JPH06203109A - Method for restoring polygon from there-sided drawing with slack matching method - Google Patents

Abstract

PURPOSE:To restore a polygon from a three-sided drawing containing error with less calculated variable concerning the polygon composed of planes. CONSTITUTION:The respective sides of the three-sided drawing are numbered. The coordinate of an apex on a side (i), first adjacent side not on the same plane as this side (i) and second adjacent side with the possibility of connecting this side are extracted. A wire frame model is calculating by oppositely projecting the three-sided drawing, and a number (k) is given to th side with possibility corresponding to the side (i) as a candidate side. The certainty of correspondence to the plural candidate sides (k) of the side (i) is expressed by a probability variable Pik<t>. The candidate side of a first adjacent side (j) of the side (i) is defined as (l), and a first adaptability coefficient to be enlarged when the (l) is non-parallel to the (k) and is separated is defined as rijkl<1>. The candidate side of a second adjacent side (h) of the side (i) is defined as (m) and a second adaptability-coefficient to be enlarged when the candidate (m) is away from a basic side rather than the side (k) while the (i) is a simple plane or a composite plane or when the candidate side (m) is closer from the basic side rather than the side (k) is defined as rijkl<2>. Then, the probability variable Pik<t> is updated by using these coefficients and after the fixed times of repetition, the (k) to apply the maximum probability Pik<t> is defined as the corresponding side of the (i).

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for restoring a polyhedron from a trihedral view by a relaxation matching method. In particular, it is a method that can restore a polyhedron from a trihedral drawing in which the coordinates of the vertices include an error in a short calculation time.

The three-sided view refers to three drawings which are orthogonal to each other among the six views of the plan view, the right side view, the left side view, the front view, the rear view and the bottom view. For example, a combination of a plan view, a front view, and a right side view is one example of the three views. The trihedral drawing has been used for a long time as a means for accurately expressing a polyhedron on a plane. The polyhedron restoration is to express each surface vertex, which is a feature point of the polyhedron, in three-dimensional coordinates.

For the purpose of explanation, the polyhedron will be expressed in a perspective view, but the purpose is not to make it a perspective view, but to express the vertices and sides in three-dimensional coordinates. First, there is a three-dimensional polyhedron, which is projected onto three surfaces to create a front view, a plan view, a side view, and the like. Therefore, it is called reconstruction to obtain three-dimensional coordinates and clarify the positions of vertices and edges in three-dimensional space.

The technical field of using the three-view drawing is extremely wide such as mechanical design, manufacturing, and construction. The present invention is extremely effective in these technical fields. With the development of computer technology in recent years, researches for automatically restoring a polyhedron from a trihedral drawing have been popular for accumulating drawings, managing drawings, searching drawings, inputting solid figures, and the like. The present invention follows that flow.

[0005]

2. Description of the Related Art Generally, the following three processes are considered as an algorithm for restoring a polyhedron from a trihedral view. Depending on the correspondence between the three views (plan view, front view, side view),
A wire frame model composed of candidate vertices and candidate line segments is created. Then, a surface model composed of candidate planes surrounded by line segments is created. Finally, we construct a solid model that represents a three-dimensional shape equivalent to a solid solid.

At this time, it is known that the surface model including the candidate planes includes a virtual object. The current mainstream of research is how to eliminate virtual objects from surface models. The following proposals have been made regarding virtual object removal.

(1) Masanori Desawa: "System for three-dimensional formation from three views", Machine Magazine, Vol. 38, No. 31
0, pp. 1267-1276 (1972)

(2) G. Markowsky and MA Wesley: "Fles
hing Out Wire Frames ", IBM J.Res.Dev., Vol.24, No.5, p
p.582-592 (1980)

(3) Yasuhito Sasaki, Kiyoshi Ito, Seido Suzuki: "
Automatic Synthesis of Objects from Three Views by Nonlinear Pseudo-Bulle Algebraic Solution "," Theory of Information, "Vol. 30, No. 6, pp. 6
99-708 (1989)

Among these, (1) is to eliminate a virtual object by trial and error from the wire frame. (2) is to search for a virtual object by trial and error. (3) gives a formulation for removing virtual objects from the surface model, not trial and error.

By such a method, it becomes possible to restore a polyhedron from a trihedral view. However, these methods still have serious drawbacks. These assume that the coordinate values of the vertices of the faces of the trihedral are given exactly. It is necessary that the coordinates of points are input as numerical values from the keyboard instead of being expressed simply by three views.

Naturally, the coordinate components of the same vertex should not differ between the three views. If the points are the same, the component coordinates must be common, and this is used for the determination of the same point. These methods cannot be applied if the coordinates between the three views are incorrect. These methods can only be used for very limited and accurate three-view drawings. It is essential that the numerical values are given accurately in the three-view drawing, rather than simply being written correctly.

[0013]

However, considering practical applications, it is common for the data of the three views to have a mutual error. In addition, even if the three-view drawing is accurately drawn, if the coordinate value of the point is not specifically given, the coordinate may be obtained by reading the distance from a certain reference point on the drawing.

In this case, the coordinates of the same point may be different between the three views. In many cases, a three-dimensional drawing written on a paper is read by an image scanner to make a wire frame model, but a reading error and the like are introduced in addition to the drawing error. Furthermore, in the case of a hand-drawn three-sided drawing,
Even the same point may differ in the three views.
The above methods are all strict methods that do not allow the existence of such errors. Therefore, its practical value is low.

If there is a discrepancy between the three views, applying the previously proposed method would require the addition of rules to absorb the error. Even if a rule is added, there are errors, so that the number of candidate planes increases and the number of combinations to search becomes enormous. In the conventional method, even if there is an error, it is not judged whether or not it is within the error range, and candidate surfaces are assumed for all values, so that there are many candidate surfaces. Then, the amount of calculation increases exponentially and calculation becomes impossible. This is called an explosion.

The present invention overcomes these drawbacks and is a method for accurately associating these planes even if the coordinate components of the same point are slightly different from each other in a three-dimensional view including an error or a hand-drawn three-dimensional view. The purpose is to provide. It is the first aspect of the present invention to provide a method that can restore a polyhedron from a trihedral view in a short time without setting up a candidate surface having a vertex as a vertex for all points having different coordinates and without causing an explosion in calculation amount. It is the purpose of 2.

[0017]

A method for restoring a polyhedron from a trihedral view according to the present invention comprises only a solid line showing an outline and a broken line showing a hidden line, which is formed by projecting a polyhedron composed of planes onto three orthogonal planes. A method of restoring an original polyhedron from a trihedral diagram including an error, in which the planes of the trihedral diagram are numbered i and are surrounded only by the vertex coordinates ( _xim , _yim , _zim ) of each face i and a solid line. Of the three types of planes: a simple plane (w = 0), a division plane surrounded by a solid line and a broken line (w = 1), and a composite plane (w = 2) that integrates the simple plane and the division plane. Which one it belongs to, and in the case of a simple plane or a compound plane, it is defined as a surface adjoining via a solid line or a broken line or a division plane included in it. In the case of a division plane, it is defined as a surface including this. and near surface {E _ij ^1}, constitutes a plane of each surface view More becomes feature list and the second near surface defined as a surface having a segment corresponding to one-to-one margin of error h {E _ij ^2} when projected minute in the spindle generated for each surface i, Back-projecting the three-view drawing and adding the coordinates determined from the coordinates of the line segment of the other surface to the two-dimensional coordinates of the surface i in the three-view drawing 3
A wire frame model composed of candidate surfaces having dimensional coordinates is created, and the number k is assigned to all candidate surfaces corresponding to the surface i.
, And the coordinates (x _kl ′, y _kl ′, z) of the vertices for the surface k.
_im ′) and the first neighboring surface defined as a surface that is adjacent to or overlaps with a surface or line segment that overlaps when projected onto the basic surface of the coordinate system, or a surface that this surface includes {E _kl
¹ ′} and a second neighborhood surface {E _kl ² ′} defined as a surface on which the line segments coincide with each other within the error h when projected on the coordinate axis, and a feature amount list is created, and the surface i For a plurality of candidate surfaces k of the wire frame model, a correspondence (i, k) between the surface i and the candidate surface k is created, and the probability P _ik ^t indicating the probability corresponding to i of k is repeatedly calculated. and obtaining while increasing the degree t of certainty by the initial probability P _ik ⁰ determines the nature of the surface k itself, when obtaining more probability P _ik ^{t + 1} of higher from the probability P _ik ^t of degree t Is j, the first neighboring surface of the surface i is j, and the candidate surface of the surface j is l,
The first matching coefficient r _ijkl ¹ is defined as being large when the surfaces k and l are separated from each other and non-parallel, and small when they are parallel and close to each other. If m is a candidate surface of h and i is a simple plane or a compound plane,
In the wire frame model, the surfaces k and l share two vertices within the range of the allowable error h, and the surface m is more stable than the surface k.
When the distance is larger than the existing basic surface, it is large, and when it is not, it becomes small, and when i is a division plane, the surfaces k and l share two vertices in the range of the allowable error h in the wire frame model, The first matching coefficient r _ihkm ² is defined when the surface m is larger than the surface k when the surface i extends near the existing basic surface, and the second matching coefficient r _ihkm ² is smaller when the surface i is not present, and the first matching when l is changed. The sum of j obtained by multiplying the maximum value of the coefficient r _ijkl ¹ by the t-th probability P _jl ^t corresponding to j of l that gives this, and the second matching coefficient r when m is changed
_The coefficient q _ik ^t is calculated by adding the maximum value of _ihkm ² and the t-th probability P _hm ^t corresponding to h of m that gives this, and the coefficient q _ik ^t is obtained. The probability P _ik ^t multiplied by the probability is normalized to obtain a higher-order probability P _ik ^{t + 1,} and k that gives the maximum probability after a certain number of calculations is determined to be the optimal corresponding surface of the surface i. Characterize.

