JPH0778260A - Continuous curve generator - Google Patents

Abstract

PURPOSE:To effectively suppress the overshoot of a Bezier curve when the distance between input coordinate points is long and the distance between the other adjacent input coordinate points is extremely short when the Bezier curve is generated between the input coordinate points. CONSTITUTION:A length calculation part 6-2A calculates respective lengths up to input coordinate points which is located back and forth each input coordinate point from each input coordinate point within a coordinate column buffer 6-1. A length comparison part 6-2B compares the calculated lengths. As a result, if the rear and front lengths are different from each other by an amt. more than a prescribed rate, a coordinate calculation part 6-2C moves a control point to the location near the corresponding input coordinate point according to the length of a shorter side. Based on the control point obtained by this, a Bezier plotting part 7 plots a continuous curve by connecting each input coordinate point with a cubic Bezier curve.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention, when drawing an arbitrary figure in a word processor, a personal computer or the like, connects each input coordinate point with a cubic Bezier curve based on input coordinate sequence data. The present invention relates to a continuous curve generator that generates a continuous curve.

[0002]

2. Description of the Related Art Conventionally, in a word processor, when a cursor key is operated to sequentially input coordinate points when drawing an arbitrary figure, the input coordinate points are continuously connected by Bezier curves. A continuous curve generator for generating a continuous curve is installed. This type of continuous curve generator operates as follows. Now, the process of generating one Bezier curve based on the input coordinate sequence data will be described with reference to FIG.

In FIG. 8, (A) shows four input coordinate points a, b, c and d, and a cubic Bezier curve connecting points b and c among these input coordinate points is generated. I shall. Generally, a cubic Bezier curve is drawn by four coordinate points, that is, a start point, an end point, and two control points. FIG. 8B shows the first coordinate point between the input coordinate points b and c. FIG. 8C is a diagram for explaining how to set a control point, and FIG. 8C is a diagram for explaining how to specify a second control point between input coordinate points b and c. Further, FIG. 8D is a diagram showing a state in which a Bezier curve is drawn between the input coordinate points b and c.

First, the first control point P is placed between the input coordinate points b and c.
When 1 is set, as shown in FIG.
The set position of the control point P1 is parallel to the straight line connecting the input coordinate points a and c, and the next input coordinate point c from the input coordinate point b.
The distance from the input coordinate point b is obtained by multiplying the length between the input coordinate points a and c by a proportional multiplier. If this is expressed by an equation, as shown in the figure, P1 = (c-
a) × k1 + b, a to c are vector quantities having the coordinate values of the input coordinate points a and c, and k1 is a proportional multiplier (for example, 1/2). After the first control point P1 is set between the input coordinate points b and c in this way, the second control point P2 is set next. As shown in FIG. 8C, the set position of the second control point P2 is parallel to the straight line connecting the input coordinate points b and d, and the input coordinate point b before the input coordinate point c is located.
The distance from the input coordinate point c is obtained by multiplying the length between the input coordinate points b and d by a proportional multiplier. If this is expressed by an equation, as shown in the figure, P2 = (b-
d) × k2 + c, d to b are vector quantities having the coordinate values of the input coordinate points d and b, and k2 is a proportional multiplier (generally k1 = k2, but a positive value other than “0”). The numbers may be slightly different). Drawing the first control point P1 and the second control point P2 thus obtained, and a cubic Bezier curve with the input coordinate point b as the Bezier start point and the input coordinate point c as the Bezier end point are shown in FIG.
(D).

FIG. 9 shows that there is 1 between each input coordinate point as described above.
It shows a continuous curve drawn by drawing bezier curves for each book and connecting them. here,
In the figure, a, b, c, d, e, f indicate input coordinate points, and b1, c1, d1, e1 between the input coordinate points are first control points, and b2, c2, d2, e2. Indicates the second control point. Although not shown in the figure, a1 and f2
The control point a1 becomes the input coordinate point a, and the second control point f2 becomes the input coordinate point f. That is, the starting point a of the continuous curve and the first point
The control points a1 become equal, and the end point f of the continuous curve becomes equal to the second control point f2. In this way, the control points adjacent to each input coordinate point are on a straight line passing through the input coordinate points, and the straight line connecting the input coordinate points and the first control points is the start direction of the Bezier curve or the input coordinate points and the second control points. Since the straight line connecting the control points represents the ending direction of the Bezier curve, it is possible to smoothly connect the adjacent Bezier curves.

