JPH05159036A - Method and device for plotting - Google Patents

Abstract

PURPOSE:To provide a plotting device capable of easily plotting a smooth curve. CONSTITUTION:When coordinate data is inputted from a coordinate input part 11 consisting of a mouse and the like, a sampling part 12 fetches coordinate data inputted at every prescribed time as a representative point. The coordinate of a point which is inputted from a coordinate input device with the representative point and which is near the representative point is obtained, and a vector calculation part 13 obtains the tangent vector of the representative point from coordinate data. Such a processing is executed on two representative points, and the smooth curve connecting two representative points is obtained from the obtained two representative points and tangent vector. The processing is continuously executed on the plural representative points and therefore the curve passing through the sampled representative points can be obtained. When the curve is displayed by a picture, the smooth curve can easily be plotted without being conscious of a slight blur at the time of inputting the coordinate.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a drawing method and apparatus capable of drawing a curve on a display screen with a coordinate input device such as a mouse or a tablet.

[0002]

2. Description of the Related Art In the case of a drawing device which can draw a curved line in a freehand by moving a pointer on a screen by inputting from a coordinate input device such as a mouse or a tablet, it is necessary to continuously connect the points passed by the pointer. Thus, the operator draws a curve drawn using the input device on the screen.

[0003]

However, in the above-mentioned conventional example, since the locus of the pointer is a curved line as it is, a jagged line is drawn due to camera shake or the like before the operation is accomplished, and a smooth curve is drawn well. It has the drawback of being difficult.

In order to deal with this drawback, there are drawing apparatuses which provide a tool for designating three or four points and defining one curve by the positions of these points.
To draw a curve by hitting a point impairs the ease of freehanding, and it still requires skill to draw the line you want.

The present invention has been made in view of the above-mentioned conventional example, and an object of the present invention is to provide a drawing apparatus capable of easily drawing a smooth freehand curve.

[0006]

In order to solve the above problems, the drawing apparatus of the present invention has the following structure.

A drawing device for drawing a desired line on a display screen, comprising coordinate input means for continuously inputting coordinate data,
The coordinate data input by the coordinate input means is sampled at regular intervals to obtain coordinates of sampling points, and an interpolation means for interpolating a curve smoothly connecting the sampling points. To do.

The drawing method of the present invention has the following configuration.

A drawing method for drawing a desired line on a display screen, comprising a coordinate input step of continuously inputting coordinate data,
The coordinate data input by the coordinate input means is provided with a step of sampling the coordinate data at fixed intervals to obtain coordinates of sampling points, and an interpolation step of interpolating with a curve that smoothly connects the sampling points. To do.

[0010]

With the above construction, the drawing method and apparatus of the present invention are
The input coordinate data is sampled at regular intervals. Furthermore, the sampled points are interpolated with a smooth curve to draw a smooth curve.

[0011]

【Example】

(Embodiment 1) As an embodiment of the present invention, a description will be given of a drawing device to which a Hermite interpolation curve is applied and which can be drawn by a freehand using a mouse. <Structure> FIG. 1 is a block diagram showing the structure of a drawing apparatus according to an embodiment of the present invention. In FIG. 1, the coordinate input unit 11
The coordinate data input from is sampled by the sampling unit 12 at regular intervals. Vector calculator 13
Is based on the coordinate data obtained by the sampling unit 12,
Calculate the vector at that coordinate. Curve calculator 14
Calculates an interpolation curve based on the obtained coordinates and vector, and displays the obtained curve on the display unit 15.

The appearance of the apparatus of this embodiment is as shown in FIG. In FIG. 2, the operator inputs coordinate data for freely drawing a line by using the mouse 2 while looking at the pointer 2 displayed on the display 1 displaying the drawn image. For input, the operator first positions the pointer at the point where he wants to draw and presses the mouse button. That point becomes the starting point of the curve, and when the mouse is moved (drag) while the button is pressed and the pointer is moved, the locus is displayed as a curve on the display 1. When the operator releases the mouse button, that point becomes the end point and the continuous curve input ends there. The coordinate data input while dragging the mouse is processed by the drawing device 3 including a computer, and as a result, curve data is obtained.