[0018]

The limitation of the object to be treated in the present invention will be clarified first. It is assumed that the target object treated here can be uniquely restored to a polyhedron from the trihedral view if there is no error included in the vertex coordinates.

Furthermore, it is assumed that the target object is a polyhedron which satisfies the following three conditions. (1) The three-view drawing representing the target object is composed of a solid line and a broken line, and does not use other auxiliary symbols. (2) The target object is composed of a straight ridge and a plane. (3) The number of planes sharing an edge line with respect to an arbitrary edge line of the target object is an even number of two or more.

The condition (1) is that the line segment treated in the present invention is only a straight line and a broken line and does not include auxiliary lines such as a center line, a dimension line, a hatching line and a lead line.

The condition (2) is that the polyhedron is composed only of planes,
This means that it does not include curved surfaces.

The condition (3) is that the rectangular polyhedron as shown in FIG. 1 is not handled. Although a figure like a dice is shown in FIG. 1, it is not so. It is a square tube with an opening in the front. The ridgeline in the foreground belongs to only one plane. Of course, it can be said that the cylindrical back surface and the front surface belong to two surfaces, but the back surface is a back surface and is not included in the surface. So the ridgeline in the foreground belongs to only one plane. A graphic without such a thickness is not treated.

An object of the present invention is to restore a polyhedron satisfying the above three conditions from a trihedral view. Considering a real system, a three-dimensional drawing is read by a scanner and a wire frame model is created based on this, which includes many errors between the coordinates of corresponding vertices. It results in absorbing many errors contained in the data and determining the appropriate corresponding surface.

[1. Face Labeling] First, label each plane shown in the three-view drawing. For ease of explanation,
The method of the present invention will be described by taking the three-view drawing of FIG. 2 as an example. This three-sided drawing is drawn on paper. This is input to the computer by an image scanner.

Of course, the image may be drawn on the display from the beginning with a mouse, a digitizer, or the like.
On input, the drawing is binarized and quantized into an NxN mesh. It may be either trigonometric or monogonal, but here it is assumed to be drawn by trigonometry. The figure on the XY plane may be referred to as a plan view, the figure on the YZ plane may be referred to as a right side view, and the figure on the ZX plane may be referred to as a front view.

In the normal construction method, the center line, the lead line,
Although lines such as a shadow line and a hatch are drawn, all the lines which are not directly necessary for representing the outer shape are omitted in the three-view drawing of the present invention. The three-view drawing of the present invention includes only lines showing the outer shape. That is, the three-view drawing of the present invention includes only outlines and hidden lines (represented by broken lines). The hidden line is hidden by the surface on this side, but on the other side it is a line corresponding to the shape. Included in the outline line.

Although three image data are obtained, all of them become N × N digital data. Since only the outer shape is targeted, it is binarized into black and white binary data. The three-view drawing to be input in this way consists of a solid line and a broken line. Since these are outlines, these are ridges of the surface, and the lines are not cut in the middle.

The plane of the three views separated by the solid line is called a simple plane. A plane divided by a solid line and a broken line is called a division plane. A plain plane and a division plane are adjacent to each other, and a plane in which these are merged is called a composite plane.

First, a label is attached to a simple plane separated only by a solid line. When a simple plane is divided by a broken line, a dividing plane occurs inside, so labels are added to these dividing planes. If the simple plane and the dividing plane are adjacent to each other, a label is added to the compound plane obtained by merging them.
Candidate planes that can be restored are three types of planes: simple planes, division planes, and compound planes.

A method of labeling a surface will be described with reference to FIG. This is a simple example, but shows a further portion of one of the three views. The shape is such that two triangles overlap each other. Explanations are given by adding symbols I to E at vertices and intersections. The surfaces separated by the solid line are the triangular hanilo and the triangular iniho. This is a simple plane as it is surrounded by a solid line. Label them as face 1 and face 2, respectively.

Since the simple plane Inho has a broken line Rojo delimiter inside, it is divided by the broken line Rojo. It becomes Rohoni and Rohoi This is a dividing plane because it is separated by a solid line and a broken line. Label Rohoni as 3 and Rohoy as 4.

The broken line corresponds to the outer shape to the last, and represents the surface which is covered with the near surface and cannot be seen from here. The importance is equivalent to the solid line. Roughly speaking, the broken line corresponds to the far surface and the solid line corresponds to the near surface.

Since the simple plane 1 and the division plane 3 are connected via the solid line Roni, the plane Haniho which integrates them is a compound plane. This is designated as surface 5. In this example, five surfaces will be labeled. When defining the composite plane 5, the simple plane 1 and the division plane 3 have line segments halo and rojo and are continuous, so that one composite plane is assumed. If the solid line and the broken line are continuous, a compound plane is created. It may be straight or polygonal.

FIG. 4 shows an example of labeling the three views of FIG. Since there are only two simple planes on the ZX plane (front view), they are labeled as 1 and 2 respectively. Since there are two simple planes in the XY plane (plan view), they are labeled as 3 and 4. The YZ plane (right side view) has one simple plane and two division planes separated by a broken line therein. Label the simple planes 5 and the split planes 6, 7. There are no compound planes in this example.

[2. Extraction of Surface Feature Amount] Next, the feature amount is extracted from each labeled plane, and a feature list of each plane of the three views is created. The feature amount of a surface means the coordinates of the vertices of the surface and the type of the plane. In the present invention, since a figure including a curved surface is not targeted, all lines that bound the surface are line segments (a part of straight lines). Therefore, the outline of the surface can be specified by the coordinates of the vertices.

The vertex coordinates are represented by three-dimensional coordinates. When the vertex is represented by (X, Y, Z), 1 ≦ X, Y, Z ≦ N. However, since it is the vertex of the surface in the trihedral view, the coordinate value in the direction perpendicular to the surface cannot be known. For example, in the case of the XY plane, the Z coordinate of the apex is unknown. It is necessary for the polyhedron to restore the polyhedron to find the Z coordinate in this case.

Next, the types of surfaces are the three types of simple planes, division planes, and compound planes, as described above.

The feature list is a list of feature quantities for each surface. Table 1 shows a feature list for the example of FIG. The label of the surface is listed at the left end, the coordinates of the vertices are listed in the middle column, and the type of surface is listed at the right end. Type of surface is parameter w
Express with. The simple plane is represented by w = 0, the division plane is represented by w = 1, and the composite plane is represented by w = 2. Of course, the choice of this parameter is arbitrary.

[0039]

[Table 1]

Surface 1 is the Γ of the XZ plane (front view) in FIG.
It is the surface of the mold. In order from the vertex closest to the origin, To, Chi, Li,
Explanations will be given with nu, le, and wo symbols. Table 1 is a list of characteristic surfaces, and symbols such as G, J, and so on are not originally included, but these symbols are included here for the sake of clarity. The vertex is X = 1 and Z = 1. I do not know the XZY coordinates. If you don't understand, use *.

The vertex G is therefore (1, *, 1). This is the beginning of the (x, y, z) column for surface 1 of Table 1. The apex is X = 1, Z = 124, and Y is unknown. The coordinates of this can be written as (1, *, 124). This is the second one for surface 1 in Table 1. Vertex is
Since X = 128 and Z = 124 and Y is unknown, (12
It can be written as 8, *, 124). The apex is X = 127, Z =
At 60, Y is unknown and can be written as (127, *, 60). Since the vertex Le is X = 64 and Z = 64, (64,
*, 64). Similarly, the vertex is (64, *, 1).

Such coordinate values are obtained as the coordinates of the vertices when the data is read by an image scanner and binarized to obtain the vertices. This is mentioned as a feature amount in relation to the surface. Finally, since surface 1 is a simple plane, w = 0. This is listed in the rightmost column.

Although the surface 2 has four vertices, three of wo, le and n overlap with the vertices of the surface 1. The unique apex is mosquito. Also in the field of surface 2, the coordinates of w, le, and n are shown.
Since the points are listed in counterclockwise order from the point near the origin, the order is slightly different from that of surface 1, but there are three points that are the same. The vertex point is a unique point on the surface 2. Since this is X = 126 and Z = 1, (12
Write 6, *, 1). Since surface 2 is a simple plane, w =
It becomes 0.

The surface 3 is the XY surface. Since it is on the XY plane, the Z coordinate cannot be determined. From the one closest to the origin, counterclockwise is marked with yo, ta, le, and se. X is 6 at the top
Since 4, Y = 1, it becomes (64, 1, *). The vertex is (126,1, *), and the vertex is (126,61,
*) And the vertex S is (64, 61, *).

The feature quantity is extracted in the same manner as described below. Surface 5 is a simple plane (w = 0). The symbol "Wannom" is attached to the top. Since the surfaces 6 and 7 are the dividing planes of the surface 5,
Let W = 1. The vertices of surface 6 are u, d, ko, fu, and the vertices of surface 7 are d, ヰ, no, mu, fu, ko. Next, the coordinates of these vertices are listed together.