[0006]

A smooth continuous curve can be obtained by connecting the input coordinate points with the Bezier curve in this way. For example, as shown in FIG. When the distance between c is long and the distance between the input coordinate points b and a, or the distance between the input coordinate points c and d is extremely short, an overshoot appears on the Bezier curve between the input coordinate points with a short distance. . That is, in the process of operating the cursor key to move the cursor position dot by dot, if the distance is extremely short, such as between the illustrated input coordinate points b and a or between the illustrated input coordinate points c and d,
A bezier curve bulging in an acute angle is generated. This is because the control point (outer control point) on the straight line passing through the input coordinate point b or the input coordinate point c is the input coordinate point b or the input coordinate point c.
It is caused by being set at a position far away from. When drawing a figure in which a long curve and a short curve are combined in this way, there is a drawback in that a desired figure cannot be obtained due to overshooting. In addition, when input coordinate points are successively specified, 1 If you move the 1-dot cursor to specify the next point after confirming one point, a sudden unintended large overshoot will appear, which will make the operator uncomfortable or hesitate. It was difficult. An object of the present invention is to generate a Bezier curve between input coordinate points when the distance between certain input coordinate points is long and the distance between other input coordinate points adjacent thereto is extremely short. It is to be able to effectively suppress overshoot.

[0007]

The means of the present invention are as follows. Focusing on each input coordinate point sequentially, generate two new control points between each input coordinate point from the positions of the coordinate points located before and after that, and use a cubic Bezier curve between each input coordinate point. In the continuous curve generating device that generates a continuous curve by tying, (1), the length detecting means detects the length from each input coordinate point to the input coordinate points located before and after it. (2) The length comparing means compares the lengths before and after detected by the length detecting means. (3) The control point setting means corresponds to the control point according to the shorter length when the length comparing means detects that the front and rear lengths have a difference of a predetermined ratio or more. Set to a position close to the input coordinate point.

[0008]

The operation of the means of the present invention is as follows. Now, when generating two new control points between the input coordinate points based on the values of the coordinate points located before and after each input coordinate point, from each input coordinate point to the input coordinate points located before and after it. The length of each is detected. Then, the detected front and back lengths are compared, and if there is a difference of a predetermined ratio or more,
The control point is set at a position close to the corresponding input coordinate point according to the shorter length. Therefore, when generating a Bezier curve between input coordinate points, when the distance between certain input coordinate points is long and the distance between other input coordinate points adjacent to it is extremely short, the overshoot of the Bezier curve is effective. Can be suppressed.

[0009]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment will be described below with reference to FIGS. FIG. 1 is a block diagram showing a word processor equipped with a continuous curve generator. The main control unit 1 controls the whole operation of this word processor according to various programs. When the coordinate sequence data for drawing is input from the key operation unit 2, the main control unit 1 fetches this and stores it in the document memory 3. Store. The main control unit 1 gives the content of the document memory 3 to the external storage control unit 4 in response to the save command from the key operation unit 2, and causes the external storage device 5 to register the contents.

The continuous curve generator 6 converts the input coordinate sequence stored in the document memory 3 into a continuous Bezier curve, and a coordinate sequence buffer for temporarily storing the input coordinate sequence from the document memory 3. 6-1 and a control point generation unit 6-2 that generates a control point together with a start point and an end point as a coordinate sequence for drawing a Bezier curve based on the contents of the coordinate sequence buffer 6-1; and this control point generation unit. 6-2 has a bezier buffer 6-3 for temporarily storing the coordinate sequence data for drawing the bezier curve. In particular, in this embodiment, the control point generator 6-2 further includes a length calculator 6-2 for calculating the distance between the input coordinate points.
A, a length comparison unit 6-2B that compares each distance calculated by the length calculation unit 6-2A, and this length comparison unit 6-2
The coordinate calculation unit 6-2C that calculates the set position of the control point based on the comparison result of B is included. In this case, the coordinate calculation unit 6-2C performs calculations such as scalar product and addition using the coordinates between two points as a vector.