The drawing device configured and operated as described above can be realized by combining a CPU, a memory, and other peripheral devices and executing a program by the CPU.

FIG. 3 is a block diagram showing a configuration for that purpose. In FIG. 3, the mouse 31 is a coordinate input unit and displays the image drawn on the display 35. CP
U34 is a processing unit that controls the entire apparatus, and includes a memory 32.
Execute the program stored in. The memory 33 is used to store data to be referred to. Memory 32
The memory 33 and the memory 33 may be one memory. These are connected to each other by a bus 36. The programs stored in the memory 32 include a mouse control program 321 and a display control program 32.
2. There is a drawing control program 323. Of course, other various control programs and application programs are also stored therein, but since they are not essential to the essence of the embodiment of the present invention, description thereof will be omitted. A coordinate data memory 331 for storing sampled coordinate data, a vector data memory 332 calculated based on the coordinate data memory 333, and a curve data memory 333 are secured in the memory 33, and a work area 334 is also provided. .. Like the memory 32, this is also used in various other ways, but description thereof will be omitted. Although it is a vector data memory, since the Hermite interpolation curve is used to calculate the curve in the present embodiment, the coordinates of the sampling point and the vector of the tangent line at that point are necessary, and are provided for that purpose. ing.

Of the programs stored in the memory 32, the mouse control program 321 is for controlling the input from the mouse 31, and the display control program 322 forms image data and displays it on the display 35. This is to control the situation. The curve is calculated from the coordinate data by the drawing control program 323, which realizes the sampling unit 12, the vector calculation unit 13, and the curve calculation unit 14 in FIG. <Flowchart of Drawing Control> FIG. 4 is a flow chart showing an algorithm of the drawing control program 323, which is executed by the CPU 34.

When the operator designates an appropriate position with a pointer, first, the coordinate data is stored in the coordinate data memory 331 with the coordinate as a starting point. (S41).

After a lapse of a certain period of time, the coordinates of the pointer on the screen are sampled (this coordinate is called a point of interest) and stored in the coordinate data memory 331 (S42), and the tangent vector of the curve at that point is obtained. It is stored in the vector data memory 332 (S43). From the coordinate data thus obtained and the tangent vector data, a parametric curve connecting the point of interest and the point immediately before it is calculated (S44).

If a curve connecting the two points is obtained in this way,
An image is displayed based on it (S45.

With the above procedure, a curve from the starting point to the next sampling point can be drawn. After this, it is tested whether it is the end point, that is, whether the mouse button has been released (S46), and if it has been released, the process ends. If it is not separated, the coordinates of the pointer are sampled after a certain period of time from the immediately preceding sampling, and a parametric curve that connects the immediately preceding attention point is drawn with this as a new attention point. This is repeated until the end point. <Curve Calculation Processing> Now, the apparatus of the present embodiment is smooth along the locus of the mouse pointer on the screen from the point where the mouse button is pressed (start point) to the point where the mouse button is released (end point). It draws a curve. Therefore, the following method is used to calculate the curve from the coordinates of the sampled points.

In the apparatus of the present embodiment, a cubic curve called Hermite interpolation curve is used as a parametric curve connecting between the point sequences sampled at a constant time interval T.

Since there are four boundary conditions (two points and a tangent vector at each point), it would be a natural idea to connect two points with a cubic curve having four unknown coefficients. In addition, studies on outline fonts have confirmed the usefulness of a cubic curve as a smooth curve connecting two points.

Since the Hermite interpolation curve is determined by the coordinates of two points and the tangent vector at those points, if the drawing apparatus has a sufficiently high calculation capability, it is possible to display the curve in near real time. is there. The Hermite interpolation curve is calculated by the following calculation. It should be noted that the sampling interval T in the description may be experimentally determined to be an optimum value for an actual device, or may be determined according to user preference.