C (*, 1,1) d (*, 61,1) (*, 124,1) no (*, 128,128) m (*,
1,128) Hu (*, 1,65) (*, 64, 65)
In this way, Table 1 is created. Table 1 shows a feature list.

[3. Creation of Near Surface List] The following two kinds of near surface lists are created for the extracted planes. The near surface includes a first near surface and a second near surface.

[First Near Surface]

In the case of the simple plane w = 0 and the complex plane w = 2, the surface adjacent to each other through the solid line in each plan view is defined as the first neighboring surface.

When the simple plane w = 0, when the simple plane includes division planes, these division planes are also the first neighboring planes.

When the division plane w = 1, the simple plane including the division plane and the division plane adjacent to each other via the broken line are defined as the first neighboring surface.

The first neighboring surfaces are surfaces parallel to each other or surfaces oblique to each other. This is because the surfaces appear in the same drawing. However, when the polyhedron is restored, the first neighboring surface is not in the same plane as that surface. This is because there is no way that a solid line will appear between the simple and compound planes if they are on the same plane and are adjacent to each other.

If the simple plane includes a plurality of division planes, these division planes should be farther from the projection plane than the simple plane. In the division plane, the simple plane including this is closer to the projection plane and cannot be on the same plane. If another division plane adjacent to this is on the same plane, a broken line should not appear between them. Therefore, even in the split plane, the first neighboring surface should be on a surface different from that surface.

[Second Near Surface]

Line segments forming all the planes (simple planes, divided planes, compound planes) of each plan are projected on each axis, and line segments projected from other plan on each axis are 1 When they match with each other, these surfaces are defined as the second neighboring surface.

The second neighboring surface of a certain surface is a surface that may be adjacent to that surface in the polyhedral restoration result. Since adjacent planes share vertices, if these vertices are projected on different views, the line segments connecting these vertices should coincide when projected on the axis.

However, in the present invention, since the original drawing may include an error, even if the line segments represent the same line segment, they do not always match in each of the drawings. Therefore, a range h is set that allows the positional deviation of both end points of the line segment. In other words, even if the projection of the line segment on each axis does not match, it does not exactly match, but the difference between the end points of the line segment is h
If it is within the range, it is assumed that there is a one-to-one correspondence.

Generally, when a certain surface A has a first neighboring surface B, the surface A is the first neighboring surface of the surface B. . In addition, surface C is surface A
If it is the second neighboring surface of, the surface A is the second neighboring surface of the surface C. Thus, the first and second neighboring surfaces are reciprocal.

Further, one surface is not the first near surface and the second near surface at the same time as the other surface. That is, the first neighboring surface,
The second neighboring surface is complementary. Reciprocity and complementarity are common characteristics of the first and second neighboring surfaces.

A list of the first and second neighboring surfaces for each surface is the neighboring surface list. Table 2 shows an example of the near surface list in the case of FIG. The first column is the surface i in the three-view drawing, the second column is the first neighboring surface, and the third column is the second neighboring surface.

[0061]

[Table 2]

The surface 1 is in contact with the surface 2 on the XZ plane via a solid line. Therefore, the surface 2 is the first neighboring surface of the surface 1. The second neighboring surfaces of the surface 1 are the surfaces 3, 4, 5, 6, and 7. Surface 3
Since the line segments Tayo and Reso of No. 2 coincide with the line segment null of the surface 1 in the projection line, the surface 3 is the second neighboring surface of the surface 1. Since the line segment dust of the surface 1 and the line segment Nera of the surface 4 coincide with each other in the projection line, the surface 4 is also the second neighboring surface of the surface 1.

Since the line segment tochi of the surface 1 coincides with the line segment um and the square of the surface 5 in the projection line, the surface 5 is also the second neighboring surface of the surface 1. Since the line segment of the surface 1 coincides with the line segment Uhu and Echo of the surface 6 in the projection line, the surface 6 is the second neighboring surface of the surface 1. Since the line segment Tochi of the surface 1 and the line segment Eno of the surface 7 coincide with each other in the projection line, the surface 7 is also the second neighboring surface of the surface 1. In this way, the second neighboring surface of the surface 1 becomes the surfaces 3, 4, 5,
It can be seen that they are 6 and 7.

The surface 2 has the surface 1 as the first neighboring surface. This is because they are adjacent to each other via a solid line. Surfaces 3, 4, 6 and 7 are surface 2
Is the second neighboring surface of. Since the projection lines of the line segment Kao and the line segment Tayo on the X axis match, the surface 3 is the second neighboring surface of the surface 2.
Since the projection of the line segment null and the line segment lithograph on the X-axis matches, surface 4
Is the second neighboring surface of the surface 2. Line segment eco and line segment Rwo
Since the projections on the axes coincide, the surface 6 is the second neighboring surface of the surface 2. Since the projection of the line segment Eco on the Z axis coincides with the projection of the line segment Rwo, the surface 7 is the second neighboring surface of the surface 2.

Surfaces 3 and 4 are very similar to surfaces 1 and 2 and will not be described.

The surface 5 is a simple plane (w = 0). There is no surface on the yz plane that contacts it via the solid line. However, when the simple plane includes the dividing plane from the above definition of the dividing plane, the simple plane and the dividing plane have the relation of the first neighboring surface. Although it is a simple plane, the plane 5 includes the dividing planes 6 and 7, so that the plane 6
And 7 are the first neighboring surfaces of the surface 5.

The second neighboring surfaces of the surface 5 are the surfaces 1 and 4. Since the Z-axis projections of the line segment tochi and the line segment um are the same, surface 1 is the second
It is a near surface. Since the line segment and the line segment coincide with each other in Y-axis projection, the surface 4 is the second neighboring surface. Besides this, the surface 5 has no second neighboring surface.

The surface 6 is a division plane (w = 1). Since the simple plane including this is the surface 5, the surface 5 is the first neighboring surface. The surface 7 contacting via the broken line is also the first neighboring surface. Face 6
The second neighboring surfaces of are surfaces 1, 2, 3, and 4. Since the Z-axis projections of the line segment eco and the line segment match, it can be seen that the surface 1 is the second neighboring surface.

For the same reason, it can be seen that the surface 2 is the second neighboring surface of the surface 6. The surface 3 is the second neighboring surface of the surface 6 because the line segment width and the line segment width coincide with each other in the projection onto the Y axis. For the same reason, the surface 4 is the second neighboring surface of the surface 6. In this way, the neighbor surface list in Table 2 in which the first neighbor surface and the second neighbor surface can be assigned to all the surfaces can be created in this way.

In general, the features of a surface are the coordinates of each vertex, the type of surface, and the labels of the first and second neighboring surfaces. This is summarized and expressed as follows. Information about the plane of the three views O

O = [O_i ]_{i = 1} ^M P = [[X_im, Y_im, Z_im]_{m = 1} ^MiV, W_i , [E_ij ¹]_{j = 1} ^Mi1, [E_ij ²]_{j = 1} ^{Mi  2} ]_{i = 1} ^M P (1)

Here, i is a number given to each plane, and O _i is information about each plane. MP is the total number of planes and should be written as M (P).
Since there are no parentheses in the suffix, it is unavoidably written as MP here.

Since the following equations cannot be accurately expressed in JIS, equations (1) to (7) are shown in FIG. 16 and equations (8) to (13) are shown in FIG. The formulas written in the specification are abbreviated ones due to JIS restrictions. Not accurate.

M is the number of the vertex on the surface i. [X
_im , y _im , z _im ] are the coordinates of the m-th vertex. MiV
Is the total number of vertices of face i. V is a superscript suffix enclosed in parentheses, but since the parentheses cannot be raised to suffixes in JIS, parentheses are omitted. M _i ¹ is the number of first neighboring surfaces of the surface i. This too should be enclosed in parentheses and raised to the suffix, but JIS does not allow such notation, so it is written like this. E _ij ¹ is the label of the first neighboring surface of the surface i. j indicates the number of the first neighboring surface.

E _ij ² is the label of the second neighboring surface of the surface i. j indicates the number of the first neighboring surface. j is the number of the second neighboring surface, which is different from j in the above, and has a ‘
Since S cannot write a suffix with ', it is written in a simplified manner like this. Further, 2 on the right shoulder is not the square, but 2 on the second neighboring surface. The brackets do not fit on the right shoulder, so it is written like this. Don't be confused.

[4. Creation of wire frame model] A wire frame model is created from three views. This is a three-dimensional view and is made by backprojecting the faces of the three views. Back-projection means that a known three-view drawing is set up so as to be represented by three-dimensional coordinates, a group of normals is set up from each line, and a solid is created by the intersection of the groups of normals.

Back projection is the reverse of projection, but it is not unambiguous but ambiguous. Backprojection allows many intersections of normal groups. Therefore, many planes occur in the wire frame model. Some of them are the planes shown in the first three views. This is the real aspect.

However, some real faces do not appear in the first three views. This is because the starting drawing is a three-view drawing, not a six-view drawing. If the hexagonal view could be used as a starting drawing, all real planes would have been numbered from the beginning.

However, the characteristic feature of the wire frame model is, of course, that it is not the case, that is, many imaginary planes that do not exist are generated because the planes are formed by many intersecting line groups.

