JP3166875B2 - Arc calculation method for curve section input of figure processing device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION The present invention relates to a method for inputting a figure such as a map as coordinate data by means of a figure input device, storing the input coordinate data as digital data in a storage device, forming a database, and using the stored data. The present invention relates to a method for calculating a circular arc in a curve processing input of a graphic processing device such as a so-called computer mapping system, which is displayed on a display device or displayed on an output device in accordance with the method.

[0002]

2. Description of the Related Art In a mapping system, when a figure drawn on a paper such as a map is input using a figure input device such as a digitizer, a line segment input operation and a curve portion input operation are performed. is necessary. For example, when inputting a map, the sidewalk edge near the intersection is drawn as a curve corresponding to the actual shape, and an input operation corresponding to the curved portion is required. For example, in a mapping system that uses a map with a scale of about 1/500 for input, the width of the sidewalk
If it is 2 m, the curved portion on the map corresponding to the sidewalk edge is only about 4 mm, and input work corresponding to such a curved portion is required.

Conventionally, a curve portion is input by a method schematically shown in FIG. That is, when inputting a line as shown in FIG. 10, the operator firstly enters a line segment L1 reaching the curved portion L2.
Is moved to the start point p1 and the end point p2, and the coordinates of the start point p1 and the end point p2 of this line segment are input as data of the line segment L1. Next, the curve portion L2 from the end point p2 of the line segment L1 to the start point p8 of the next line segment L3 is equally divided into a predetermined number by the amount of a rule, and the positions P3, P
The input cursor is sequentially moved to 4, P5, P6, and P7, and their coordinates are sequentially input. Then, the input cursor is sequentially moved to the start point p8 and the end point p9 of the line segment L3, and their coordinates are input as data of the line segment L3. In this manner, the curved line portion L2 is input as a set of line segments from the position p2 to the position p8 via the p3, p4, p5, p6, and p7 sequentially.

[0004]

However, such a conventional input method has the following problems. a. Since the curved portion is equally divided by the amount of the eye, the lengths of many line segments constituting the curved portion are not uniform. b. In general, the width of a line drawn on the paper is 0.2 mm or more, and the input accuracy of a digitizer or the like is about 0.2 mm. Become. The irregularities of about 0.5 mm are often ignored as not being large in absolute value, but are relatively large for an arc having a radius of about 4 mm.
It doesn't look good despite struggling with typing.

By the way, in the above-mentioned mapping system in which input is performed using a map of a scale of about 1/500, if the width of the sidewalk is 2 m, the curved portion on the map corresponding to the sidewalk edge is Since it is only about 4 mm, this can be approximated as a circular arc, but there is no problem in practical use.
The present invention has been made in view of such a point, and aims at solving the above-mentioned problems.

[0006]

Means for solving the above problems will be described. First, in the invention according to claim 1, a figure input device for inputting a figure as coordinate data,
In a graphic processing device provided with a storage device for storing a graphic based on the input coordinate data, and a coordinate processing device interposed between the graphic input device and the storage device, the coordinate processing device includes a curve portion of the graphic. Is provided, an arc calculating means for calculating an arc approximating the curved part is provided, and the arc calculating means receives coordinate data of a line segment located before and after the curved part to be inputted, and, based on the coordinate data,
These new endpoints are calculated by calculating these new endpoints so that the value obtained by dividing the sum of the distances between the intersections of the line segments and the endpoints on the intersection side of each line into two equals the distance between the intersections and the new endpoints. And proposes a method of calculating a circular arc at the input of a curve part of a graphic processing apparatus in which a circular arc tangent to these new end points is calculated, and the circular curve is approximated by the circular arc. It is.

According to the second aspect of the present invention, an arc calculating means is provided.
Is the coordinate data of the line segment before and after the curve to be input.
Data and the coordinates of one point on the desired arc are input.
And a tentative arc passing through the three points on the intersection side of each line segment
To calculate the radius, and the coordinate data of the line segment
From the intersection of the line segment and the angle formed by the line segment passing through it
Calculate the bisector of the degree, have a center on this bisector,
The arc is calculated as having the radius of the temporary arc.
A configuration that approximates the above-mentioned curved portion with this arc;
As well as the line segment that is in contact with this arc
A diagram that calculates data as points and changes line segment data
Proposal of arc calculation method for curve part input of shape processor
Is what you do.

[0008]

According to the first aspect of the present invention, in the operation of inputting a graphic as coordinate data by the graphic input device, when inputting a curved portion, the arc calculating means of the coordinate processing means applies the line segment on both sides to The curved portion is approximated by a predetermined arc that touches the curved portion.

According to a second aspect of the present invention, in the above-described input operation, the arc calculating means of the coordinate processing means determines that the radius of the arc passing through the end point of the line segment on both sides and one point designated by the input is equal. The curved portion is approximated by an arc tangent to the line segment on both sides.

The arc approximated by each of the above methods is stored as the arc itself based on the data of its center position, radius, start angle and end angle, and is divided into a plurality of equal-length chords by an appropriate line data conversion method. Then, the set of coordinates of these strings can be stored in the storage device.

[0011]

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows an embodiment of the present invention including a conventional example.
explain about. First, FIG. 1 conceptually shows the configuration of a graphic processing device to which the arc calculation method of the present invention is applied. Reference numeral 1 denotes a graphic input device such as a digitizer, 2 denotes a cursor, and 3 denotes a map placed on a tablet. The figure drawn on this drawing 3 is designated as a position by the cursor 2 and input as coordinate data. Reference numeral 4 denotes a storage device such as a magnetic disk.
Is stored in the storage device 4.
Is stored. Coordinate processing means 5 is interposed between the graphic input device 1 and the storage device 4, and the coordinate processing means 5 is provided with an arc calculation means 6 to which the method of the present invention is applied.

Further, in the graphic processing apparatus of this embodiment, in order to easily perform affine transformation of the stored coordinate data, the circular arc is used as the circular arc itself, that is, the center position and the radius as described above. , But not as data of the start angle and the end angle, but as an aggregate of many continuous line segments. For this purpose, the coordinate processing means 5 is provided with a line data conversion means 7 for processing the data of the arc calculated by the arc calculation means 6 and converting the data into line data.

A plurality of graphics processing apparatuses having the above configuration are connected and controlled by a common host computer, but components such as the host computer are not shown.

In the above configuration, when the graphic input device 1 performs the input operation of the graphic drawn on the drawing 3,
In the input of the line segment, the coordinate processing means 5 does not operate the arc calculating means 6 and the line data converting means 7, so that the coordinate data of the start point and the end point of the line segment inputted by the cursor 2 are not changed. Or through appropriate processing such as coordinate conversion corresponding to the position, angle, and expansion / contraction, and the storage device 4 together with the attribute.
Is stored.

Meanwhile, the at the input of the curved portion coordinate processing means 5 operates the arc calculation means 6 and the line data means 7, according to an instruction from 2 like cursor, the arc calculation means 6 First, as described above Referring to the coordinate data of the line segment located on both sides of the curve to be input, an arc approximating the curve is calculated, and the calculated arc is divided into a plurality of equal-length chords by the line data converting means 7. Then, the respective coordinates are calculated. Then, the coordinate data of the curved portion is output as a set of the coordinates of these strings, and stored in the storage device 4. Therefore, the specific operation of the arc calculation method in the arc calculation means 6 and the line data conversion method in the line data conversion means 7 will be described below with reference to flowcharts and schematic diagrams.

FIG . 2 is a flow chart showing the specific operation of the arc calculation method according to the first aspect together with the operation of the line data conversion means 7. The steps enclosed by "6 ｛" are the operation of the arc calculation means 6, and Steps enclosed by “7 °” correspond to the operation of the line data conversion unit 7. 3 and 4 are schematic diagrams showing the respective operations. First, the operation of the arc calculation means 6 will be described with reference to FIGS.

Firstly in step S101, the front and rear of the line segment AB of the curve portions, CD is input. Line segments AB and CD before and after this
Are the coordinates of A, B, C, and D in FIG. 3, (Xa, Y
a), (Xb, Yb), (Xc, Yc), and (Xd, Yd).
In step S101 or steps before and after this step,
The command corresponding to the input of the curve portion is appropriately given by the graphic input device 1.
To the coordinate processing means 5.

[0018] In step S102 and then, calculates the coordinates of the front and rear of the line segment AB, the intersection of the CD P (Xp, Yp). This intersection P
Can be calculated, for example, by solving the following simultaneous equations. (Xa-Xb) Yp + (Yb-Ya) Xp + YaXb-XaYb = 0 (Xc-Xd) Yp + (Yd-Yc) Xp + YcXd-XcYd = 0

[0019] In step S103 Next, each line segment AB, the new two-point B in contact with the circle at the CD ', C' coordinates (Xb ', Y
b ′) and (Xc ′, Yc ′) are calculated. The value obtained by dividing the sum of the distances between the intersection points P and the end points B and C on the intersection point P side of each input line segment by two into two is the distance between the intersection points P and the new end points B 'and C'. It is calculated so that That is, PB '= PC' = (pb + pc)
Calculate the end points B 'and C' that are / 2. This is L ₁ = PB, L ₂ = C
Assuming that P and L = (L ₁ + L ₂ ) / 2, the following equation can be obtained. Xb ′ = (L / L ₁ ) (Xb−Xp) + Xp Yb ′ = (L / L ₁ ) (Yb−Yp) + Yp Xc ′ = (L / L ₁ ) (Xc−Xp) + Xp Yc ′ = (L / L ₁ ) (Yc-Yp) + Yp

[0020] Next, at step S104, the end point B calculated at step S103 ', C', and registered as the end points of each line segment,
Hereinafter, the line segment sandwiching the curved portion is changed to AB ', C'D and handled.

Next, in step S105, the above-mentioned end point
A perpendicular is drawn from B 'and C', and the coordinates of the intersection O (X ₀ , Y ₀ )
And the distance from the end points B 'and C' to the intersection O, that is, the end point
The radius R of the circle tangent to the line segments AB 'and C'D in B' and C 'is calculated. The coordinates (X ₀ , Y ₀ ) of the intersection O can be calculated, for example, by solving the following simultaneous equations: (Ya−Yb ′) Y ₀ + (Xa−Xb ′) X ₀ − (Ya− Yb ') Yb'-(Xa-X
b ′) Xb ′ = 0 (Yc′-Yd) Y ₀ + (Xc′-Xd) X _0- (Yc′-Yd) Yc ′-(Xc ′
-Xd) Xc ′ = 0 The radius R can be calculated using the Pythagorean theorem shown by the following equation. R ² = (Xb′-X ₀ ) ² + (Yb′-Y ₀ ) ²

[0022] Through the steps S101~S105 explained above, an arc that approximates the curved portion is calculated. In the arc calculation method including these steps, regarding the input of the curved portion, the input corresponding to the curved portion is unnecessary, and only the coordinates of the end point need to be obtained, and these coordinates are obtained by inputting the line segment. Therefore, the input operation is simple.

Next, subsequently 2, the operation of the line data means 7 by FIG. First, in step S106, whether the point D is on the left side with respect to the vector AB '
Determine if it is on the right. At this time, when it is on the left side, θ0 described in FIG. 4 is positive, and when it is on the right side, it is negative. This determination method is, for example, when F = (Ya-Yb ') Yd- (Xa-Xb') Xd + YaXb-XaYb, and when the value of SGN (F) × SGN (Ya-Yb) is positive, There is a point D, and when it is negative, it can be determined that it is on the right side. SGN is a function that displays only positive and negative signs.

[0024] is in step S107 and then, calculates the arc angle theta _0. The angle θ ₀ can be obtained by the following equation using the cosine theorem of a trigonometric function. | θ ₀ | = arccos [1-{(Xb′-Xc ′) ² + (Yb′-Yc ′) ² } / 2R
² ] Accordingly, when shown together with the positive / negative judgment in step S106, the arc angle θ ₀ can be expressed as the following equation. θ ₀ = SGN (F) × SGN (Ya-Yb) · | θ ₀ |

[0025] Next, at step S108, the system of coordinates of the reference, for example, the relative X-coordinate, arc start angle θs
Is calculated by the following equation. θs = arctan {(Yb'-Y ₀ ) / (Xb'-X ₀ )}

[0026] Then entering the division number n of the arcs at step S109. The input of the division number n can be performed at an appropriate step preceding this step S109, for example, at an appropriate place such as step S101, or between step S105 and step S106.

[0027] Then in step S110, based on the value calculated at the above step, and calculates the coordinates of each string by the following equation. That is, assuming that Δθ = θ ₀ / n, the coordinates (Xqi, Yqi) of the i-th (where i = 1 to n−1) chord are calculated by the following equations, respectively. Xqi = cos (θs + iΔθ) + X ₀ Yqi = cos (θs + iΔθ) + Y ₀

[0028] Through the above steps S106 to S110, the division number n of the arc that approximates the curved part, entered
Can be divided into a plurality of equal-length strings, and a set of coordinates of these strings can be calculated. In the operation of the line data converting means 7 of this embodiment, the number of divisions n is designated by input as described above, but the number of divisions n can be set in advance as appropriate. It is also possible to automatically determine the number of divisions n according to the radius R of the arc calculated by the arc calculating means 6.

FIG . 5 is a flowchart showing the specific operation of another arc calculation method having steps common to the embodiment corresponding to the arc calculation method of the present invention described later, and FIG. 6 shows the operation. It is a schematic diagram represented.

[0030] In First in step S201, step S1
Input the line segments AB and CD before and after the curve part in the same way as 01.

[0031] Then in step S202 inputs the dimensions that are listed numerically on the drawing as the radius R of the curved portion.

[0032] then is in step S203, step
Similarly to S102, the coordinates of the intersection P (Xp, Yp) of the front and rear line segments AB and CD are calculated.

Next, in step S204, step
A bisector of the angle formed by the line segments AB and CD passing through the intersection point P calculated in S203 is calculated. The bisector is, for example line segments in PD line PB = C "P become the point C" in the coordinates (Xc ", Y c") seeking can be obtained by the following equation. _{(X 0 '-Xp) Y +} (Yp-Y 0') X + Y 0 'Xp-X 0' Yp = 0 _{where, X 0 '= (Xb +} Xc ") / 2, Y 0' = (Yb + Yc ″) / 2.

Next, in step S205, the above-mentioned step S2
On the bisector calculated in 04, the coordinates (X ₀ , Y ₀ ) of the center of the circle having a radius R in contact with the line segment AP and the contact points on the line segments AB and CD, respectively
The coordinates (Xb ', Yb') and (Xc ', Yc') of B 'and C' are calculated, and the end points B 'and C' are registered as the end points of each line segment. Line segments are changed to AB 'and C'D. These coordinates are, for example, the coordinates (X ₀ ″, Y ₀ ″) of the center of the circle tangent to the point B on the bisector and the radius
R ′ can be calculated by the same method as in step S105, and thereafter, can be calculated by a proportional relationship.

[0035] the circular arc calculated to approximate the curve portions Through the above steps S201 to S205, in the case where the radius of the curved portion on the drawing 3 is described as a number the arc calculation method, exact You can make input.

[0036] Next Fig. 7 in a manner similar to that other above, after
Common to the embodiment corresponding to the arc calculation method of the present invention described below
FIG. 8 is a flowchart illustrating a specific operation of another arc calculation method having steps , and FIG. 8 is a schematic diagram illustrating the operation.

[0037] First, in step S301 step S1
Similarly to 01, the line segments AB and CD before and after the curved portion are input, and the coordinates (Xe, Ye) of one point on the arc corresponding to the curved portion to be input are input.

[0038] then calculates the center O of the coordinates of a circle having an arc CEB step _{S302 (X 0, Y 0)} . For the coordinates of the center of the circle, for example, first, the coordinates (Xf, Yf) and (Xg, Yg) of the midpoints F and G of the line segments BE and EC are obtained, and the perpendicular passing through these midpoints is obtained. Can be obtained as the intersection of the perpendiculars.

[0039] That is, the perpendicular OF, OG is expressed by the following equation, by solving the simultaneous equations, the center O of the polar coordinate (X _0, Y
₀ ) can be calculated. (Ye-Yf) Y + (Xe-Xf) X- (Ye-Yf) Yf- (Xe-Xf) Xf = 0 (Ye-Yg) Y + (Xe-Xg) X- (Ye-Yg) Yg- (Xe -Xg) Xg = 0 Then, in step S303, the radius R of the circle can be obtained by using the Pythagorean theorem as described above.

[0040] the circular arc calculated to approximate the curve portions Through the above steps S301 to S303, this arc calculation method, the front and rear of the line segment AB, CD of the curved portion, the coordinate data is processed as it is entered You. In this arc calculating means 6, an appropriate curved portion which does not touch the line segment can be input.

Next, FIG. 9 is an arc calculated according to claim 2 of the present invention
5 is a flowchart illustrating a specific operation of the embodiment corresponding to the method . The arc calculation means 6 receives coordinate data of a line segment located before and after a curve portion to be input and coordinates of a point on a desired arc, and calculates three points of this one point and an end point on the intersection side of each line segment. The above-mentioned claim 3 until the calculation of the passing arc.
Through the same steps as the circular arc calculating means 6.

[0042] That is, step S401, S402, S403 are the same as each step S301, S302, S303. However, the circular arc obtained through the above steps is a temporary circular arc for calculating the radius of the circular arc approximating the curved portion, and this circular arc does not approximate the curved portion.

[0043] Then, in the arc calculation method, step
The coordinate data of the line segment input in S401 and step S4
From the radius obtained in 03, an arc is obtained through the same steps as in the above-described arc calculation method shown in FIG . That is, steps S404, S405, and S406 are performed in steps S203, S204, and S205, respectively.
Is the same as

The arc calculation method described above is troublesome because another point must be input in addition to the coordinates of the end point of the curved portion.
This corresponds to the above-described invention of claim 1 and the method shown in FIG.
There is an advantage that it can be performed more accurately for the operator's intention as compared with the above.

[0045] As described above, the arc approximated by the method described above, the center position, the radius, the data of the start angle and end angle, other stored as arc itself, multiple equal by appropriate line data Method It can be divided into long strings and stored in a storage device as a set of coordinates of these strings. In the latter case, there is an advantage that the affine transformation of the coordinate data can be easily performed.

[0046]

As described above, according to the present invention, a curve portion drawn as a curve corresponding to an actual shape on a map or the like is approximated as an arc and converted into coordinate data. It is easy and has the effect of good appearance.

Each of the claimed inventions has the following effects. First, according to the first aspect of the present invention, it is possible to input an arc that is in contact with a line segment by a simple input operation. According to the second aspect of the present invention, the input of the arc tangent to the line segment is
Compared to the other methods described above,
It can be done more accurately.

[Brief description of the drawings]

FIG. 1 is an explanatory diagram conceptually showing the configuration of a graphic processing apparatus to which the method of the present invention is applied.

FIG. 2 shows a specific operation of an embodiment corresponding to the arc calculating method according to claim 1 of the present invention, and the arc calculated by this method is divided into a plurality of equal-length chords by a line data converting means and converted into data. 4 is a flowchart illustrating a specific operation of the embodiment of the method.

FIG. 3 is a schematic diagram showing an operation of an arc calculation method in the embodiment shown in FIG. 2;

FIG. 4 is a schematic diagram showing an operation of a line data converting means in the embodiment shown in FIG. 2;

FIG. 5 is an arc calculation method having steps common to the present invention .
It is a flowchart showing the specific operation of the method.

FIG. 6 is a schematic diagram showing the operation of the example shown in FIG.

FIG. 7 shows another arc calculation having steps common to the present invention .
It is a flowchart showing the specific operation of the output method .

FIG. 8 is a schematic diagram showing the operation of the example shown in FIG. 7;

FIG. 9 is a flowchart showing a specific operation of the embodiment corresponding to the arc calculating method according to claim 2 of the present invention .

FIG. 10 is a schematic diagram showing a conventional method of inputting a curved portion.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Graphic input device 2 Cursor 3 Drawing 4 Storage device 5 Coordinate processing means 6 Arc calculation means 7 Line data conversion means

Continuation of the front page (58) Field surveyed (Int.Cl. ⁷ , DB name) G06T 11/20 110 G06T 11/60 300 G06T 11/80 G09G 5/20

Claims (2)

(57) [Claims] 1. A graphic input device for inputting a graphic as coordinate data, a storage device for storing a graphic based on the input coordinate data, and a graphic processing device interposed between the graphic input device and the storage device. In the processing equipment,
The coordinate processing means is provided with an arc calculating means for calculating an arc approximating the curved part when inputting the curved part of the figure, and the arc calculating means comprises a line segment positioned before and after the curved part to be inputted. With the coordinate data as input, a value obtained by bisecting the sum of the distance between the intersection of the line segment and the end point on the intersection side of each line segment from the coordinate data is the distance between the intersection and the new end point. A graphic processing apparatus characterized in that these new endpoints are calculated to change line segment data, an arc tangent to these new endpoints is calculated, and the above-described curved portion is approximated by the arc. Arc calculation method in curve part input 2. A graphic input for inputting a graphic as coordinate data.
And a device for storing figures based on input coordinate data.
Storage device, and the graphic input device and the storage device.
In a graphics processing device with coordinate processing means interposed between
This coordinate processing means is used when inputting the curved part of a figure.
To calculate an arc approximating this curved part
Steps are provided, and the arc calculation means is provided before and after the curve portion to be input.
Coordinate data of the line segment located at
With the mark as input, this one point and the 3
Calculate a temporary arc passing through a point and calculate its radius.
Then, based on the coordinate data of the line segment,
Calculate the bisector of the angle formed by the above line segment,
It has a center on the bisector and has the radius of the provisional arc
The arc is calculated as
A part that approximates the part and a line that touches this arc
Is calculated as the new end point of the line
Curve portion input of graphic processing device characterized by changing
Calculation method for arc