The bezier drawing unit 7 is a continuous curve generator 6
A cubic Bezier curve is drawn based on a coordinate sequence for drawing a Bezier curve that is output from the display control unit 8 and is output from the display device 9 or is output to the print control unit 10. It is given and printed out from the printer 11.

Next, the operation of this embodiment will be described with reference to FIGS.
And explain. First, the operating principle of this embodiment will be briefly described.
I'll do it. At the input coordinate point b in FIG.
When obtaining, the distance dist between the input coordinate points a and b R
And the distance dist between the input coordinate points b and c S and input seat
Distance dist between gauge points a and c Find L and find this distance dis
t R or dist S is the distance dist Compared to L
When it is considerably short, it is shown in FIG. 8 (B) and (C) above.
The values of the proportional multipliers k1 and k2 for determining the control point
dist R, dist Proportional to the shorter of S
I try to make it smaller. By this,
For example, as the input coordinate points a and b get closer, the control point is also input.
It is possible to move the control point so that it approaches the position of coordinate point b.
It Continuous curve generator with such an algorithm
6 is the input coordinate sequence in the coordinate sequence buffer 6-1.
Bezier buffer 6-
The continuous curve generator 6 moves at that time.
Figure 3 shows the work using a flow chart.
Among them, the most characteristic first control point movement processing, second control
The point movement processing is shown in the flowcharts of FIGS. 4 and 5.
Is.

When the input coordinate sequence from the document memory 3 is stored in the coordinate sequence buffer 6-1, the continuous curve generator 6 executes the operation according to the flowchart of FIG. First, the continuous curve generator 6 sets an initial address at the current point pt for accessing the coordinate sequence buffer 6-1 (step S1). In this case, X indicating the first input coordinate point among the input coordinate points stored in the coordinate sequence buffer 6-1.
An address for reading the Y coordinate is set at the current point pt as an initial address. Next, according to the value of the current point pt, the data [PT] indicating the first input coordinate point is read from the coordinate string buffer 6-1 as the Bezier start point, and the value obtained by adding “1” to the content of the current point pt is set. Therefore, the data [PT + 1] indicating the second input coordinate point is read from the coordinate sequence buffer 6-1 as the bezier end point (step S2).

Next, the length calculation unit 6-2A uses this [P
The length dist between the bezier start point and the bezier end point based on the data of T] and [PT + 1]. S is obtained (step S3). That is, the length calculation unit 6-2A is dis
t The calculation of S = | [PT + 1]-[PT] | is performed. Note that the operation || represents that the length between two points is calculated,
The result is a scalar quantity. Length dist between these two points
Since S is used in the first and second control point movement processing, which will be described later, S is obtained as a preprocessing thereof.

Next, the bezier starting point is set as the default value of the first control point (step S4). Then, the process proceeds to the next step S5, and it is checked whether or not the input coordinate point exists immediately before the input coordinate point indicated by the value of the coordinate sequence pointer pt. Now, it is indicated by the value of the coordinate sequence pointer pt. Since the input coordinate point is the first point and there is no previous point, step S6 (first control point moving process) is skipped and the process proceeds to step S7. That is, if it is the first input coordinate point, the first control point = start point is left and the calculation of the second control point is started. Here, the default value of the second control point is the Bezier end point, and that value is first set as the second control point (step S7). Then, the process proceeds to step S8, and it is checked whether or not the next next input coordinate point exists in the coordinate sequence buffer 6-1.
If the number of points is equal to or more than the points, there is a next input coordinate point after counting from the first input coordinate point, and therefore the second control point moving process shown in FIG. 5 is executed (step S9). Note that when the input coordinate points are only the first point and the second point, that is, when only two points are input, the first input coordinate point is the first control point, and the second input coordinate point is the second point. However, the moving process of the second control point is performed when three or more points are input.