In other words, when one observes the surface of the three-view drawing, when the surface of the wire frame model is projected on the three-view drawing, there are many surfaces projected on the surface i of one certain three-view drawing. A plane that matches the plane i when the wire frame model is projected onto a three-view drawing is called a candidate plane.

Since there are several candidate planes for one surface, the surface in the wire frame model corresponding to the surface i must be determined. Only one of the candidate planes corresponds to the actual plane i. The other planes are imaginary planes and are generated by backprojection to create a wireframe model.

FIG. 5 shows a wire frame model created by back-projecting the three-view drawing shown in FIGS. Although it is a simple example, it can be seen that many extra non-existing surfaces occur. For reference, surface numbers are given to the surfaces corresponding to the surfaces i = 1 to 7 in the three-view drawing.

There is a point to note here. If it is a plane parallel to the basic planes (XY plane, YZ plane, ZX plane) of the three views,
It does not appear on more than one of the three basic views. However, the surface that is inclined with respect to the basic surface appears in two surfaces. It has two labels in the three-view drawing. FIG. 6 shows such an inclined surface. This appears in both the plan view and the right side view. On the same side, but with two labels. When it is tilted in three directions, it also appears in the front view and is labeled as 3.

[5. Label the Faces of the Wireframe Model] The wireframe model has many faces, but all of these faces are numbered. The number of the surface is called a label, and the numbering on the surface is called a label.
This label is different from the first three-view drawing label (denoted by i). A surface in the wire frame model is represented by k.

FIG. 7 shows an example in which the surface of the wire frame model of FIG. 5 is labeled. Label all the faces that may correspond to face i in the three-view drawing, but in any order. Since it is a three-sided view, not all outer surfaces are labeled. Therefore, not all surfaces are labeled even in the wire frame model.

The plane has several corners. A circular arc is drawn in any of the corners in the direction including the surface, and the number k in the wire frame model is written beside the circular arc. In the case of the three-view drawing, the broken line was used, so there were split planes and compound planes, but in the wire frame model, the plane is created only by the solid lines, so there is only a simple plane. More faces appear than in the tri-view, with k = 1 to 17 in this example.

These planes are obtained by back-projecting the planes in the trihedral view. However, since the trihedral planes themselves include errors, the vertices of the respective planes in the wire frame model do not always match, and there is some discrepancy. ing. FIG. 7 also shows the coordinates of different vertices. However, the range of the discrepancy between the vertices is predetermined to be within a constant value h. The plane correspondence list is a list of correspondences between the corresponding surfaces i and k by projection and back projection. Table 3 is a plane correspondence list showing the correspondence between the three views of FIG. 2 and the respective surfaces of the wire frame model of FIG. 7.

[0088]

[Table 3]

[6. Extraction of Feature Amount of Surface of Wire Frame Model] Similar to the extraction of the feature amount on the surface of the three-view drawing, the feature amount is also extracted for each plane in the wire frame model. The feature amount is the coordinates of the vertex of the surface, the type of the surface, and the neighboring surface. However, since there are no division planes and compound planes in the wire frame model consisting only of solid lines, the plane types are only simple planes (w = 0).

Information about a plane in the wire frame model is represented by T. This is information T _k (k =
1, 2, ..., N (T)). T _k itself is composed of coordinates of vertices, surface type, first neighborhood surface, and second neighborhood surface.

T = [T _k ] _{k = 1} ^{N T} = [[x ′ _kn , y ′ _kn , z ′ _kn ] _{n = 1} ^NkV , w _k , [E ′ _kl ¹ ] _{l = 1} ^Nk1 , [E ′ _Kl ² ] _{l = 1} ^Nk2 ] _{k = 1} ^{N T} (2)

Here, n is the number of the vertex of the surface k.
[X ′ _kn , y ′ _kn , z ′ _kn ] are the coordinates of the vertices of the surface k. The ‘’ indicates coordinates on the plane of the wire frame model. NkV is actually _Nk
It is written as (V) and is the total number of n-th vertices of the surface k. JI
Parentheses are omitted in S because parentheses cannot be suffixed.

W _k is the type of surface k. E ′ _kl ¹ is face k
Shows a first neighboring surface of the. It is because it is for the plane of the wire frame model. l is the surface k
Is the number of the first neighboring surface of. Nkl is the total number of first neighboring surfaces of the surface k. l = 1, 2, ..., Nkl. 1 indicates the first surface, and k indicates the th surface. The capital letter N represents the total number.

_E'kl ² indicates the second neighboring surface of the surface k. l is the number of the second neighboring surface. Actually, it should be attached with ′ to distinguish it from the number of the first neighboring surface described above.
It is not possible to put the suffix in the JIS, so omit '. For exact notation, refer to FIG.

The definitions of the first neighborhood surface and the second neighborhood surface are almost the same as the definitions in the three views. However, the wire frame model has only a simple plane. This is because it was back-projected by a solid line, and it should include those that are split planes, compound planes, and the like. Therefore, it is defined as follows.

[First Near Surface] A surface which is in contact with the surface k via a line segment when a solid is projected on a three-dimensional view. A surface that includes or is included in a plane when a solid is projected on a three-dimensional view.

[Second Near Surface] A surface having common line segments when the surface is projected on a trihedral view.

If the surfaces i and j in the three views have the relationship of the first neighboring surface, the surfaces i and j in the wire frame model are obtained.
The surfaces k and l corresponding to are in the first neighboring surface. If the surfaces i and h in the trihedral view have the relationship of the second neighboring surface, the surfaces k and m corresponding to the surfaces i and h in the wire frame model.
Are in the relationship of second neighboring surfaces. This is called the principle of neighborhood surface invariance, and its attribute is called neighborhood surface invariance.

As described above, when one surface is the other surface, the former is the latter. This is called reciprocity of the near surface. Also, what is the second neighboring surface with respect to a certain surface cannot be the first neighboring surface with respect to the same surface. This was called the complementarity of the near surface. Reciprocity, complementarity,
Invariance is the main property of the near surface.

[7. Creation of Feature Amount List in Wire Frame Model] A feature amount list is created by obtaining feature amounts for the surfaces of the wire frame model. This is a list of the coordinates of the vertices, the labels of the first neighborhood surface, and the labels of the second neighborhood surface. Table 4 is a feature amount list for an example of the wire frame model of FIG.

The first column is the surface number k, the second column is the vertex coordinates of the surface, the third column is the label of the first neighboring surface, and the fourth column is the label of the second neighboring surface. The vertices are numbered in counterclockwise order starting with the one closest to the origin. There are 17 faces in all, so 1 from top to bottom
The feature amount for seven planes is described. The surface in the trihedral view of FIG. 4 is i, and the surface in the wire frame model of FIG. 7 is k.
Express with.

[0102]

[Table 4]

There are six vertices on the surface 1. Close to the origin (1,
Counterclockwise from (1,1) (1,1,124), (128,
1,124), (127,1,60), (64,1,6)
4), determine the coordinates as (64, 1, 1). In the three-view drawing, x is on the first row of Table 1 for the plane i = 1.
The z coordinate is listed.

(1, *, 1) (1, *, 124) (12
8, *, 124) (127, *, 60) (64, *, 6
4) (64, *, 1)

Since the i = 1 plane is a projection on the xz plane, there is no y coordinate. When backprojecting to make a wireframe model, the plane k = 1 emerges from the plane i = 1. The y-coordinate is obtained from the y-coordinate of the line segment of i = 4 and i = 5, and y = 1
Becomes Therefore, 1 is assigned to the y coordinate which is blank for i = 1 to obtain the vertex coordinate of the surface k = 1.

Since the surface k = 1 is a surface parallel to the xz surface, y
It seems natural that the same values are entered as coordinates. But not always.

The surface k = 2 also comes from the trihedral view i = 1, but the y coordinate is different. Not just different, but not the same y coordinate. In Fig. 4, the points that give the y-coordinate of k = 2 are four points of ne, la, ヰ, and no.
8, La is y = 124, ヰ is y = 124, No is y = 128
Is.

Therefore, the coordinate of k = 2 is the same as the above-mentioned three-view drawing in which the part of * in i = 1 is replaced by any of 128, 126, and 124, and is not the same. This is due to an error, and the surface is not inclined.

(1,124,1) (1,128,12)
4) (128,128,124) (127,128,6)
0) (64, 126, 64) (64, 126, 1)

The reason that the y coordinate at the beginning of the six points is 124 is because it corresponds to the point la in FIG. Second point y
The coordinates become 128 because they come from the points in FIG. The third point is also y = 128 from the negative point. Although the corresponding point of the 4th point does not exist in FIG. 4, y = 128. 5
There is no corresponding point in FIG. The 6th point has no corresponding point, but is in the middle of the ne and the la, so y = 126 is given.

Since the surfaces k = 3, 4, 5 come from the surface i = 2 in FIG. 4, the xz coordinates are determined as follows.

(64, *, 1) (64, *, 64) (1
27, *, 60) (126, *, 1)

Since the y coordinate cannot be determined, it is necessary to give the y coordinate.

For k = 3, the y coordinate is determined by ta, t, u, and m in FIG. 4, but since y is 1 in all cases, i = in Table 1
By substituting 1 for the y coordinate of 2, the coordinate of k = 3 can be determined.

For k = 4, the y-coordinate is determined based on the values shown in FIG. The former three have a y-coordinate of 61 and the last coordinate is 64. Therefore, the 2nd and 3rd points of k = 4 become y = 64.
The 1st and 4th points are y = 61.

For k = 5, the y-coordinate is determined from ne, la, square and no in FIG. Since points 3 and 4 correspond to ne, y = 128. Points 1 and 2 have no corresponding points. Since it is the midpoint of Nera (ne = 128, la = 124), y = 126 is given. This y coordinate does not exist as the coordinate of the original drawing, but it is adopted as the intermediate value.

The k = 6, 7, and 8 planes are the planes resulting from i = 3 in the three-view drawing. Since it is the xy plane, x,
The y coordinate is determined, but the z coordinate is not determined.

(64,1, *) (126,1, *) (1
26, 61, *) (64, 61, *)

The surface k = 6 comes from the positions k, w, u, etc. in FIG. 4, but since all z = 1, the vertex coordinates of k = 6 are determined by substituting 1 for *.

The surface k = 7 is determined by nu, le, hu, and ko in FIG. 4, but the z coordinate of nu is 60, the z coordinate of le is 64, and the z coordinate of hu is z.
The coordinates are 65, and the z coordinate of them is 65. Since the first point comes from Ruff and the fourth point comes from Ruko, the z coordinate is 64. Two
Since the number is from Nufu and the third is from Nuco, the average value is taken as z coordinate = 63 here. Originally z = 6
The point 3 did not exist in FIG. 4 of the original drawing, but here it occurs due to the averaging operation.

The surface k = 8 is determined from the positions r, j, m, and no in FIG. The z coordinates are Li = 124, Chi = 124, Mu = 12.
Since 8 and No = 128, these do not match. The first point is above Mu and is in the middle of Richi. So the intermediate value 1
I will take 27. The second point is on the rim. Therefore, the intermediate value 126 is set. The third point is 128 because it is on the top of the line and at the midpoint of Muno. The fourth point is the middle point of Richi and also the middle point of Muno. Here, the z coordinate is 127.

Similarly, the vertex coordinates of the surface of the wire frame model are determined in the same manner. In any case, the original surface is present in the three-view drawing, so the coordinates of the two components are known.
All you have to do is determine the coordinates of the other component.

Next, the first neighboring surface is determined. In the three-view drawing, the surfaces are adjacent to each other via solid lines. Since the wire frame model is created by back-projecting a three-view drawing, all of the surfaces obtained by back-projecting that surface are the first neighboring surfaces.

A plurality of planes are generated in the wire frame model from one plane i in the three-view drawing. This is caused by back projection from the same plane. These are completely equivalent and have the same first neighborhood surface and second neighborhood surface with respect to the first neighborhood surface and the second neighborhood surface. Therefore, for the surfaces generated from the same surface, only the first surface and the second surface may be considered. The first neighboring surface is parallel to that surface. The second neighboring surface is not parallel to that surface.

The first neighborhood surface of the surface k = 1 is k = 3, 4, 5
There are three. This is because there is a possibility that they are adjacent to each other via the solid line due to the projection on the xy plane.

The first neighborhood surface of the surface k = 2 is also k = 3, 4, 5
There are three. k = 2 is the same as k = 1, i =
This is natural because it originates from 1.

From the reciprocity, the first neighboring surface of the surface k = 3 is k =
1 and 2. Other than this, there is no first neighboring surface. Surface k =
The first neighboring surfaces 4, 5 also have k = 1, 2. Originally k
= 3, 4, and 5 are formed from the same i = 2, and thus the first neighboring surfaces are the same.

The first neighboring surface of the surface k = 6, 7, 8 is the surface k =
9 and 10. This is natural since k = 6, 7, 8 results from the same i = 3 backprojection.

Due to reciprocity, the first neighboring surfaces of the surfaces k = 9 and 10 have k = 6, 7 and 8. Other than this, there is no first neighboring surface.

The plane k = 11 is projected on the same plan view and there are no planes adjacent to each other via the solid line. In the three views, the simple planes including the division planes were the first neighboring planes. k = 11 is k
= 13 and 16, they are the first neighborhoods for k = 11. Since k = 14 and 15 match with k = 13 by projecting, k = 14 and 15 are also the first neighboring surfaces with respect to k = 11. Also, k = 17 is k by projection
= 16, which is also the first neighborhood surface of k = 11.

Since k = 12 corresponds to k = 11 in projection, it has the same first neighboring surface. Therefore, the first neighboring surfaces with k = 12 are 13, 14, 15, 16, and 17. k
= 13 is in contact with k = 16 via the solid line. K =
17 results from i = 7 as well as k = 16. k = 1
1 includes k = 13. For this reason, the first neighborhood surface with k = 13 has k = 11, 12, 16, and 17.

Similarly to k = 13, k = 14 and k = 15 also occur from i = 6. Naturally, the first neighborhood surface is k =
11, 12, 16, and 17.

K = 16 includes k = 11 including this, and k = 12 generated from i = 5 which is the same as k = 16 is the first neighboring surface. Further, k = 13 adjacent to each other via the solid line is also the first neighboring surface. k
= 14 and 15 also occur from the same i = 6, so these are also the first neighboring surface. After all, the first neighborhood surface of k = 16 has k = 11, 12, 13, 14, and 15.

Since k = 17 arises from i = 7 like k = 16, the first neighborhood surface has k = 11,1.
2, 13, 14, and 15.

As described above, the first neighboring surface has been clarified for all the surfaces. Attention should be paid to the first neighboring surface in the wire frame model. The invariance of the first neighborhood surface is stated. This is the property that the surface in the first vicinity surface in the trihedral view is also in the first vicinity surface in the wire frame model. However, since the wire frame model has a large number of planes, the first neighborhood plane loses the significance defined in the trihedral view. Since the first neighboring surface in the three-sided view is a surface adjacent to each other via a solid line or a broken line, it is determined whether the surfaces are separated or bent on both sides of the line segment. There is no possibility of being on the same plane.

However, the first in the wire frame model
Near surfaces are coplanar (1 and 3, 2 and 5, 16 and 1
3 etc.) exist. This should be prohibited in principle, but this is caused by the ambiguity when creating the wire frame model from the three-view drawing. For this reason, similarly, it can be said that even if it is referred to as the first neighboring surface, there are one that conforms to the original definition and one that does not. That is, a rank occurs between the first neighboring surfaces. Therefore, it becomes possible to correctly determine the surface relationship by selecting the most suitable first neighboring surface.

Next, the second neighboring surface will be described. This is defined as a surface that coincides when the line segments that form the surface are projected on the three axes in the three-view drawing. Therefore, in the wire frame model, the surface sharing the ridgeline of the target surface is the second neighboring surface. Further, the surface that matches this surface by projection onto the basic surface is also the second neighboring surface. The second vicinity surface of a certain surface is the second vicinity surface of the surface.

The surface k = 1 has surfaces k = 9, 11, 10, 17, 7, 14 sharing the ridge line around it. These are, of course, the second neighboring surface. k = 12 is k = 11 and YZ
Since they match in the projection of the XY plane onto the plane, k = 1
2 is also the second neighboring surface of k = 1. k = 6 and k = 8 are k
= 7 and projection match (resulting from i = 3)
Therefore, these are also the second neighboring surface with k = 1. Since k = 13 and 15 are generated from i = 6 which is the same as k = 14,
k = 13 and 15 are also the second neighboring surfaces with k = 1. After all, k
The second neighborhood surface of = 1 is 6, 7, 8, 9, 10, 11, 1
2, 13, 14, 15, 16, and 17. That is, k
= 1, the surface that is not the second neighboring surface is k = 2, 3, 4,
It is the fifth side. Of these, since 3, 4, and 5 are the first neighboring surfaces, it is natural that they are not included in the second neighboring surface due to their complementarity. Since k = 2 is a surface having the same generation source that overlaps in projection, it is neither the first near surface nor the second near surface. Surface k =
Since 2 is the same occurrence as k = 1, the neighboring surfaces are equal.
The second neighboring surface is 6, 7, 8, 9, 10, 11, 12, 1
3, 14, 15, 16, and 17.

Since the surface k = 3 shares the ridge line with k = 6, 7, 14, and 15, these are the second neighboring surfaces. k = 8
Is the second neighboring surface because it has the same occurrence as k = 7. k =
In No. 13, since k = 15 or 14 is the second near surface, this is also the second near surface. When k = 17, there is a projection of a line segment that coincides with k = 3, so this is also the second neighboring surface. k
Since = 16 is the same generation surface as 17, it is also the second neighboring surface. Since k = 12 shares a part of the ridgeline but does not completely match, this is not the second neighborhood surface. Equivalent k
= 11 is not the second neighboring surface. k = 9 is the second neighboring surface of k = 3 because it has a line segment that does not share the ridge line but matches when projected on the axis. The same applies to k = 10. After all, the second neighboring surface of k = 3 is k = 6, 7, 8, 9, 10, 13, 1,
4, 15, 16, and 17. The remaining k = 1, 2 is the first
It is a near surface. k = 4 and 5 are the same occurrence planes. k =
11 and 12 are neither. The planes k = 4 and 5 coincide with k = 3 by projection, and thus have the same second neighboring plane as k = 3.