As shown in FIG. 5, the coordinates of the two points to be connected by the Hermite interpolation curve are: P [n] = (x [n], y [n]) P [n + 1] = (x [n + 1] , Y [n + 1]) and the tangent vectors at both points are V [n] = (r [n], s [n]) V [n + 1] = (r [n + 1], s [n + 1]) ..

The Hermite interpolation curve connecting these two points is
It is expressed as follows using k as a parameter.

C (k) = (f (k), g (k)), 0 ≦ k ≦ 1 (1) (2) collectively equation to be written as _{C (k) = A 3 k} 3 + A 2 k 2 + A 1 k + A 0 ... (3).

First, from the conditions of both ends P [n] and P [n + 1], C (0) = A ₀ = P [n] (4) C (1) = A ₃ + A ₂ + A ₁ + A ₀ = P [ n + 1] (5).

The tangent vector on the curve is C '(k) = dC / dk = 3A ₃ k ² + 2A ₂ k + A ₁ (6), so C' (0) = A ₁ = V [n] (7) C ′ (1) = 3A ₃ + 2A ₂ + A ₁ = V [n + 1] (8)

Solving equations (4), (5), (7) and (8), Next, the curve C (k) is, C (k) = (2P [n] -2P [n + 1] + V [n] + V [n + 1]) k 3 + (- 3P [n] + 3P [n + 1] -2V [n ] −V [n + 1]) k ² + V [n] k + P [n], 0 ≦ k ≦ 1 (10)

A point P [n] (n = 0, 1, ...,
m) is obtained by sampling and storing the coordinates of the mouse pointer.

On the other hand, the tangent vector at the point P [n] is obtained as follows.

As shown in FIG. 6, the point P [n] is set at a time interval Td (for example, 1/100 second) much shorter than the time interval T (for example, 1/10 second) for sampling the point P on the curve.
The pointer coordinates Qb [n] and Qa [n] immediately before and immediately after are sampled. The vector connecting these two points Qb [n] and Qa [n] is the tangent vector at the point P [n]. That is, V [n] = (Qa [n] -Qb [n]) / (2Td / T) (11).

Since the limit of Td → 0 is the definition of the tangent vector at the point P [n] itself, the value of equation (11) becomes sufficiently close to the true tangent vector if Td is made sufficiently small.

From the above, each point on the curve and the tangent vector at those points can be obtained, and the Hermite interpolation curve can be drawn by the equation (10).
Since the value of Qa [m] cannot be obtained at [0] and the end point, there remains a problem of how to define the tangent vector at the start point P [0] and the end point P [m] of the curve.

In order to solve this, the present embodiment introduces a condition that the curvature at the start point and the end point is 0 (the value of the second derivative of the curve C is 0).

Since C ″ (k) = dC ′ / dk = 6A ₃ k + 2A ₂ (12), in the case of the curve from the starting point P [0] to P [1], C (0) = A ₀ = P [0] (13) C (1) = A ₃ + A ₂ + A ₁ + A ₀ = P [1] (14) C ″ (0) = 2 A ₂ = 0 (15) C ′ (1) = From 3A ₃ + 2A ₂ + A ₁ = V [1] (16), Next, P [0] is equivalent to curve up P [1] from the C (k) = {(P [0] -P [1] + V [1]) / 2} k 3 + {(- 3P [0] + 3P [1] −V [1]) / 2} k + P [0], 0 ≦ k ≦ 1 (18)

In the case of the end point, the problem becomes a little complicated. This is because the timing at which the mouse button is released is not necessarily exactly after the time T (sampling interval) from the sampling point immediately before that.

Therefore, in the present embodiment, the sampling point immediately before the time when the mouse button is released is defined as the end point P [m], and the curvature there is set to 0, and P [m-1] to P [m].
I decided to draw a curve up to.

The reason why the curvature at the end point is 0 is that the timing at which the mouse button is released is unpredictable as described above, so that the point Qa [m] after the time Td from the end point P [m] is always sampled. This is not always possible, and the tangent vector cannot be obtained by the equation (11).