First, when the flow of FIG. 5 is started, the length
The calculation unit 6-2A calculates the current input coordinate point and the next next input coordinate.
Distance dist of line connecting points While seeking L, the next ward
Between (the next input coordinate point and the next next input coordinate point with respect to the present
Distance between) dist Find R (step S9-
1). That is, in FIG. 6A, the current point is [pt],
Let the next point be [pt + 1] and the next next point be [pt + 2].
Then, the tangential distance dist L is dist L = | [pt]
-[Pt + 2] |
R = | [pt + 1]-[pt + 2] |
Then, the length comparison unit 6-2B calculates d in this way.
ist L and dist Comparing the length relationship with R
On, dist L or dist R and di previously obtained
st Compare with S, dist R or dist S
Is dist Judge whether it is considerably shorter than L.
Based on this judgment result, the second control point is moved from the input coordinate point
Movable selection process of the second control point indicating how much to move
Is performed (step S9-2).

FIG. 7 shows this criterion and the corresponding criteria.
7 is a diagram showing whether a mobile type such as
(A) corresponds to the first control point, (B) corresponds to the second control point
It Here, (1), (2), (3), and (4) are figures
In (1), (2), (3), and (4) shown in (B) of 6,
Corresponding and attached, dist R and dist With S
It represents the length relationship. Also, in the figure,
Corresponding to the discrimination result (YES) and (NO) of the discriminant of
The values of "n", "ks", and "k" are
It is a specific value determined by the experiment, and according to the experiment,
“N” = 2/3, “kn” = 1 / (dist L ×
3), good results can be obtained with "k" = 1/2
It was Now, when selecting the moving type of the second control point,
t R or dist Figure depending on which one of S is short
Discrimination according to the discriminant shown in FIG.
Result, dist The length relationship with L is more than a certain ratio
If it is determined that there is a
Make a dynamic choice. That is, as shown in (3) of FIG.
To dist If R is shorter, discriminant dist R x
n <dist L? According to dist Length relation with L
If it is "NO" as a result, the mobile type
([Pt] − [pt + 2]) × k is selected, but di
st R is dist It is considerably shorter than L and "YES"
If it is determined, it is a moving type ([pt] − [pt + 2]) × d
ist R × ks is selected. On the other hand, in FIG.
As shown in (4), dist If S is shorter, the discriminant
dist S × n <dist L? According to dist
The length relationship with L is determined, and as a result, "NO"
Then, the moving formula ([pt] − [pt + 2]) × k is selected.
But dist S is dist Considerably shorter than L
If it is determined to be "YES", the moving type ([pt]-[pt]
+2]) × dist S × ks is selected.

The coordinate calculation unit 6-2C calculates the set position of the second control point based on the movement formula selected in this way. That is, the amount by which the second control point is shifted is determined according to the selected movement formula, and this is added to the above default value.
This value is the distance from the current point on the line parallel to the line connecting the current point and the next next point, and the moving position of the second control point is determined by this (step S9-
3). As described above, as a result of determining the shift amount of the second control point based on the movement formula corresponding to the determination result YES, the second control point is set to a position close to the coordinate position of the current point.

As a result, four points (start point, end point and first control point, which are necessary to draw one Bezier curve,
When the second control points) are complete, the control point generator 6-2 writes them in the bezier buffer 6-3 (step S in FIG. 3).
10). Then, the value of the coordinate sequence pointer pt is updated to specify the next input coordinate point (step S11). The completion of drawing all lines is detected based on whether or not the value of the coordinate sequence pointer pt exceeds the address for accessing the final input coordinate point stored in the coordinate sequence buffer 6-1 by updating the coordinate sequence pointer pt ( If not exceeded in step S12), the process returns to step S2, and the above operation is repeated. As a result, the next second input coordinate point is designated, but in this case, it is detected in step S5 that there is an input coordinate point before that, so the flow proceeds to step S6, and the second input coordinate point is set according to the flowchart of FIG. One control point moving process is performed.

