JPH0581431A - Method for calculating area of polygon - Google Patents

Abstract

PURPOSE:To shorten the processing time for calculation of the area of a polygon in a drawing recognition device where a graphic consisting of a polygon of a map or a floor plan is inputted as segment data by a computer. CONSTITUTION:When the area of a polygon formed by connecting plural apexes having coordinate values of two orthogonal axes will be calculated, a vactor is set to each apex of the polygon from the coordinate origin. Triangles are successively formed while overlapping every two vectors out of these vectors, and their exterior product values are calculated. Calculated exterior product values are integrated as they are, and finally, a half of the absolute value of the integral value is adopted as the area value.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a calculation method for calculating the area of a polygon with a drawing recognition device for inputting a polygonal figure such as a map or floor plan to a computer as line segment data, and particularly to a processing time. The present invention relates to a method of calculating a polygonal area for shortening.

[0002]

2. Description of the Related Art In recent years, with the technical progress of image scanners and the like, the reading and recognition of graphics have been frequently used. When checking administrative divisions on a map, grasping the floor plan by various floor plans, and assuming the overall image after assembly of parts with CAD, the polygons that form the composite figure and its unit figure are drawn as lines. Very often it has to be entered into the computer as minute data. FIGS. 4 and 5 are explanatory views showing an example of a method of dividing a composite figure into polygonal unit figures in such a drawing recognition device, in which 41 is a line segment and 42 to 45 are the line segments 41. The turning points 46 and 47 are branch points of the line segment 41. In the figure, the line segment 41 of the complex figure is traced twice in the forward direction and the reverse direction, and the first branch point 46 of the desired line segment is traced.
Then, the line segment 41 is searched counterclockwise and the line segment first discovered is selected and traced. Similarly, at the next branch point 47, the line segment is traced counterclockwise, and when the vector is a plain phrase, this is made a polygon 48. When the line segment is traced twice, polygons 49 and 50 are further obtained. One of these polygons is a peripheral loop, but its discrimination is surprisingly complicated. For example, the nodes 51 to 56 shown in FIG.
There is also a method in which the polygons 48 and 49 are unit polygons and the polygon 50 is a peripheral polygon by summing up the direction change angles in the above, and the polygons are usually formed by the vector 57 and the vector 58. The area of the polygon to be calculated is calculated, and the one with the largest value is used as the outer loop.

[0003]

By the way, in the above drawing recognition apparatus, the input image is once expanded in the bit map memory and then the subsequent processing is executed. The calculation of the polygonal area has conventionally been performed by counting the number of bits included in the polygon of the image developed in the bitmap. However, it goes without saying that such a counting method requires a great deal of processing time and has a considerable influence on the overall processing. The present invention was devised in view of such problems, and an object thereof is to provide a method for calculating a polygonal area that can reduce the processing time.

[0004]

Means for solving the above-mentioned problems in the present invention is to provide a polygonal area calculating method in which a plurality of vertices having coordinate values of two orthogonal axes are connected to each other. While overlapping, combine 2 points each,
The area of each triangle formed by two vectors from the coordinate origin to the two points is calculated by the cross product value, and the area of the polygon is calculated by adding and subtracting those areas, which is a calculation method. And

[0005]

The present invention is a method of calculating the area of a polygon using the cross product value of vectors. Here, the cross product value of a vector is a product of a first vector and a vertical component of the second vector with respect to the first vector when two vectors are present, and the vector has an orthogonal biaxial coordinate (xa , X
a) and (xb, xb), they are represented by xa yb-ya xb regardless of the angle formed by both vectors. Moreover, the area of the triangle is, as is known, the base x height ÷
Since it is 2, it corresponds to 1/2 of the absolute value of the outer product value. On the other hand, when a polygon whose area is to be calculated exists on the coordinate system of the two orthogonal axes, a vector from the coordinate origin is assumed for each vertex of the polygon, and two of them are combined to form a triangle. Are formed, and the areas of the polygons are obtained by adding and subtracting the areas of the triangles.

[0006]

Embodiments of the present invention will now be described in detail with reference to the drawings. FIG. 1 is a flowchart showing an embodiment of the present invention. In the figure, the process of the present invention is
A vector is set from the coordinate origin for each vertex of the n-gon on the axis coordinates, two of them form a triangle in sequence, the outer product value is calculated, and 1/2 of the absolute value of the sum is calculated as the area. The value.