[0039] Now, the case of the curve from the P [m-1] to _{P [m], C (0} ) = A 0 = P [m-1] ... (19) C (1) = A 3 + A 2 + A ₁ + A ₀ = P [m] (20) C ′ (0) = A ₁ = V [m−1] (21) C ″ (1) = 6A ₃ + 2A ₂ = 0 (22) Next, P is the curve from [m-1] to P [m] C (k) = {(P [m-1] -P [m] + V [m-1]) / 2} k 3 + {3 (-P [m-1] + P [m] -V [m-1]) / 2} k 2 + V [m-1] k + P [m-1], is given by 0 ≦ k ≦ 1 ... (24 ) ..

As described above, equations (10) and (18)
By obtaining a smooth curve along the locus of the mouse pointer by the formulas and (24) and drawing it on the screen, it is possible to realize a drawing device that can easily draw a smooth curve.

The coordinate input device may be any device other than a mouse that can continuously input coordinates, and for example, a digitizer or a tracking ball may be used.

[0042]

[Other Embodiments] (Embodiment 2) As a second embodiment, a description will be given of a drawing apparatus which devises a method of obtaining a tangent vector at a start point and an end point, and draws all curves only by the expression (10) in the above first embodiment. ..

First, regarding the tangent vector at the starting point P [0], as shown in FIG. 7, a time interval Td ₁ (for example, 1/100 second) that is much shorter than the sampling time interval T (for example, 1/10 second). ), The coordinate Qa [0] of the mouse pointer immediately after P [0] is sampled, and P [0] and Qa
The vector connecting [0] is the tangent vector at the starting point.
That is, V [0] = (Qa [0] −P [0]) / (Td ₁ / T) (31).

Next, the tangent vector at the end point P [m] is obtained.

Similar to the first embodiment, the sampling point immediately before the mouse button is released is defined as the end point P [m].

As in the case of the starting point, a time interval T much shorter than the sampling time interval T (for example, 1/10 second).
The coordinate Qa [m] of the mouse pointer immediately after P [m] is sampled at d ₂ (for example, 1/100 second), and the vector connecting P [m] and Qa [m] is set as the tangent vector at the end point. This state is shown in FIG.

That is, V [m] = (Qa [m] -P [m]) / (Td ₂ / T) (32).

At this time, even if the mouse button is just released at the point P [m], the tangent vector at the end point is defined by sampling the coordinates of the pointer to obtain Qa [m].

By defining the tangent vectors at the start point and the end point as described above, the curves P [0] to P [1] and the curves P [m-1] to P [m] are specially defined. It is not necessary to handle it, and it becomes possible to draw the entire curve only with the equation (10).

Further, in this embodiment, the point P on the curve is
For the tangent vector in [n], the device is simplified by adopting the same calculation method as the start point and the end point. That is, in the first embodiment, the point Qb [n] immediately before P [n] is not sampled, and P [n] and Qa are not sampled.
The vector connecting [n] is the tangent vector at the point P [n].

That is, V [n] = (Qa [n] -P [n]) / (Td / T) (33).

Since it is a smooth curve to be drawn, the values of the equations (11) and (33) when Td → 0 are the same.

If Td is made sufficiently small, the tangent vector may be defined by the equation (33).

Further, by making the values of Td, Td ₁ and Td ₂ the same, it is possible to unify the method of obtaining the tangent vector at all points on the curve.

As described above, by unifying the method of obtaining the tangent vector at all points and the method of drawing the curve in all the sections connecting the points, the drawing algorithm is simplified and the apparatus is simplified. You can

(Embodiment 3) When drawing a freehand curve with a mouse, there may be a time delay from when the mouse button is pressed until the mouse starts to move.

In the second embodiment, this time delay is T
If it is larger than d ₁ , the tangent vector at the starting point becomes 0. Further, even if the time delay is smaller than Td ₁ , the tangent vector at the start point is evaluated smaller than it actually is.