Since k = 6 shares a ridgeline with k = 3, 4, 15, and 14, these are second neighboring surfaces. k = 1,
2 is the second neighboring surface because it has a line segment that matches the projection on the x-axis. k = 16 and 17 have line segments that match in the projection on the y axis. After all, k = 1, 2, 3, 4, 5, 1
3, 14, 15, 16, and 17.

K = 7 and 8 have the same second neighboring surface as k = 6.

When k = 9, the edge is shared, and k = 9.
= 1, 14, 4, 17, 17, 2 and 11. These are the second
It is a near surface. K = 13 generated from these same planes,
15, 3, 5, 16, and 12 are also second neighboring surfaces. The second neighboring surfaces in total are k = 1, 2, 3, 4, 5, 11, 12, 1
3, 14, 15, 16, and 17.

Of course, k = 10 also has the same second neighboring surface.

K = 11, 12 means that k = 1, 2, 9, 10
Only the second neighboring surface is used.

When k = 14, the edges are shared, and
There are k = 1, 3, 6, 4, 7, 9. In addition to these same generation surfaces, the second neighboring surface is 1, 2, 3, 4, 5, 6,
7, 8, 9, and 10. k = 13, 14, and 15 have the same second neighboring surface.

K = 17 is a surface sharing an edge line, and k = 17
It has 1, 7, 4, 9, 10 and these are the second neighboring surfaces. Adding the same occurrence planes as these, k = 1, 2, 3,
4, 5, 6, 7, 8, 9, 10 are the second neighboring surfaces. k
= 16 is also the same.

Attention should be paid to the second neighboring surface. The second neighboring surface in the three-view drawing was two surfaces sharing the ridgeline and had to be adjacent. However, in the wire frame model, the second neighboring surface of the three-view drawing is widened to all the surfaces that may correspond to it, so that a surface that is not originally the second neighboring surface is also included as the second neighboring surface. That is, there is a true second neighborhood surface and an imaginary second neighborhood surface. Therefore, by using a random variable, it is evaluated whether the relationship between the target surface and the second neighboring surface is true or imaginary, and the degree of correspondence between the surface i of the three-view drawing and the surface k of the wire frame model is examined. You can

[8. Selection of Candidate Surface] FIG. 9 shows the method of the present invention in order. What has been described so far corresponds to the part written as "beginning" in FIG. The step of "creating a set of planes extracted from the three-view drawing and surfaces of the wire frame model" will be described below. Surface i of the three-sided view
And the plane k in the wire frame model is made to correspond.
All vertices of the surface k have three-dimensional coordinates. The surface i has two-dimensional vertex coordinates and lacks another coordinate. Surface i corresponds to any surface k. Calculate which face it corresponds to by calculation. If all the faces i and all the faces k are directly corresponded, the number [M (P)! / {M (P) -N (T)}! } Must deal with a huge number of correspondences. For example, M
Even in a very simple case of (P) = 5 and N (T) = 3, there are 5 × 4 × 3 = 60 cases. It can be seen that if the number of faces is large, the amount of calculation by the brute force method becomes enormous and it cannot be solved. However, upon careful consideration, it is possible to limit the range of the surface k that can be initially dealt with regarding i.

In the present invention, the surface k, which is the same as the vertex coordinates of the surface i in the two-dimensional coordinates, is associated with the surface i. That is, when projected on a three-view drawing, the surface k that overlaps i is associated. In this way, the surface k which is limited from the beginning and has a possibility of being corresponded to is a candidate surface of the surface i. This relationship is written as (i, k). There are multiple candidate surfaces k for one i. By performing the calculation, if this correspondence can be made 1: 1, the surface will be determined.

In the example of FIGS. 4 and 7, the candidate surface with i = 1 is
k = 1, 2. The candidate surfaces with i = 2 are k = 3, 4, 5,
Is. The candidate surfaces with i = 3 are k = 6, 7, and 8. i
= 4, the candidate surfaces are k = 9 and 10. The candidate planes with i = 5 are k = 11,12. The candidate surface of i = 6 is k = 1.
3, 14, and 15. The candidate surface of i = 7 is k = 16,
Seventeen. This is shown in Table 3 as the corresponding surface list (i, k).

[9. Setting Initial Probability of Correspondence Height] Correspondence (i, k) is only two or three in the above example. However, if the figure is complex, a larger set of correspondences will hold. From the candidate planes that make these correspondences, we investigate which is the best.

What indicates the corresponding height from the relationship with the neighboring surface is called the adaptation coefficient. The probability of correspondence is obtained using this, and the initial probability P _ik ⁰ is given first. Initial support P
_ik ′ is defined as follows. (However, suffix k
Should be enclosed in parentheses, and 0 indicating the order of approximation should be enclosed in parentheses, but since such an expression cannot be made in JIS, parentheses are omitted. )

(A) When the surface i is a simple plane w = 0,

P _ik ′ = [Σ _{n = 1} ^NkV {x ′ _kn ² + y ′ _kn ² + z ′ _kn ² } ^1/2 ] ⁻¹ (3)

N is the number of the vertex of the candidate surface k, and (x ' _kn ,
_y'kn , _z'kn ) are the coordinates of the vertex. NkV is the total number of vertices. This is the reciprocal of the sum of the distances from the origin of all the vertices of the surface k in the wire frame model.

When i is a simple plane, it appears as a solid line when projected on the basic surface, which means that it is closer to the basic surface in the three-view drawing. Then, the surface k in the wire frame model corresponding to this should be closer to the origin. Therefore, the initial correspondence is determined so that the probability that a distance between the vertex of the surface k and the origin is as small as possible is increased.
Although there are a plurality of corresponding surfaces k of i, the number of vertices is the same and the shapes are geometrically congruent. Therefore, when the above formula is calculated, the one corresponding to the distance from the origin to the surface centroid is obtained. Therefore, it is possible to give a high initial correspondence to those far from the origin by the above formula.

For example, the candidate surface of i = 1 has k = 1 and 2, and in reality k = 1 is the corresponding surface, but k =
One can be given a high probability. However, the situation is different for i = 2. Of the candidate surfaces k = 3, 4, 5, the one with the largest initial correspondence is k = 3, but the actual corresponding surface is k = 4, and it can be seen that the initial correspondence is not necessarily optimal.

(B) When the surface i is the division plane w = 1 or the composite plane w = 2,

P _ik ′ = Σ _{n = 1} ^NkV {x ′ _kn ² + y ′ _kn ² + z ′ _kn ² } ^1/2 (4)

This is the initial correspondence by calculating the sum of the distances between the vertices of the surface k and the origin. In the case of a dividing plane or a compound plane, it is drawn from a broken line, so it should be far from the basic plane. Therefore, a higher initial correspondence is given to a surface k having a large distance from the origin. However, this also does not give the correct probability from the beginning. i = 6 is a division plane and has candidate surfaces k = 13, 14, and 15. The initial correspondence P _ik ′ has the largest k = 15, but the actual correspondence surface is k =
It is 14.

Of course, the initial correspondence does not necessarily have to be in the order of the optimum probability. The initial correspondence is just an initial value and may be a constant. The above formula is selected in order to speed up the calculation convergence, but other determination methods may be used.

0 indicating that the candidate surface k is the corresponding surface of i
The next probability P _ik ⁰ normalizes the initial correspondence,

P _ik ⁰ = P _ik ′ / {Σ _k P _ik ′} (5)

Given by As already mentioned, this is determined so that the candidate plane closer to the origin in the case of a simple plane has a higher probability of being farther from the origin in the case of a division plane or a compound plane, and more Has been converted. Thereafter, the order t of the approximation is increased, but the random variable is
It is normalized so that the sum of the variables related to k is always 1 (Σ _k P _ik ^t = 1).

The initial probability P _ik ⁰ is determined by the characteristics of the surface i itself in the three views. However, it is not possible to decide the correspondence aspect with this alone. In order to accurately determine the corresponding surface, it is necessary to modify the probability stepwise by using the relationship between the first neighborhood surface and the second neighborhood surface. The property of the actual surface i itself is used only when setting the initial probability, and is not used thereafter. The isolated nature of the surface itself is of little use in determining the position of the surface. Conversely, the relationship with the near surface bears more information.

[10. Correcting the probability by the relative relationship with the neighboring surface] From the invariant principle of the neighboring surface, the first neighboring surface of the plane i and the second neighboring surface in the trihedral view are the first neighboring surface of the candidate surface k of i, 2 should match the near plane. The relationship between a certain surface and the near surface should be the same whether it is a three-view drawing or a wire frame model surface.

However, since many imaginary surfaces are formed in the wire frame model, some surfaces do not exist. Such a surface is often coplanar with the first neighboring surface. Further, it is often separated from the second neighboring surface. In the wire frame model, the improper relationship with the first and second neighboring surfaces is that this is an imaginary surface and does not correspond to the planes of the three views.

Therefore, among the candidate surfaces k of a certain surface i, if the correspondence between the first neighboring surface and the second neighboring surface is suitable as the original correspondence between the first neighboring surface and the second neighboring surface, then that surface k is , I is likely to be the corresponding surface. On the contrary, the first of the candidate surfaces k
The correspondence between the near surface and the second near surface is the original correspondence between the first near surface and the second
If the surface is not suitable for correspondence, it is an imaginary surface and i
It does not correspond to.