FIG. 2 is an explanatory diagram showing an example of area value calculation in the above embodiment, and illustrates a method for obtaining the area of a triangle by using the outer product value. In FIG. 2, the vector O
The outer product value of A and the vector OB is the product of the vector OA and the vertical component of the vector OB with respect to the vector OA, and is defined by | OA | · | OB | · Sinθ.

The inner product value of the vector OA and the vector OB is the vector OA and the vector OA of the vector OB.
│OA│ ・ │OB│
-Defined by Cosθ.

The point to be noted here is that both the inner product value and the outer product value take positive and negative values. Further, the signs of the outer product value of the vector OA and the vector OB and the outer product value of the vector OB and the vector OA are inverted to Sin (−θ) = − Sinθ.

Since the outer product value is | OA |. | OB | .Sin.theta., This value uses the biaxial coordinate components (xa, ya) and (xb, yb), and the Cartesian coordinates are the vector OA and the vector OB. From the inclination α of the vector OA and the inclination β of the vector OB, θ = β−α, and by the addition theorem of the trigonometric function, Sin (β−α) = Sinβ · Cosα−Cosβ · Sinα Cos (β −α) = Cosβ · Cosα + Sinβ · Sinα, so │OA│ ・ │OB│ ・ Cosθ ＝ │OA│ ・ │OB│ ・ (Cosβ ・ Cosα + Sinβ ・ Sinα) = │OA│ ・ Cosα ・ │OB│ ・ Cosβ + │OA│ ・ Sinα ・ │OB│ ・ Sinβ ＝ xa ・ xb ＋ ya ・ yb │OA│ ・ │OB│ ・ Sinθ ＝ │OA│ ・ │OB│ ・ (Sinβ ・ Cosα-Cosβ ・ Sinα) = │OA│ ・Cosα ・ │OB│ ・ Sinβ-│OA│ ・ Sinα ・ │OB│ ・ Cosβ = xa ・ yb-ya ・ xb That is, if two-axis coordinate components (xa ・ xa) and (xb ・ yb) are used, OA│・ │OB│ ・ Sinθ ＝ xa ・ yb-ya ・ yb That. Therefore, the area S _{OAB of the} triangle OAB formed by the vector OA and the vector OB can be calculated by S _OAB = 1/2 | (xa · yb-ya · xb).

FIG. 3 is an explanatory view showing an example of the area value addition / subtraction of the above embodiment, showing a method of calculating the area of a vector triangle from the outer product value and then calculating the original polygon area by these addition / subtraction. Is. Here, the original triangle that is the target of the area calculation is the three vectors O.
It is a triangle ABC formed by arrowheads of A, OB, and OC, and its area S _ABC is S _ABC = S _{OAB +} S _OBC- S _OCA . Converting this to the cross product value, S _ABC = 1 / 2│ (xa ・ yb-ya ・ xb) │ + 1 / 2│ (xb ・ yc-yb ・ xc) │-1 / 2│ (xc ・ ya- yc ・ xa) = 1 / 2│ (xa ・ yb-ya ・ xb) + (xb ・ yc ・ xc) + (xc ・ ya-yc ・ xa). That is, generally, the area Sn of a polygon having n vertices has the coordinates of each vertex as (xo, yo), (xl, y
l), ... (xn, yn)

[0012]

[Equation 1]

It can be obtained by However, since it is a vertex of a polygon, it is determined by xn = xo and yn = yo. Incidentally, it is of course possible to perform the same calculation process by using the above coordinate values as relative coordinates from an arbitrary point on the coordinate system.

[0014]

As described above, according to the present invention, it is possible to provide a method for calculating a polygonal area that requires only simple calculation and can reduce the processing time.

[Brief description of drawings]

FIG. 1 is a flowchart of an embodiment of the present invention.

FIG. 2 is an explanatory diagram of an embodiment of the present invention.

FIG. 3 is an explanatory diagram of an embodiment of the present invention.

FIG. 4 is an explanatory diagram of composite figure division processing.

FIG. 5 is an explanatory diagram of composite figure division processing.

[Explanation of symbols]

41 ... Line segment, 42-45 ... Direction change point, 46, 47 ... Bifurcation point, 48-50 ... Polygon, 51-56 ... Node, 5
7 and 58 ... Vector.

Claims (1)

[Claims] 1. In a polygonal area calculation method comprising a plurality of vertices having coordinate values of two orthogonal axes, the vertices are overlapped, and two points are combined to form two points from a coordinate origin. An area calculation method for a polygon, characterized in that the area of each triangle formed by the vector is calculated by an outer product value, and the area of the polygon is calculated by adding and subtracting the areas.