JPH0132545B2 - - Google Patents

Description

[Detailed Description of the Invention] (a) Technical Field of the Invention The present invention relates to a curved surface in a space consisting of mutually perpendicular (X, Y, Z) axes, to a plane parallel to the XY plane, for example, a plane with an altitude of Z=Zo. The present invention relates to an improvement in a contour line tracing processing method for obtaining contour lines, which are the contour lines of the cut end of a curved surface formed when cutting the curved surface.

(b) Prior Art and Problems A conventional contour tracing processing method for obtaining contour lines using a data processing device will be described with reference to FIG. 1, which shows the relationship between triangular meshing and a table. Multiple coordinates on the curved surface (Xi, Yl, Zi; i=
1, 2, 3, ...) is input, first, three coordinate points that are close to each other are detected using a known method, and triangles with the three points as vertices are used as constituent elements to create an approximate plane of the curved surface. form a triangular mesh.

Then, a triangle identification code (for example, I, J, K, ...) for identifying each triangle is assigned to a plurality of triangles constituting the triangle mesh, and a vertex code (for example, I, J, K, etc.) for identifying the vertices of the triangle is assigned For example, , , , .

Additionally, there is a diagram showing the relationship between the vertex codes of triangles and the coordinates of the vertices corresponding to the vertex codes (see the coordinate table of the triangle vertices in Figure 1b), and a diagram showing triangles that share sides with each other (Figure 1). A table for finding the contour lines of a triangle mesh as shown in the diagram showing the relationship between triangle identification codes and vertices (see the triangle vertex table diagram in Figure 1d). create.

Next, a third process is performed to determine whether a contour line of elevation Z=Zo exists in one triangle arbitrarily extracted from among the plurality of triangles that make up the triangle mesh, for example, triangle Perform it using the method shown in the figure.

This determination process begins with the coordinates (X1,
Y1, Z1), (X2, Y2, Z2), and (X3, Y3, Z3)
Start by reading out.

Then, the altitude value "Zo" inputted in advance into the data processing device and the coordinates (X1, Y1, Z1), (X2,
Using Z1, Z2, and Z3, which are the Z coordinate values of Y2, Z2) and (X3, Y3, Z3), it is determined whether or not there is a contour line of Z=Zo in triangle I.

This determination process is performed by checking whether Z ₀ is a numerical value between Z1 and Z2, whether it is a numerical value between Z1 and Z3, and whether it is a numerical value between Z2 and Z3.

And for example Z ₀ is between Z1 and Z2, and Z2 and Z3
If the value is between, triangle I will have one contour line.

Considering the contour lines in triangle I as line segments,
If this is a contour line segment “I′”, the contour line segment “I′”
The coordinates of both ends are one point a on the side connecting the vertices and one point b on the side connecting the vertices.
It becomes a line segment that connects.

Since triangle I is a minute planar triangle, there are no more than two contour lines, and the coordinates of both ends of contour line segment "I'" are determined by proportional calculation.

X of the coordinates (a, b) of both ends of the contour segment “I′”,
When determining the Y coordinate by proportional calculation, the coordinate of one end is [X1 + (X2 - X1) (Zo - Z1) / (Z2 - Z1), Y1 +
(Y2−Y1) (Zo−Z1)/(Z2−Z1)], the coordinates of the other end are [X3+(X2−X3)(Zo−Z3)/(Z2−Z3),
Y3+(Y2-Y3)(Zo-Z3)/(Z2-Z3)].

Then, when the coordinates (Xa, Ya; Then, the process of determining the coordinates of both ends of the contour line segment "I'" in triangle I is completed.

Next, the data processing device selects triangle J adjacent to triangle I from FIG. The coordinates are the coordinates b of the other end of the contour segment "I'" of triangle I [X3 + (X2 - X3) (Zo - Z3) / (Z2 - Z3), Y3 +
(Y2−Y3) (Zo−Z3)/(Z2−Z3)] is adopted.

Furthermore, in order to find the coordinates of the other end of the contour line segment "J'", extract the vertices according to Figure 1 d, and add the altitude Z= to the side connecting the vertices and the side connecting the vertices. It is determined whether a point corresponding to Zo exists or not using the method described above.