As described above, if there is a time delay, a curve different from the intended curve may be drawn.

If the sampling time interval T is sufficiently small, the deformation of the curve due to this time delay is so small that it can be ignored on the screen, but if it is not, some measure is required.

In the second embodiment, in order to deal with the problem of the time delay, the starting point is defined as follows.

The mouse normally converts the movement amount in two directions (x, y) into a pulse train by an encoder and transmits the pulse train to the drawing device,
The drawing device moves the pointer on the screen according to the number of the pulses.

Therefore, the point at which the total sum of the pulses sent after the mouse button is pressed is a fixed value S (for example, 5) or more is defined as the starting point, and the drawing of the curve is started from that point. I decided to avoid the problem of delay.

Here, the value of S is the resolution of the mouse (the number of pulses with respect to the moving distance) so that the start point defined as described above and the point where the mouse button is actually pressed are sufficiently close on the screen. It shall be appropriately determined in consideration of the above.

As described above, even if there is a time lag between when the mouse button is pressed and when the line is actually started,
It is possible to realize a drawing device that can draw a curve as intended by the operator.

The present invention may be applied to a system composed of a plurality of devices or an apparatus composed of a single device. Further, it goes without saying that the present invention can be applied to the case where it is achieved by supplying a program to a system or an apparatus.

[0066]

As described above, the drawing method and apparatus according to the present invention has an effect that anyone can easily draw a smooth freehand curve.

[Brief description of drawings]

FIG. 1 is a block diagram of a drawing apparatus according to an embodiment of the present invention.

FIG. 2 is an external view of a drawing apparatus according to an embodiment.

FIG. 3 is a block diagram of a drawing apparatus according to an embodiment.

FIG. 4 is a flow chart showing a curve drawing algorithm.

FIG. 5 is a drawing showing a smooth cubic curve connecting two points.

FIG. 6 is a diagram showing how to obtain a tangent vector in the first embodiment.

FIG. 7 is a diagram showing a method of obtaining a tangent vector of a starting point in the second embodiment.

FIG. 8 is a diagram illustrating a method of obtaining a tangent vector at an end point according to the second embodiment.

─────────────────────────────────────────────────── ─── Continuation of the front page (51) Int.Cl. ⁵ Identification code Office reference number FI technical display location G09G 5/20 8121-5G 5/36 8121-5G

Claims (7)

[Claims] 1. A drawing apparatus for drawing a desired line on a display screen, wherein coordinate input means for continuously inputting coordinate data, and coordinate data input by the coordinate input means are sampled at regular intervals. And a means for obtaining the coordinates of the sampling points, and an interpolating means for interpolating with a curve smoothly connecting the sampling points. 2. The interpolation means comprises calculation means for calculating a tangent vector at the sampling point, obtains a Hermitian interpolation curve based on the coordinate data of the sampling point and the tangent vector, and interpolates with the curve. The drawing apparatus according to claim 1, wherein: 3. The calculation means obtains coordinate data of two points, a point immediately before and a point immediately after the sampling point, and sets a vector connecting the two points as a tangent vector. Drawing device. 4. The calculating means obtains coordinate data of a point immediately after the sampling point, and sets a vector connecting two points of the sampling point and the point immediately after as a tangent vector. 2. The drawing device according to 2. 5. The drawing apparatus according to claim 2, wherein at the first sampling point and the last sampling point of continuously drawn lines, the curvature is regarded as zero and interpolation is performed. 6. A drawing method for drawing a desired line on a display screen, comprising: a coordinate input step of continuously inputting coordinate data; and sampling of coordinate data input by the coordinate input means at regular intervals. And a step of obtaining the coordinates of the sampling points, and an interpolation step of interpolating with a curve that smoothly connects the sampling points. 7. The interpolation step includes a calculation step for calculating a tangent vector at the sampling point, a Hermite interpolation curve is obtained based on the coordinate data of the sampling point and the tangent vector, and the curve is interpolated. The drawing method according to claim 6, further comprising: