JPH0949724A - Figure-measuring apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a figure-measuring apparatus which calculates an area of an arc part or the like only by measuring coordinates of both ends and a middle point of the arc part in a closed figure. SOLUTION: The figure-measuring apparatus consists of a main body 1 having a roller 5 linearly movable in one direction, and a measuring rod 2 having a trace part 6 and a point key 9 at a front end. The measuring rod 2 is rotatable on a horizontal plane in a right/left direction to the main body 1. The measuring rod 2 is provided with an arc key 8. Since the trace part 6 presses the point key 9 at a start point of an arc part, the arc key 8 at a middle point and the point key 9 at a final point, an area of the arc part, etc., is calculated.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a graphic measuring device for measuring graphic parameters such as the area, the first moment of area and the length of a planar graphic, and the centroid coordinates by tracing the contour of the planar graphic. Regarding

[0002]

2. Description of the Related Art Conventionally, in the case of a linear figure as shown in FIG.
The centroid is divided into known triangles (abg, bgf, bfh) and rectangles (cdeh) including squares, the first moment of area is calculated individually from each area and centroid, and the linear moments (agfedchba) are summed up. ) Was calculated by dividing by the area.

Further, in the case of a figure having a curved contour as shown in FIG. 4, there is no choice but to divide the figure into a large number of triangles and obtain the centroid by the above method. However, FIG.
In the case of a straight line like
As the number of edges increases, the amount of calculation work also increases, which requires a long time.

Further, in the case of FIG. 4, since it is an approximate method originally, it is difficult to expect correctness, and it is necessary to subdivide the division in order to approach the correct value. It is impossible by work.

In order to solve these problems, the present applicant has proposed a previously improved device as Japanese Patent Application No. 4-208013.
Proposed issue. This is a main body 1 provided with a roller 5 which can travel in a straight line direction, a main body 1 which is pivotally supported by the main body 1 so as to be rotatable in the left-right direction on a horizontal plane with respect to the traveling direction of the main body 1, and a trace portion 6 on the tip side. Also, in the figure measuring device provided with the measuring rod 2 equipped with the point key 9 for inputting the current coordinate values of the tracing section 6, the main body 1 is provided with the display device 3, the input device 4 and the calculating means, and the measuring rod 2 At the same time as the operation of tracing and measuring the coordinates, area, length, etc. in the trace part 6 of, the calculating means successively calculates the first moment of area required for the centroid calculation, and finally, the total first moment of area in the area of the target figure. Is calculated to calculate the centroid coordinates, and the display device 3 displays the difference between the coordinates of the current position of the mark needle 7 close to the trace section 6 and the centroid coordinates, and the mark is made so that this display becomes zero. By moving the needle 7, the mark needle 7 A centroid coordinate measuring device configured to be positioned in the centroid coordinates.

The theory used in this conventional improved device will be described by taking the figures of FIGS. 5 and 6 as an example. The first moment of area Mx with respect to the x-axis is

[Equation 1] It is represented by

The y coordinate of the centroid is divided by the area A of the area D.

[Equation 2]

Similarly, the x coordinate of the centroid is

(Equation 3) Is defined as

Here, the first moment of area M _x is

(Equation 4) It can be expressed as Here, the union of the areas D and E is zero. This means that the difference becomes the first moment of area of the area D if the first moment of area of the small area E is subtracted from the first moment of area of the large area (D + E) without directly obtaining the first moment of area of the area D. Means If the first moment of area of the region formed between the contour line and the x-axis is calculated while moving along the contour line of the region D, the area is obtained by following the contour line on the upper side of the region D. The first moment of area of the area (D + E) is obtained, and the first moment of area of the area E is obtained by following the contour line on the lower side of the area D. In this case, since the moving directions of the upper and lower contour lines are opposite, the sign of the obtained first moment of area becomes opposite,
Therefore, the primary moment of area of the area E is canceled by adding the primary moment of area of the area obtained by making one round of the contour line of the area D, and the primary moment of area of only the area D is obtained.

FIG. 7 is a flow chart showing the specific processing by the calculation means of the centroid coordinate measuring apparatus based on the above theory. When the trace unit 6 reaches the target vertex P _{n of the} figure and the point key 9 is pressed for the first time (step 10), it starts (step 10), and at step 12, the coordinates of the vertices x _n , y _n are measured and calculated by the calculating means. Is entered. Then, it is determined whether the vertex is the last vertex (step 14).
If it is the last vertex, then the measurement figure is closed and therefore coincides with the first coordinate, so step 15
Then, set P _n = P ₁ and proceed to step 18. On the contrary, if it is not the last vertex in step 14, it is determined in step 16 whether or not the vertex is the first point. If it is the first point, after setting P _n-1 = P ₁ in step 17, the process returns to step 12 and waits for the input of the next vertex P _n . Step 1
If the vertex is not the first point in step 6, the process proceeds to step 18. In step 18, the area F _{n of the} area element surrounded by two consecutive vertices, two lines parallel to the x axis and the y axis.
And the first moments of area My _n , Mx _n of the element determined by two consecutive vertices are calculated, and F _n itself, My _n , Mx
_By adding to _n itself, the total of the area element and the first moment of area is calculated.

It is again judged whether or not the vertex is the last vertex, that is, whether or not the figure has gone around once (step 20).
If it is not the last vertex, set P _n-1 = P _n (step 19), return to step 12, repeat step 20 and repeat step 22 if it is the last vertex.
After it is determined whether the moving direction of the vertex is clockwise or counterclockwise, when it is counterclockwise, the signs of the first moments of area Mx _n and My _n are reversed (step 23) and clockwise. In some cases, the sign of the area F _n is reversed (step 24), the total first moment of area is divided by the total area obtained in step 26 to calculate the centroid coordinates, and the process ends in step 28.

Next, this calculation will be described in detail.
First, considering the case of calculating the first moment of area for the x-axis in the n-polygon of FIG. 2, two consecutive vertices P ₁ (x ₁ ,
y ₁ ), P ₂ (x ₂ , y ₂ ), which is an element determined by the trapezoid P ₁ P ₂ x ₂ x _{1 has} a first moment of area My ₁ of two triangles P ₁ P ₂ x ₁ , P ₂ x ₂ x ₁ Can be obtained by the method of dividing into, and the result is given by the following equation. My ₁ = (x ₂ −x ₁ ) (y ₂ ² + y ₂ y ₁ + y ₁ ² ) / 6 Similarly, a trapezoid P _n−1 P _n x _n x _{n−1 formed} by the n−1 th side is formed.
The cross-section first moment My _n, My _n = become _{(x n -x n-1)} (y n 2 + y n y n-1 + y n-1 2) / 6 ··· (1) ( step 18 see ). Note that this expression is for the case of tracing in the clockwise direction, and the sign is inverted when tracing in the counterclockwise direction.

Similarly, the first moment of area Mx _n of the trapezoid on the y-axis of the trapezoid formed by the (n-1) th side is Mx _n = (y _n-1 -y _n ) (x _n ² + x _n x _{n- 1} + x _n-1 ² ) / 6 (2) (see step 18). Note that this expression is for the case of tracing in the clockwise direction, and the sign is inverted when tracing in the counterclockwise direction.

In the equations (1) and (2), the point P _n (x _n , y _n )
Corresponds to the point P ₁ (x ₁ , y ₁ ), and the figure is closed.

Here, the coordinates of the vertices P ₁ , P ₂ , ... P _n of the figure are traced in order,

(Equation 5) Is calculated, the geometrical moments of area from the larger area (D + E) to the smaller area E in FIG. 6 are offset, and only the area D, that is, the geometrical moments of inertia My and Mx of the target figure are obtained.

It is generally known that the area S of the target graphic is obtained by the following formula.

(Equation 6)

Therefore, by checking the sign of F, it is possible to determine in which direction the figure has been traced, and it is not necessary to limit the way in which the trace is traced. Thus cross-sectional first moment My _n, by dividing the Mx _n in n polygonal area F _n centroid x and centroid y-coordinate is calculated (see step 26).

[0018]

However, in the case of the straight line figure as shown in FIGS. 2 and 3, it is possible to calculate the centroid of the whole figure only by measuring the coordinates of each vertex.
In the case of a figure having a part with an arcuate side, there is a problem that at least the arcuate part must be traced accurately. It is an object of the present invention to provide a device for accurately calculating a figure along an arc by simply measuring the coordinates of the above-mentioned arc portion and three points at both ends and the middle of the arc.

[0019]

In order to solve the above-mentioned problems, according to the invention of claim 1 of the present invention, a main body provided with a roller capable of traveling in a straight line direction, and a traveling direction of this main body With respect to the main body, which is pivotally supported on the main body so as to be rotatable in the left-right direction on a horizontal plane, and which has a trace portion on the tip side, and the coordinates of the current position of the trace portion positioned on a point on the contour of the figure. Using the first coordinate input means for sequentially inputting values and the coordinate values sequentially input from the first coordinate input means, the figure parameters of the measurement figure are sequentially calculated and the total of the figure parameters is calculated. And a second coordinate input means for inputting the coordinate value of the current position of the trace portion positioned at an arbitrary intermediate point on the contour of the arc portion of the figure. Prepare The calculation means calculates a figure parameter for the arc portion from the coordinates of three points, that is, the intermediate point input by the second coordinate input means and the end points of the arc portion input by the first coordinate input means. At the same time, the graphic parameter relating to the arc portion is added to or subtracted from the graphic parameter of the measured graphic calculated using the coordinate values sequentially input from the first coordinate input means.

According to a second aspect of the present invention, in the first aspect, the figure parameters of the measurement figure are an area and a first moment of area, and the calculating means is the first aspect. The area and first moment of area of the element defined by the coordinates of two adjacent points sequentially input by the coordinate input means are calculated, and finally the total first moment of area is divided by the total area of the measured figure. When the centroid coordinates are calculated, and the coordinates are input in the order of the first coordinate input means, the second coordinate input means, and the first coordinate input means, the initial point and the end point of the input three points The area of the arc passing through the midpoint and the first moment of area, and the area of the element defined by the coordinates of the two adjacent points sequentially input by the first coordinate inputting means. Disconnection The first moment, adding or subtracting, respectively the area and cross-sectional first moment of arc portion, characterized in that.

The invention according to claim 3 is the one according to claim 2, wherein the calculating means is a moving direction for measuring a point on a contour of a figure and a moving direction for the three measuring points of an arc portion. Are in the same direction, the area of the circular arc portion defined by the three points is added to the area of the element defined by the coordinates of the two adjacent points sequentially input by the first coordinate input means. In the opposite direction, the area of the circular arc portion defined by the three points may be subtracted from the area of the element defined by the coordinates of the two adjacent points sequentially input by the first coordinate input means. Characterize.

Further, the invention according to claim 4 is the invention according to claims 1 to 1.
In any one of 3 above, the measuring rod is provided with a mark needle provided in the vicinity of the trace portion, and the figure measuring device is further calculated by the coordinates of the current position of the mark needle and the calculating means. A display device for displaying the difference from the centroid coordinates is provided.

In an actual drawing, since the area is rarely represented by a function, the apparatus according to the present invention moves the trace portion along the contour line of the figure and divides the figure contour into minute sections, thereby separating each point. By inputting coordinate values and sequentially calculating the first moment of area and area, the overall first moment of area and total area are obtained. When the figure measurement is completed, the total moment of inertia of area is divided by the total area of the figure to calculate the centroid. In this case, for the arc part, enter the coordinates of both ends and the middle point of the arc,
The area of the arc or the first moment of area is automatically calculated and added to or subtracted from the overall figure.

Therefore, it is not necessary to trace the contour line of the figure for the arc portion, and the calculation means can calculate the figure parameter such as the area of the arc portion only by measuring the coordinates of the starting point, the end point and the intermediate point of the arc portion. You can If the movement direction of each measurement point on the figure body and the movement direction of the three points on the arc are the same, add to the area of the polygon connecting the arcs with straight lines, and subtract in the opposite direction. By doing so, an accurate total area can be obtained. The calculation of the centroid can also be simplified.

[0025]

FIG. 1 is a plan view of a figure measuring apparatus of the present invention, which is almost the same as the improved centroid or figure measuring apparatus of the related art and has a main body provided with a roller 5 capable of traveling in a straight line direction. 1 and a point for pivotally supporting the main body 1 so as to be rotatable in the left-right direction on the horizontal plane with respect to the traveling direction of the main body 1, and for inputting the trace portion 6 and the current coordinate value of the trace portion 6 at the tip end side. The measuring rod 2 provided with the key 9 (first coordinate input means) is provided, and further, the display device 3, the input device 4 and the calculating means are provided in the main body 1, and the trace portion 6 of the measuring rod 2 is used for the coordinates, area, Simultaneously with the operation of tracking and measuring the length etc., the calculation means successively calculates the first moment of area required for centroid calculation, and finally divides the total first moment of area by the area of the target figure to obtain the centroid coordinates. The present of the mark needle 7 which is calculated and is close to the trace portion 6 The display device 3 displays the difference between the position coordinates and the centroid coordinates, and the mark needle 7 is moved so that this display becomes zero, so that the mark needle 7 is positioned at the centroid coordinates. Is.

Further, in the figure measuring device of the present invention, an arc key 8 (second coordinate input means) is provided in a part of the measuring rod 2, and the point key 9, the arc key 8 and the point key 9 are arranged in this order at three consecutive points. By pressing with, the centroid of the figure along the arc passing through these three points is calculated.

The measurement according to the flowchart shown in FIG. 7 can accurately determine the centroid in the case of an n-polygon, but it is determined if an arc portion exists on at least one of the n sides. Becomes inaccurate. Therefore, the calculation means of the device of the present invention performs the processing according to the following flowchart that can be accurately obtained even in such a case.

FIGS. 13 to 16 are flow charts which describe the processing of the calculation means for accurately calculating the centroid coordinates (TGx, TGy) of a figure partially or wholly composed of an arcuate contour. Since this flow chart is huge from the start to the end, it is divided into FIG. 13 to FIG. 16, and ∇ symbols 1 to 5 in each figure show mutual relationships.

As shown in FIG. 13, when the trace unit 6 reaches the target vertex P _n of the figure contour and the point key 9 is pressed for the first time, the trace unit 6 starts (step 30) and then step 3
At 2, the X _n and Y _n coordinates of the apex are measured and input to the calculation means. Then, it is determined whether the vertex is the last vertex (step 34). If it is the last vertex, the measured figure is closed and therefore coincides with the first coordinates. Therefore, in step 35, P _n = P _{1 is set,} and the process proceeds to step 40. On the contrary, if it is not the last vertex in step 34, it is determined in step 36 whether or not the vertex is the first point. If it is the first point, P in step 37
_{After setting n-1} = P ₁ , the process returns to step 32 and the next vertex P
Wait for _n . If the apex is not the first point in step 36, it is determined in step 38 whether the point P _n is a point on an arc. This determination is made based on whether or not the coordinates are input by pressing the arc key 8. If the point at step 38 is a point on the arc, at Step 39 X _a = X _n, and Y _a = Y _n, the process returns to step 32 and waits for input of the next vertex P _n.

If the point is not a point on an arc in step 38,
Proceeding to step 40, the area F of the area element surrounded by two consecutive vertices, two lines parallel to the X axis and the Y axis.
Calculate the total X-axis moment TX and the total Y-axis moment TY of the element determined by _n and two consecutive vertices, and
Add to _n , TY, and TX itself.

Next, as shown in FIG.
If the point of is the point on the arc,
If so, go to step 44. In step 44,
Midpoint of arc (arc point (X_a, Y_a)) And its endpoints (X
_n-1, Y_n-1), (X_n, Y_n) Using the coordinates of three consecutive points
, The attribute radius r of the arc, the circle center P of the arc_c(Xc, Y
c), central angle θ of arc, arc area A_arcCalculate, etc., and then
In step 46, circle center P _cCentroid P of arc from_gDistance to
Distance D_g, Rotation discriminant of arc trace D_a， The length of the arc chord
L_aIs calculated.

In step 48 shown in FIG. 15, D _{g <} L _a (Y _n -Y _n-1 ) is obtained by discriminating the direction (right / counterclockwise) on the arc contour of the measurement by D _a <0. D _g / L _a (X _n
-X _{n -1} ) and the addition / subtraction with
_{After obtaining g} (X _g , Y _g ) (step 49, step 5)
0), in step 52, the first moment of area elements Mx and My of the arc portion are calculated. Then in step 54, again D _a
Direction of the arc contour of measurement (right / left)
Is determined to determine addition / subtraction of A _arc , Mx, My (steps 55 and 56), and then step 5 as shown in FIG.
In step 8, these A _arc , Mx, My are calculated as the area total value F _n of the area element, the X-axis total moment TX, and the Y-axis total moment TY.
The total moment of area F, the first moments of area TX and TY calculated by adding them to the total of
Calculate _n .

It is again judged whether or not the vertex is the last vertex, that is, whether or not the figure has made a round (step 60),
If it is not the last vertex, set P _n-1 = P _n (step 61), return to step 32 again, repeat steps up to step 60, and if it is the last vertex, step 62
After determining whether the moving direction of the apex is clockwise or counterclockwise, when the counterclockwise rotation is performed, the signs of the first moments of area TX and TY are inverted (step 63) and obtained in step 64. The total moment of inertia TX, TY of the whole area is divided by the absolute value TA of the total area to calculate the whole centroid coordinates (TGx, TGy), and the process ends at step 66.

Next, the calculation of the above flow chart will be described in detail. FIG. 8 is an explanatory view of the shape of this arc portion, in which the vertices P _n-1 (X _n-1 , Y _n-1 ) and P _n (X _n ,
When Y _n ) is an arc, the middle point (arc point) of the arc P _a (X
_a, Y _a) the arbitrarily determined, the calculation of the area and the centroid of the arc portion by the following equation (3).

In this case, the arc portion shown in FIG. 8 is the moving direction of the measuring point at the coordinate position of each vertex of the polygonal body (including the curved figure) and the movement of the three points (start point, intermediate point, end point) of the arc portion. It should be noted that the signs in the following formulas are different depending on whether the directions are the same or opposite.

When the coordinate values of the above-mentioned three points, P _n , P _a , and P _n-1 are determined, the equation of the circle is given by the following formula, where the center of the circle is P _c (X _c , Y _c ), and the radius is r: Since X−X _c ) ² + (Y−Y _c ) ² = r ² (3), solve the simultaneous equations with the coordinate values of the three points P _n , P _a , and P _n-1. Thus, the center P _c (X _c , Y _c ) and the radius r can be obtained (see the equation in step 44).

Next, in FIG. 9, the angle connecting the ends of the arc to the center and the arc side is θ, and the angle connecting the ends of the arc to a point on the arc is α. First, α is obtained by the cosine theorem. When,

(Equation 7) It can be expressed as

Here, since the relationship of circumferential angle = (center angle) / 2 holds, θ = 2 (π−α). Note that α ≧
If π / 2, then a small arc (see FIG. 9a (θ ≦ π)), α <
If it is π / 2, it becomes a large arc (see FIG. 9b (θ> π)). Further, the area of the arc P _n P _a P _n-1 is A _arc =
(Θ- sinθ) becomes r ^2/2.

Further, the centroid of the arc is obtained. 10, the centroid _G (X _g, Y _g) Do the first calculated from the center P _c at the center line passing through the arc center to center P _c of the circle to how much distance D _g. The first moment of area Mx of the small arc on the X-axis is obtained by Mx = ∫∫ydydx (area: arc) and divided by the area to obtain D _g . In the case of a large arc, it is easy to find the balance with the small arc. as a result

[0040]

(Equation 8) (See step 46).

Then, after the distance D _g between the arc center G and the circle center P _c is obtained as described above, the center coordinate G is obtained.
Before finding (X _g , Y _g ), the direction of turning on the arc contour (right /
In order to determine (counterclockwise), the rotation discriminant D _a of the arc trace is obtained. The way around the arc contour can be determined by the positive or negative of the area of the arc triangle C shown in FIG.

[0042] That is, the rotation discriminant D _a of the arc, the area of the arc triangle _{C D a = X n-1} (Y a -Y n) + X a (Y n -Y n-1) + X n (Y n- ₁
-Y _a ), and when D _a > 0 ··· counterclockwise When D _a <0 ··· clockwise. The length L _a of the chord of the arc is equal to the end points (X _n-1 ,
Y _n-1), a (X _n, since a Y _n) the distance _{between, L a = Root {(X} n-1 -X n) 2 + (Y n-1 -Y n) 2}.

The centroid coordinates G (X _g , Y _g ) are determined by the direction of rotation on the arc contour (right / left rotation). When clockwise, X _g = X _c − (D _g / L _{a ) (Y n -Y n-1} ) Y g = Y c + (D g / L a) (X n -X n-1) when the _{left-handed, X g = X c + (} D g / L a _{) (Y n -Y n-1} ) Y g = Y c - become _{(D g / L a) (} X n -X n-1). M of the first moment of area of the arc about the X and Y axes
Let x and My be Mx = arc area × centroid Y _g = A _arc · Y _g My = A _arc · X _g .

Next, the above-obtained arc area A _arc and cross first moment Mx, the area F _n obtained for polygons, as shown in FIG. 12 My, cross the first moment T
A method of adding to X and TY will be described.

The area F _n of the n-polygon is, as shown in step 40,

[Equation 9] Is given by By comparing the rotation direction of the whole figure and the rotation direction of the arc triangle C shown in FIG. 12, it is possible to determine whether the area of the arc or the primary moment of area is increased or decreased. In other words,
When the arc is concave with respect to the polygonal figure, the trace direction of all figures and the trace direction of the arc are always opposite. When the arc is convex, the tracing direction of all figures and the tracing direction of the arc portion are always the same. Therefore, again using the arc rotation discriminant D _a , it is judged whether the tracing direction of the arc is counterclockwise or clockwise.

Since A _arc can always be calculated only with a positive value, the positive and negative signs of the arc triangle C are given. If D _a <0, then new A _arc = -A _{arc If} D _a ≥0, then new A _arc = A _arc, and by obtaining F _n = F _n + new A _arc , the total area of the figure including the arc part Is obtained. Note that there may be any number of arcs here. Since F _n has positive and negative signs, the final area is set to | F _n |.

N polygonal first moments of area TY, TX
Is

(Equation 10) It is given by the following two equations. When adding the first moments of area My and Mx to these two equations, it is necessary to invert the sign in the counterclockwise tracing, as opposed to the case of the area (see step 56).

That is, if D _a <0 (clockwise circular arc) ... (4) If TY = TY + My TX = TX + Mx D _a ≧ 0 (counterclockwise circular arc) ... (5) TY = TY -My TX = TX-Mx.

[0049] (4), if D _a <0 summarized (5), the new My = My new Mx = Mx D _a ≧ 0 if the new My = My × (-1) New Mx = Mx × (- 1) and the total first moment of area can be summarized as follows: TY = TY + new My TX = TX + new Mx

When the figure is closed: If F _n > 0 (counterclockwise), TY = TY × (-1) TX = TX × (-1) and the total area TA is TA = | F _n | centroid coordinates (TGx, TGY) is _{TGx = TY / | F n |} TGy = TX / | F n | a (see step 64).

Although the above description is for a polygon including an arc portion, it is needless to say that the above method can be applied to the measurement of the arc portion even in the case of a figure having a curved contour including the arc portion.

[0052]

As described above, when an arc portion is present in a part of an n-polygonal shape or a curved shape, the coordinate values of one point at both ends of the arc and in the middle are input only for the arc portion. By doing so, the geometrical parameters relating to the circular arc portion such as the area of the circular arc and the first moment of area can be calculated.
By adding or subtracting to / from the figure parameter of the polygonal or curved contour figure, a more accurate figure parameter of the whole figure can be obtained, and its measurement is greatly simplified.

[Brief description of drawings]

FIG. 1 is a plan view of an example of a graphic measuring device of the present invention.

FIG. 2 is an explanatory diagram of centroid measurement of a graphic having a straight line contour.

FIG. 3 is an explanatory diagram of conventional centroid calculation of a graphic having a straight line contour.

FIG. 4 is an explanatory diagram of conventional centroid calculation of a curved contour graphic.

FIG. 5 is an explanatory diagram of a conventional improved centroid measurement theory.

FIG. 6 is an explanatory view of a conventional theory of improved centroid measurement.

FIG. 7 is a flowchart of a conventional improved centroid measurement.

FIG. 8 is an explanatory diagram of a circular arc portion when measuring the centroid or area of the present invention.

FIG. 9 is an explanatory view of an arc portion, where (a) is a small arc,
(B) is a case of a large arc.

FIG. 10 is a detailed explanatory view of an arc portion, where (a) is a small arc and (b) is a large arc.

FIG. 11 is an explanatory diagram of a position on a coordinate of an arc portion.

FIG. 12 is an explanatory diagram of adding an arc portion to a polygon.

FIG. 13 is part of a flow chart for calculating the centroid and arc area of the device of the present invention.

FIG. 14 is part of a flow chart for calculating the centroid and arc area of the device of the present invention.

FIG. 15 is part of a flow chart for calculating the centroid and arc area of the device of the present invention.

FIG. 16 is part of a flow chart for calculating the centroid and arc area of the device of the present invention.

[Explanation of symbols]

 1 Main Body 2 Measuring Rod 3 Display Device 4 Input Device 5 Roller 6 Tracing Part 7 Mark Needle 8 Arc Key (Second Coordinate Input Means) 9 Point Key (First Coordinate Input Means)

Claims (4)

[Claims] 1. A main body provided with a roller capable of traveling in a straight line direction, a main body pivotally supported on the main body so as to be rotatable in the left-right direction on a horizontal plane with respect to the traveling direction of the main body, and a trace portion on the tip side. And the first coordinate input means for sequentially inputting the coordinate value of the current position of the trace portion positioned on the point on the contour of the figure, and sequentially input from the first coordinate input means. In a figure measuring device provided with a calculation means for sequentially calculating figure parameters of a measured figure using coordinate values and calculating the sum of the figure parameters, the figure measuring apparatus is positioned at an arbitrary intermediate point on the contour of the arc portion of the figure. And a second coordinate input unit for inputting coordinate values of the current position of the trace unit, wherein the calculation unit includes the intermediate point input by the second coordinate input unit and the first coordinate. Of the measured figure calculated by using the coordinate values sequentially input from the first coordinate inputting means while calculating the figure parameter relating to the arcuate portion from the coordinates of the three points at both ends of the arcuate portion input by the force means. A figure measuring device characterized by adding or subtracting a figure parameter relating to the arc portion to a figure parameter. 2. The graphic parameter is an area and a first moment of area, and the calculation means is an area of an element defined by the coordinates of two adjacent points sequentially input by the first coordinate input means. And a first moment of area is calculated, and finally the first moment of area is calculated by dividing the total first moment of area by the total area of the measured figure, and at the same time, the first coordinate input means,
When the coordinates are input in the order of the second coordinate input means and the first coordinate input means, the area and the cross-section primary of the arc portion passing through the intermediate point with the initial point and the end point of the input three points as both ends The moment and the area primary moment of area defined by the coordinates of two adjacent points sequentially input by the first coordinate input means are respectively added to the area and primary moment of area of the circular arc portion. The graphic measuring device according to claim 1, wherein the graphic measuring device performs addition or subtraction. 3. If the moving direction for measuring a point on the contour of the figure and the moving directions of the three measuring points of the arc portion are the same direction, the calculating means defines an arc defined by the three points. The area of the part is added to the area of the element defined by the coordinates of the two adjacent points sequentially input by the first coordinate input means, and in the opposite direction, the arc part defined by the three points is added. 3. The figure measuring device according to claim 2, wherein the area is subtracted from the area of the element defined by the coordinates of two adjacent points sequentially input by the first coordinate input means. 4. The measuring rod comprises a mark needle provided in the vicinity of the trace portion, and the figure measuring device further includes coordinates of the current position of the mark needle and centroid coordinates calculated by the calculating means. The graphic measuring device according to any one of claims 1 to 3, further comprising a display device for displaying the difference between the two.