Therefore, using each plane i, the neighboring surface list, and the neighboring surface list of the candidate surface k, the correspondence between the two configurations is examined. If the surface i and the near surface are in harmony, and the surface k and the near surface are in harmony, the degree of correspondence P _ik with respect to k is strengthened, and if they are not in harmony, the degree of correspondence P _ik with respect to k is weakened. This is called TSUJI. The method of searching for the most suitable corresponding surface by combining Tsuji is called relaxation method. Even if it says the near surface, there are a first near surface and a second near surface. Therefore, it is necessary to carry out scrutiny on both the near surfaces.

[First Fitting Coefficient for First Neighboring Surface] This characterizes the correspondence between the surface of the three-view drawing and the surface in the wire frame model from the sameness of the relationship of the first neighboring surface. Let k be a candidate surface in the wire frame model for the surface i in the three views. The first neighboring surface of the surface i is j. Let l be a candidate surface in the wire frame model for the surface j.

From the above-mentioned invariant principle of the near surface, l is the first near surface of k. However, the first neighborhood surface in the wire frame model includes the original first neighborhood surface and the original first neighborhood surface. The first neighboring surface is a surface that is parallel and separate, or is bent and adjoins. However, in the wire frame model, parallel and contacting surfaces are also included. Such a first neighboring surface is far from its original meaning.

If l is the original first neighborhood of k, then i
The correspondence between k and k should be deeper. Therefore, the first neighboring surface can be evaluated in terms of its significance. A first value indicating the probability that l and k are mutually original first neighboring surfaces.
The matching coefficient r _ijkl ¹ is defined as follows. The suffix 1 means that it is for the first neighboring surface. It does not mean the 1st power.

This matching coefficient is "a plane adjacent to each other by a solid line (original first neighboring surface) does not exist on the same plane."
It reflects that. Since they appear adjacent to the same surface in the three-view drawing, the first neighboring surface cannot originally be on the same plane. Even if one side is shared, it should be slanted. That is, l and k
Is a first neighboring surface, it is required that the surfaces are separated or slanted. Therefore, the imaginary first neighborhood surface is dropped by using the following adaptation coefficient that has a large value in the case of the original first neighborhood surface.

R _ijkl ¹ = min [2 {1- | n _k · n _l | / | n _k || n _l |} + | n _k · ( _ak −a _l ) | / h, 2] (6 )

Here, min is a symbol for selecting the smallest one among [..., ...]. Inside the brackets is an expression and the number 2. Take whichever is smaller. n _k and n _l are normal vectors of the candidate surfaces k and l. You should put a → at the top, but J
This is omitted because IS cannot do this. The dot product of two vectors is represented by.

[...] means to take an absolute value. The first term of the first half of the expression in the parenthesis is, after all, obtained by subtracting 1 by the cosine of the angle Φ _kl formed by the normal line of the surfaces k and l and multiplying by 2. So it is sin ² (Φ _kl / 2). If the planes are parallel, this will be zero. If non-parallel, it will be a positive value.
The maximum is 1. This is an expression that the more the l and k are non-parallel, the higher the possibility of being the original first neighboring surface.

The second term of the expression in the parentheses will be described. a
_k is one of the vertex coordinates of the surface k other than the contact point between the candidate surfaces k and l. a _l is one of the vertex coordinates of the surface l other than the contact point between the candidate surfaces l and k. This is also a vector, but since → cannot be added, → is omitted.

This is because the more the distance between the surfaces k and l is, the higher the possibility of being the original first neighboring surface is. If the two planes are parallel, the second term of the equation will be a constant. In this case this represents the distance between the two parallel faces. h
Has already appeared, but it is the margin length of the discrepancy in the vertex coordinates. If they are not parallel, this is uncertain. It depends on how to take a _l . However, for different planes, it will be greater than 2h, so this term gives 2.

The first matching coefficient r _ijkl is a coefficient that gives the possibility that k and l are true first neighboring surfaces, but it will be small when the candidate surfaces k and l are in the same plane as a whole. It has become. This is because the true first neighboring surface should not appear in such a case. Roughly speaking, they are non-parallel, or when they are separated from each other, they are the original first neighboring surfaces. FIG. 8 is a diagram for geometrically _explaining the meaning of the matching coefficient r _ijkl .

FIG. 8A shows a case where the two candidate surfaces k and l are on the same plane. Since the normal vectors match, the first term in parentheses in (6) is 0. In addition, n _k · (a
_k -a _l) also becomes 0. Therefore, when k and l are in the same plane, r _ijkl ¹ becomes 0. These two sides are the first
It cannot be a near surface. That is, such a surface is prohibited as the first neighboring surface.

FIG. 8B shows a case where two candidate surfaces k and l share a side, but are oblique. This does not make the first term in equation (6) zero. The second term is the vector a
There is arbitrariness in the way _k and a _l are taken, but this is also not zero.
This may be 1 or more, depending on how h is selected. Therefore, in the case of two surfaces that are not parallel, the matching coefficient r _ijkl ¹ for the first neighboring surface is large.

FIG. 8C shows a case where the two candidate surfaces k and l are parallel but separated from each other. Because they are parallel,
The first term of equation (6) is 0. However, the second term is fixed, which is the distance between the surfaces divided by h. This can be greater than 2.

The first matching coefficient is a coefficient for checking whether the candidate surface k of i and the candidate surface l of j are mutually the first neighboring surfaces, with the first neighboring surface of the surface i being j. FIG. 8 (b),
It is highly possible that the two surfaces as in (c) are the first neighboring surfaces, but it will be understood that the first matching coefficient r _ijkl ¹ is determined so as to be large in these cases.

That is, r _ijkl ¹ takes a real value from 0 to 2, but it is 0 if k and l are on the same plane. This increases when the planes are tilted relative to each other or are displaced in the direction perpendicular to the planes. If the surfaces k and l are not on the same plane when they are displaced to some extent, this value is set to 2.

Since i and j are in the relationship of the first neighboring surface in the three-view drawing, if r _ijkl ¹ is large, it means that the candidate surfaces k and l are also in the relationship of the first neighboring surface. , K have a high probability of being a corresponding surface of i. However, since it cannot be said that the comparison of the first neighboring surface is reliable, it is necessary to investigate the correspondence relationship also for the second neighboring surface.

[Second Fitting Coefficient for Second Near Surface] Next, a second fitting coefficient r _ijkl ² for the second near surface is given. This is an index indicating the possibility that k and l are the original (true) second neighboring surfaces. Let the second neighboring surface j of the surface i in the three-view drawing be k, the candidate surface of i be k, and the candidate surface of j be l.
And l are the second neighboring surfaces.

However, the wire frame model includes many imaginary surfaces, and naturally includes the imaginary second neighboring surface. If l
If is an imaginary second neighboring surface, the possibility of correspondence between i and k is reduced. The imaginary second neighborhood must be excluded. If k and l are original second neighboring surfaces, there is a high possibility that i and k correspond. Therefore, r is used as a matching coefficient for knowing whether k and l are original second neighboring surfaces.
I made _ijkl ² . The suffix 2 should be parenthesized to be (2), but the parentheses are omitted in JIS, so the parentheses are omitted. It does not mean squared.

Generally, the simple plane and the compound plane are planes that are directly visible when viewed from the basic planes (xy plane, yz plane, zx plane). Therefore, there must be other planes that are farther than the base planes than these planes. On the other hand, in the case of a division plane, since it is divided by a broken line, it cannot be the closest plane to the basic plane of the polyhedron. There should be a side closer than this. By using such a property, the second matching coefficient r _ijkl ² is defined as follows.

R _ijkl ² = e ₁ × e ₂ (7)

E ₁ and e ₂ are defined as follows. (I) In the case of simple plane w = 0 and complex plane w = 2, e ₁ = 2: two adjacent vertices of the surface k and the surface l coincide with each other within the corresponding allowable range, and the plane l from the contact point Among the vectors that connect the other vertices of, there is a vector that is positive with respect to the axial direction that is not represented in the view including i. = 0: Others (8) e ₂ = 1- (sum of distances between vertices of k and l that are supposed to be the same) / 2h (9)

(Ii) In the case of the division plane w = 1, e ₁ = 2: two adjacent vertices of the surface k and the surface l coincide with each other within a corresponding allowable range, and from these contact points, the other of the plane l Among the vectors that connect the vertices, there is a vector that is negative with respect to the axial direction that is not represented in the view including i. = 0: Others (10) e ₂ = 1- (sum of distances between vertices of k and l that are supposed to be the same) / 2h (11)

The definition of e _{1 is} as follows although it may be difficult to understand. In the case of the second neighboring surface in the three-view drawing, the line segments projected on the axes match,
Originally, the line segment should be shared. Therefore, in order to express the original second neighboring surface, this is "matched by adjacent vertices".
It is expressed by the sentence.

The "axial direction not represented by the plane view including i" is an axis perpendicular to the projection plane of the plane i. Surface i
Is a plane in the xy plane, which means the z-axis direction. Since the second neighboring surface shares only one line segment, the directions of the surfaces are different. The second neighboring surface of the surface i should have a component orthogonal to the surface onto which the surface i is projected. This also represents the property of the second neighboring surface.