That is, the distance dist of the line connecting the points before and after the current point While obtaining L, the previous section (the length between the current point and the previous point) dist R is calculated (step S6-1). That is, the current point is [p
If the point before [t] is [pt-1], then the tangential distance dist L is dist L = | [pt + 1]-
[Pt-1] | R is dist R = | [pt]-[pt-1] | Then, these lengths are compared with each other, and the moving type selection process of the first control point is performed (step S6-2). That is, FIG.
As shown in (1) of (B), dist If R is shorter, discriminant dist R × n <dist L? According to dist The length relationship with L is determined, and as a result,
If “NO”, ([pt + 1]-[pt-1]) ×
n mobile type is selected, but if "YES",
([Pt + 1]-[pt-1]) * dist R × ks
The mobile type is selected. Similarly, as shown in (2) of FIG. If S is shorter, discriminant dist
S × n <dist L? According to dist The length relationship with L is determined, and if the result is "NO",
A moving expression of ([pt + 1] − [pt−1]) × n is selected, but if “YES”, then ([pt + 1] − [pt]
−1]) × dist A mobile type of S × ks is selected.
The amount of displacement of the first control point is determined by the selected movement formula, and this value is added to the default value described above, so that this value is on a line parallel to the line connecting the current point and the next point. , The distance from the current point is reached, and the first control point is moved to this position (step S6-3).

By repeating the operation according to FIG. 2 until the end of the whole line, it is possible to obtain a continuous curve in which the input coordinate points are sequentially connected by a cubic Bezier curve. Here, as shown in FIG. 2, even if the input coordinate points b and a or the input coordinate points c and d are extremely close to each other, the control point on the straight line passing through the input coordinate point b or the input coordinate point c is Accordingly, since the position is designated to approach the input coordinate point b or the input coordinate point c, the overshoot as shown in FIG. 10 can be effectively suppressed, and the desired swelling with natural swelling can be achieved. Bezier curves can be drawn.

In the above embodiment, the dist R, di
st S, dist I tried to detect L and compare their length relations. Without considering the length relationship with L, simply dist R, dist The moving type of the control point may be selected based on the length relationship with S.

[0023]

According to the present invention, when a Bezier curve is generated between input coordinate points, the distance between certain input coordinate points is long and the distance between other adjacent input coordinate points is extremely short. Since the overshoot of the Bezier curve in can be effectively suppressed, it is possible to obtain the intended Bezier curve with a natural bulge, and it is possible to accurately and easily draw a continuous curve. .

[Brief description of drawings]

FIG. 1 is a block diagram of a word processor equipped with a continuous curve generator according to an embodiment.

FIG. 2 is a diagram specifically showing a drawn state of a continuous curve in which overshoot is suppressed.

FIG. 3 is a flowchart showing the operation of the continuous curve generator 6.

FIG. 4 is a flowchart showing in detail step S6 (first control point movement processing) of FIG.

5 is a flowchart showing in detail step S9 (second control point movement processing) of FIG.

FIG. 6 shows di in the first and second control point movement processing.
st S, dist R, dist The figure for demonstrating the length relation at the time of discriminating the length relation with L.

FIG. 7 shows di in the first and second control point movement processing.
st S, dist R, dist The discriminant that serves as a reference for discriminating the length relation based on the length relation with L and the moving formula selected based on the discrimination result are shown. (A) is a first control point, FIG. 6B is a diagram associated with the second control point.

FIG. 8 is a diagram for explaining a conventional example, showing a process of generating a Bezier curve.

FIG. 9 is a diagram for explaining a conventional example, showing a continuous curve generated by connecting input coordinate points with a Bezier curve.

FIG. 10 is a diagram for explaining a conventional example and is a diagram showing a continuous curve when an overshoot appears.

[Explanation of Codes] 1 main control unit 2 key operation unit 3 document memory 6 continuous curve generator 6-1 coordinate sequence buffer 6-2 control point generator 6-3 bezier buffer 6-2A length calculator 6-2B Length comparison unit 6-2C Coordinate calculation unit 7 Bezier drawing unit 8 Display control unit 9 Display device

Claims (1)

[Claims] 1. Focusing on each input coordinate point in sequence, two new control points are generated between each input coordinate point from the positions of the coordinate points located before and after the input coordinate point, and the distance between each input coordinate point is set to 3. In a continuous curve generator that generates a continuous curve by connecting the following Bezier curves, length detection means for detecting the length from each input coordinate point to the input coordinate points located before and after it, and this length The length comparison means for comparing the front and rear lengths detected by the detection means, and the shorter length when the front and rear lengths are detected to have a difference of a predetermined ratio or more by the length comparison means. And a control point setting means for setting the control point at a position close to a corresponding input coordinate point according to the height.