum number of generated data points N max is
Calculate 1. Next, from Po, two straight lines P based on the straight line P0P work. Calculate the angle formed by Pl and POP. If the angle is within the allowable range, coordinate data P2
Delete. Furthermore, two straight lines P. Calculate the angle formed by P-work IPOP. If the angle is outside the allowable range,
Extract coordinate data P3. Next, the angle formed by the two straight lines r', P, , P□P is calculated using the straight line p1p3 as a reference. If the angle is within the allowable range, the extracted data P,
Delete. Furthermore, the angle formed by the two straight lines P1P, , PIF, is calculated. If the angle is outside the allowable range, the coordinate data P.

Extract. Repeating the same process, the coordinate data P OT pt+ P31 PSI・
... is determined as the coordinate data P on the curve. With this method, it is possible to reduce the number of generated data points and draw a Bezier curve with high approximation accuracy.

Furthermore, in the case of a curve that has a mixture of gentle parts and parts where the curvature suddenly becomes severe, the angle between the two straight lines will not exceed the allowable range, but will suddenly exceed it at some point. There is a possibility that this may occur, and this may lead to a decrease in Bezier curve approximation accuracy. Therefore, the angle formed by the two straight lines explained in FIG. 3(a) is set as the first parameter, and as shown in FIG. 3(b).

The larger distance between the coordinate data in the Xn direction and the y-axis direction of the coordinate data P (either ΔX or Δy) is used as the second parameter, and when either one exceeds the respective allowable range, the coordinate data is Then, the final coordinate data P is determined. With this method, it is possible to draw a Bezier curve with higher approximation accuracy.

FIG. 4 is a diagram showing another embodiment of the present invention, in which hardware is used to provide the coefficients J K, L (e) on a table in the Bezier curve equation described above for calculating the coordinate data P on the Bezier curve. The configuration is a cubic Bezier curve formula (k=3)
This will be explained in the case of

Each coordinate value 9 of the control coordinate data Ci in the curve formula and the number of threads J3. I (t) table 8 to 1 multiplier 10
Through the calculations of the adder 11, coordinate data on the curve is calculated. This hardware configuration enables high-speed Bezier curve interpolation processing. Further, by setting t to 172N and providing a table 8 in which the number of threads J is divided into a denominator and a numerator as a fraction, a faster hardware configuration in the curve interpolation described above can be realized.

Furthermore, although the embodiments described so far have been described in two dimensions, they can also be implemented in three dimensions.

[Effects of the Invention] As explained above, according to the present invention, coordinate data on a curve is generated from control coordinate data that defines a curve, and one generated coordinate data is connected with a straight line, thereby generating a pseudo curve. In the curve interpolation method, the number of generated coordinate data points is determined based on the correlation of distances in each coordinate axis direction between control coordinate data and coordinate data on one curve is calculated, so curve interpolation with high interpolation accuracy can be performed at high speed.

Furthermore, according to the present invention, in the curve interpolation method described above, coordinate data on the curve is generated, and the coordinate data is extracted based on the angle formed by two straight lines connecting the end points of three adjacent coordinate points and the other two points. The accuracy of single-curve interpolation can be improved.

[Brief explanation of drawings]

1 is an explanatory diagram of the curve interpolation method for generating a Bezier curve according to an embodiment of the present invention; FIG. 2 is an explanatory diagram of the curve interpolation method when the curve is gentle in the embodiment of FIG. 1;
Figure 1 is an explanatory diagram of a curve interpolation method in generating a Bezier curve according to another embodiment of the present invention, Figure 4 is a block diagram of a calculation device for coordinate data on a Bezier curve in hardware according to an embodiment of the present invention, and Figure 5 The figure is a conceptual diagram showing the configuration of means for calculating the number of generated data points from the sum of distances. 2... Bezier curve expressed by the Bezier curve formula. 60 to C1... Third-order Bezier curve prescribed control coordinate data, P0 to Pn-+... Occurrence coordinate data on the Bezier curve.

Claims (1)

[Claims] 1. A curve interpolation method that generates a pseudo curve by generating coordinate data on a curve from control coordinate data that defines the curve and connecting the generated coordinate points with straight lines, The length in each coordinate axis direction between each adjacent coordinate point of the above control coordinate data is calculated, and the sum of the lengths in the longer coordinate axis direction is calculated for each adjacent coordinate point. A curve interpolation method characterized by determining the number of coordinate data points. 2. Classify the total length in the direction of the longer coordinate axis in advance into a plurality of ranges, and calculate the number of points of the coordinate data by referring to a table that determines the number of points of the coordinate data generated for each of the plurality of ranges. The curve interpolation method according to claim 1, wherein the curve interpolation method is determined. 3. When the lengths of the longer coordinate axes of the adjacent coordinate points all belong to the same axial direction, the number of generated coordinate data points is determined to be a smaller value than when they do not belong to the same axial direction. The curve interpolation method according to claim 1 or 2. 4. In a curve interpolation method that generates a pseudo curve by generating coordinate data on a curve from control coordinate data that defines the curve and connecting the generated coordinate points with a straight line, the generated coordinate data points are Among them, find the angle formed by the two straight lines connecting the end point of the three adjacent coordinate points and the other two points, and if the angle is within a predetermined tolerance range, calculate the angle between the other end point of the three coordinate points. A curve interpolation method characterized by deleting coordinate data. 5. Find the length in each coordinate axis direction between the end points of the three adjacent coordinate points above, and if either one exceeds the predetermined tolerance range, if the angle formed by the two straight lines is within the tolerance range. 5. The curve interpolation method according to claim 4, wherein the coordinate data of the other end point is not deleted even if the coordinate data of the other end point exists.