For example, Z=Zo on the line connecting the vertices
If it is determined that there is a point c, the coordinates (Xc, Yc) of this point are determined by proportional calculation.

Then, the coordinates of both ends (b, c) of the contour line segment "J'" in the triangle J determined by the above proportional calculation are stored, and the process of determining the contour line segment in the triangle J is completed.

From now on, the above process will be performed for adjacent triangles one after another to find the contour line segments within each triangle, and when the process of finding the contour line segments for all triangles is completed, all the contour lines of Z = Zo of the triangle mesh will be It will be found as contour segments.

To search for adjacent triangles, refer to Figure 1c, but since there are one or two adjacent triangles, the order in which triangles are selected and the order in which contour lines are connected are closely related, resulting in a large number of meshes. There is a risk that unexpected contours will appear in the series of contour lines.

Note that if it is determined in the determination process that triangle I does not have a contour segment with Z=Zo, the same determination process as performed for triangle J is executed for another triangle, for example, triangle K.

However, in the conventional technology for calculating contour lines, it is necessary to make the mesh finer in order to achieve precision, and for that purpose, multiple three-dimensional coordinates (Xi, Yi, Zi),
The storage area for storing the various tables shown in Figure 1 increases, and each time a contour line segment within each triangle is calculated, it is necessary to sequentially search for adjacent triangles using Figure 1 c. Since it was necessary to read data, there was a problem in that the processing speed for determining contour segments was slow.

(c) Purpose of the Invention In view of the above-mentioned drawbacks of the prior art, it is an object of the present invention to provide a contour tracing processing method capable of reducing the storage area of a data processing device and increasing the processing speed. .

(d) Structure of the Invention The above problem is to assign coordinate point numbers to a plurality of spatial coordinate points, input coordinate values corresponding to the coordinate points, and create an identification code on a triangular plane formed by three adjacent coordinate points as vertex coordinates. and set the three coordinate point numbers to the vertex codes of the triangular plane, and what to do when the coordinate values on the line segment connecting the vertices that make up the triangular plane for each triangular plane match the common specified value. In a system that traces contour lines between triangular planes by generating coordinate values on the line segment, calculating the coordinates of both ends of a contour line segment spanning two line segments, and storing it in memory,
Extract the first contour segment from the memory, use the coordinates of one end of the contour segment as the starting point, search and extract the second contour segment that has the same coordinates at one end in the memory to establish the connection order, and then create the second contour line. A forward tracking procedure is performed to establish a connection order by searching and extracting a third contour segment whose one end has the same coordinates as the other end coordinates, and in the process of performing the tracking procedure, a contour segment with the same coordinates is found. The tracking procedure is repeated until there are no more left in the memory, and the fourth contour segment whose starting point is the other end coordinate of the first contour segment is
When the forward and backward tracing steps are completed, the common contour segments extracted by the two tracing steps are executed. This problem is solved by a contour line tracing processing method characterized in that contour line segments are excluded and connected in order.

(e) Embodiments of the invention Examples of the invention will be described in detail with reference to FIGS. 2 to 4.

In the figure, 1 is a coordinate table of the triangular vertices shown in FIG. 1b, 2 is a triangular mesh generator, 3 is a vertex table of the triangle shown in FIG. is the intersection calculation part,
8 is a contour line segment table, 9 and 10 are connected search parts,
Reference numeral 11 indicates a sorting section, and reference numeral 12 indicates a contour coordinate table.

A plurality of coordinates (Xi, Yi, Zi) on a curved surface in a three-dimensional space consisting of mutually orthogonal X, Y, and Z axes are input and stored in the triangular vertex coordinate table 1 (i= 1, 2, 3,…).

The triangular mesh generator 2 reads out the coordinates from the coordinate table 1 of the triangular vertices, and uses known techniques to create an approximate surface of the curved surface using triangles whose vertices are adjacent to the coordinates as constituent elements. Form a triangular mesh.

The triangular mesh having the triangle as an element is
By making the intervals between the plurality of coordinates (Xi, Yi, Zi) fine and inputting a large number of coordinates, a curve that closely approximates the curved surface can be obtained.

That is, the triangular mesh generator 2 assigns a triangle identification code (for example, I, J, K, . . . ) to each triangle in order to identify the plurality of triangles constituting the triangular mesh, and also assigns a triangle identification code (for example, I, J, K, . . . ) to each vertex of the triangle. assigns a vertex code (for example,,,,...), writes the data of the triangle identification code and the vertex code corresponding to the triangle identification code in the memory 3, and also writes the vertex code into the coordinate correspondence of the coordinate table 1 of the triangle vertex. Fill in the position.

Next, the information retrieval unit 5 reads the triangle I located at the beginning of the triangle vertex table 3 from the triangle vertex table 3, and simultaneously reads the vertex code (,,).

From Table 1, the vertex codes (,,
) The coordinates of the three vertices (Xi, Yi,
Zi; i=1, 2, 3) (see Figure 3).

The contour storage memory 6 is configured to be able to output contour values of contour lines to be determined in a triangular mesh having triangles as an arbitrary value.

The intersection calculation unit 7 inputs the coordinates of the vertices (Xi, Yi, Zi; i=1, 2, 3) from the information retrieval unit 5, and also inputs the contour value of the contour line to be calculated, for example, Z= from the contour storage memory 6. Read the value of Zo.

Next, the intersection calculation unit 7 calculates the coordinates (Xi, Yi, Zi;
Based on i=1, 2, 3) and Z ₀ , the coordinates (Xi,
In the triangle I formed by Yi, Zi; i = 1, 2, 3), check whether the contour segment “I′” which is the contour line segment of “Zo” exists or not. Determination is made by comparing the Z component of the coordinate point and "Zo".

For example, a line segment in triangle I ~, ~
When it is determined that the contour line segment “I′” of “Zo” exists within the contour line segment “I′”, the coordinates (Xa,
Ya;
The process of determining the contour segment "I'" of triangle I is completed by inputting the data into the table shown in FIG.

Then, the same process as performed on triangle I is performed on other triangles one after another (J, K,...
Coordinates (c, d, c,
..., h) (Fig. 4b) is determined and entered in Table 8 of Fig. 4a.

Furthermore, there is Z ₀ in the triangles that make up the triangular mesh.
As soon as it is determined that the contour line does not exist, processing of another triangle is started.

The connection search unit 9 arbitrarily selects one contour line segment, for example, the contour line segment “L”, from the table 8 of FIG. Coordinates of both ends of ′”
Read out Xc, Yc; Xd, Yd as a pair (see Figure 4b).

Then, the coordinates (Xd,
Yd) as the marking point coordinates.

Next, the connection search unit 9 searches for the coordinates of the start point and end point of the plurality of contour line segments stored in pairs in the table 8, and finds the coordinates of one end of which are the same as the start point coordinates (Xd, Yd). Detect and connect line segments that have

Next, line segments having the same coordinates as the coordinates of the other end of the line segment detected by the above search are successively detected in the same manner as described above, and the detected coordinates are connected in the order of detection. go.

When there are no coordinates that have the same coordinates as the coordinates of the final end of the connection, the coordinates are input to the sorting unit 11 in the order of connection.

For example, the above procedure will be explained using FIG. 4.

Let d be the coordinates of the starting point of the contour segment "L'".

The connection search unit 9 searches for the coordinates of both ends of the plurality of contour line segments stored in the table 8, and searches for this d
Detect a contour segment “M′” that has the same coordinates at one end as .

Next, the other end of this contour segment “M′” and the coordinate are e
Then, the contour line segment whose one end coordinate is e is not detected even if the table 8 is searched, so the connection search unit 9 inputs the coordinates “d, e” to the sorting unit 11 in the order of connection.

Further, the connection search unit 10 searches the contour line segment “L′”
The same process as that performed by the connected search unit 9 is executed using the coordinate c of the other end as the other starting point coordinate.

Then, when the connected coordinates of the connected search section 10 are input to the sorting section 11, the search for the coordinates of all contour segments of one contour line of which the contour line segment "L'" is a constituent element is completed.

For example, set the coordinates c to the other end of the contour segment “L′”.
Then, the coordinates “c,” connected by the connection search unit 10 are
By inputting "b, a" to the sorting unit 11 in the order of connection, the search for the coordinates of all contour segments of one contour line of which the contour segment "L'" is one constituent element is completed.

In the sorting unit 11, the connection search unit 9 searches the coordinates “d, e” which are connected using the coordinates of one end of the contour line segment “L′” as the starting point coordinates, and the connection search unit 10 searches for the coordinates “d, e” that are connected using the coordinates of one end of the contour line segment “L′”. Input the connected coordinates "c, b, a" using the starting point coordinates.

Then, the sorting unit 11 selects the coordinates “d,
It is determined based on the coordinates whether "e" and the coordinates "c, b, a" constitute contour lines of an open curve or contour lines of a closed curve.

As a result of this determination, since it is an open curve, the sorting unit 11 forms a single coordinate sequence starting from e or a, which is the terminal coordinate of each of the coordinate sequences.

For example, if the coordinates are composed of a sequence with a as the starting point coordinate, it becomes "a, b, c, d, e".

Then, the sorting unit 11 inputs the coordinates in the order of the arrangement into the table 12 of FIG. 4c.
If the result of the determination is a closed curve, the sorting unit 11 inputs only the coordinates input from the connection search unit 9 into the table 12 in the same order.

After this, the linked search unit 9 and the linked search unit 10
In order to search for other coordinates of the contour line, that is, contour line segments "O'" and "N'" in Figure 4a, repeat the above process for the contour line segments in Table 8 that have not yet been searched. The sorting unit 11 opens the connected “O′” and “N′”.
Performs processing including closing processing.

When all the contour line segments of Zo stored in the table 8 have been searched, it means that all the contour lines of Zo have been found.

(f) Effects of the Invention As explained in detail above, the contour line tracing processing method of the present invention can calculate contour line segments without regard to the adjacency of triangles. Even if it appears in more than one place, it can be detected without omission.

Therefore, the logic for tracing contour lines can be simplified, and the storage area and processing amount of the data processing device can be reduced, which has many advantages in tracing contour lines.

[Brief explanation of drawings]

Figure 1 is a diagram showing the relationship between triangle meshing and tables, Figure a is a triangle mesh diagram, Figure b is a coordinate table of triangle vertices, Figure c is a triangle mesh table, Figure d is a triangle vertex table. , second
The figure is a block diagram of an embodiment of the contour line tracing processing method of the present invention, FIG. 3 is a contour line segment calculation diagram, and FIG. 4 is a contour line segment tracing explanatory diagram. In the figure, 1 is a coordinate table of triangle vertices, 2
is a triangular mesh generator, 3 is a triangle vertex table, 5 is an information extraction unit, 6 is a contour value storage memory, 7 is an intersection calculation unit, 8 is a contour line segment table, 9 and 10 are a connection search unit, and 11 is a sorting unit. Sections 12 and 12 respectively show contour line coordinate tables.

Claims (1)

[Claims] 1 Coordinate point numbers (,,,
) and assign the coordinate values (Xi,
Yi, Zi; i = 1, 2, ...), assign an identification code (I) to a triangular plane formed with three adjacent coordinate points as vertex coordinates, and assign the three coordinate point numbers to the triangular plane ( I), and the corresponding coordinate value ( X, Y) is produced on the line segment, and both end coordinates (Xs, Ys; Xe, Ye) of the contour line segment (Zs = Ze = Zo) spanning the two lines
In a system that traces contour lines between triangular planes by calculating and storing it in memory, the first contour line segment (Xs, Ys;
Ye), the coordinates (Xe, Ye) of one end of the contour line segment are the starting point, a second contour line segment having the same coordinates at one end is searched and extracted in the memory to establish a connection order, and the second
A forward tracing procedure is performed to establish a connection order by searching and extracting a third contour segment whose one end has the same coordinates as the coordinates of the other end of the contour segment, and in the process of performing the tracing procedure, a third contour segment having the same coordinates as the other end coordinate of the contour segment The tracing procedure is repeated until there are no more contour segments in the memory, and at the same time, a fourth contour segment whose starting point is the coordinates (Xs, Ys) of the other end of the first contour segment is searched and extracted in the memory and connected. Perform a backward tracing procedure to establish the order, and when the forward and backward tracing procedures are completed, confirm that the contour line segments extracted in the two tracing procedures have been connected and ordered by excluding common contour segments. Characteristic contour line tracing processing method.