The above is the common property of the second neighboring surface,
Here we go further and assume that there is a positive component in the axial direction. Being positive in this axial direction means x, y,
It is positive in the z direction. That is, when the surface i is a simple plane and is a compound plane, e ₂ = 2 is set when l is in a direction farther from the origin than the shared vertex with k. When the surface i is a simple plane or a compound plane, it should be close to the basic surface, and the second neighboring surface should be farther from the basic surface than the basic surface. This is a vector that is positive. This utilizes the property of the plane i (simple plane, compound plane).

On the other hand, when the surface i is the division plane, and when l is in the direction farther from the origin than the common vertex with k, e ₂
= 2. Since the division plane should be far from the basic plane, the second neighboring plane is closer to this, and this is expressed as a vector that is negative in the axial direction.

The reason for using e ₂ is that the present invention also handles ones that have an error with respect to the vertex coordinates. This corresponds to the premise that if the difference in vertex coordinates is within the distance h, they are treated as the same point. If the vertices match, e ₂ = 1.

Even if it is considered that two sets of vertices may coincide with each other, if the sum is 2 h or more, this is not a mere error but an actually different line segment. In this case, the two surfaces k and l cannot be the second neighboring surface. That's why I write "I think it should match".
It is assumed that there are two vertices that match in the definition of e ₁ , although they are supposed to match in principle. When the sum of the disparity between the two vertices is 2 h or more, e ₂ = 0.

When no error is allowed, the limit is h → 0, and the two vertices must be exactly shared. The present invention does not, but allows the presence of error. This is evaluated by e ₂ .

E ₁ takes a value of 0 or 2. e ₂ has a value of 0 to 2. Therefore, the second matching coefficient r _ijkl ² takes a real value of 0-2.

In order to adjust the list of the first and second neighboring surfaces, the degree of correspondence P _ik ^t described above is updated by the equation using the matching coefficients r _ijkl ² and r _ijkl ² . Here, the suffix t indicates the order of the iteration of calculation. It is not the t-th power. In the explanation so far,
Although the suffixes are the same, r _ihkm ² is used for the second matching coefficient hereafter for the sake of distinction. Here, h should not be confused with h indicating the range of error.

P _ik ^{t + 1} = q _ik ^t × P _ik ^t / {Σ _k q _ik ^t × P _ik ^t } (12)

[0202] ^{_{q ik t = Σ j {max}} l (r ijkl 1 × P jl t)} + Σ h {max m (r ihkm 2 × P hm t)} (13)

Max _l and max _m mean that when l and m are changed, they take the maximum value in parentheses following them. The term q _ik ^t is an expression for evaluating the size of the correspondence between the plane i in the three-view drawing and the plane k in the wire frame model. The first term of q _ik ^t is the first neighborhood surface,
The second term is a calculation regarding the second neighboring surface. Since the correspondence between the surfaces i and k is considered, i and k are all common, but j and l and h and m are not.

In the first term regarding the first neighboring surface, the first
The fitting coefficient r _ijkl ¹ means that the first neighboring surface of the surface i is j, the candidate surfaces of the surfaces i and j are surfaces k and l, and the surfaces k and l are close to the true first neighboring surface. Is a coefficient that represents. k and l
Of course, it is the first neighboring surface, but the first neighboring surface also has a degree of difference. This is a plurality of coefficients because there are many first neighboring surfaces and several candidate surfaces for one surface. Briefly, this gives a maximum value of 2 if k and l are true first neighbors, and close to 0 otherwise.

In the three-view drawing, since the surfaces i and j are the first neighboring surfaces, the candidate surfaces k and l are in the relationship of the first neighboring surface. However, the first neighboring surface has a certain degree. If k and l are true first neighboring surfaces, this correspondence is likely to be correct. To this, it is to apply the P _jl ^t. P _jl ^t is,
It is a probability indicating the degree of correspondence between the surface j of the three-view drawing and the surface l of the wire frame model. t is the order of the iteration, which indicates the previous result. Of course, j and l are combinations of the surfaces listed in the corresponding surface list (Table 3) and not all combinations of the surfaces.

If the probability that j and l correspond to each other is high, and k and l are true first neighborhood surfaces, the probability that i and k correspond should increase more and more. On the contrary, when the probability of the correspondence between j and l is low, it cannot be said that the probability of i and k corresponding to each other is high even if k and l are the first neighboring surfaces. Since there are many first neighboring surfaces, the corresponding surface of j and k
There is a strong possibility that it is a first neighboring surface other than.

Further, when the correspondence probability between j and l is low, r
_{If ijkl} ^{1 is} also low, then l as the corresponding surface of j is wrong. Of these, the one with a different l is compared by the calculation of max _l and the largest one is adopted. Taking the maximum value of different l means that the degree of correspondence between the first neighboring surface j and the surface l is high with respect to this l, and that the surfaces l and k are highly likely to be the first neighboring surface. That's what it means.

Then, it can be said that the surface l that gives the maximum value is the most reliable as the corresponding surface of the surface j.
The other faces are not considered to be the corresponding faces of j, so
The max operation for l is performed, and the calculations for other surfaces are discarded.

There are many first neighboring surfaces of the surface i. Here, for one first neighboring surface j, the surface 1 that is probably corresponding to this and the previous corresponding probability of the surface j are , And the first matching coefficient r _ijkl ¹ . This means that the height of the correspondence between i and k is evaluated through one first neighboring surface j. Since there are a plurality of first neighboring surfaces, the same maximum value is calculated for all the first neighboring surfaces j, and all the maximum values are added (Σ _j ). The larger this is, the higher the probability that i and k correspond.

Similar calculations are performed for the second neighboring surface.
The candidate surface of the surface i is k. The second neighboring surface of i is h, and the candidate surface of the surface h is m in the wire frame model.
Naturally, k and m are the second neighboring surfaces. Second fit coefficient r _ihkm
² is a value indicating the possibility that the surfaces k and m are true second neighboring surfaces. The probability P _hm ^t is the probability that the surface h and the surface m, which is a candidate surface, correspond to each other last time. Then P _hm ^t
r _ihkm ² _{indicates the probability} that the candidate surface k of the surface i and the candidate surface m of the second neighboring surface h of the surface i are true second neighboring surfaces, and that h and m correspond to each other. .

The max _m is an operation that takes the maximum value by changing m in the expression in parentheses. Taking the maximum here, this means that the surface m is the second neighboring surface of k and the one having the highest degree of correspondence with h among the candidate surfaces of h is selected. Since there are many second neighboring surfaces h for i, the maximum value is obtained for all the second neighboring surfaces h and this is added. If this value is large, it means that the correspondence between i and k is strong. If this is small, the correspondence between i and k is weak.

Since similar equations are used for the first and second neighboring surfaces, the two can be discussed in parallel. It is important to perform the max operation.
Here, if all the sums of the neighboring surfaces j and h and their candidate surfaces l and m are taken, the result will always be a constant. Instead, leave only one of the appropriate candidates.

By the max calculation, all the candidate surfaces of the first near surface j of i and the second near surface h that are less likely to correspond are discarded. Then, only the sum calculation is performed for the surfaces l and m having the highest correspondence probability among j and h. By doing this, the maximum probability can be determined when i and k are associated.

If i and k actually correspond,
The first neighborhood surface j of i should have a plane l corresponding to the first neighborhood surface of k. This is because the relationship between the first neighboring surface and the second neighboring surface is unchanged in both the trihedral view and the wire frame model. This has already been explained as the principle of invariant surface.

If there is such a correspondence, the first matching coefficient r _ijkl ¹ should be a large value (although it does not exceed 2). For that purpose the random variable P _ik ^{t + 1} in the next order
Can be increased.

If i and k correspond to each other, the first of i
If the candidate surface 1 of the neighboring surface j is not the true first neighboring surface of k, then j and l do not actually correspond to each other due to the principle of the neighboring surface invariance. In this case, since the probability P _jl ^t of the previous correspondence between j and l is small, the max operation cannot be passed and falls here.

Only the relationship between the actual corresponding surfaces j to l survives the max operation. Since there are correspondences j to l, the probability P _ik ^t is large, and the second matching coefficient r _ijkl ² is also large because of the first neighborhood surface relationship between k and l. Therefore, the sum of products becomes large. Since q _ik ^t is larger, the probability P _ik ^t in the next order is larger.

If i and k do not actually correspond to each other, the first neighborhood surface j of i and the first neighborhood surface l of the candidate surface of j are
Given that k and l are the first neighboring surfaces, this has no real meaning. In this case, the first matching coefficient r
even _ijkl ¹ is large, since the corresponding probability P _jl ^t is small, m
The product of the coefficients selected by the ax operation is small. Therefore, the sum value of these j is also small. Therefore,
q _ik ^t also becomes smaller and acts to reduce the value of the probability P _ik ^{t + 1} in the next order. The same applies to the second neighboring surface.

In this way, P _ik ^t is obtained by iterative calculation. If P _ik ^t does not become high even by the repeated calculation, k cannot be the corresponding surface of i. If k is the corresponding surface of i, then the probability P _ik ^t should approach 1 within the iteration. The calculation is terminated at an appropriate number of times t. P _ik ^t is a correspondence probability of the surface i with respect to a plurality of candidate surfaces k, and finds k that maximizes this. Surface i
It can be seen that the corresponding surface of is k.

Since the correspondence (i, k) is known, the surface relationship is fixed. However, there is a mismatch in the coordinates of the vertices. This adjusts the coordinates between each vertex and gives the optimum coordinates.

All the candidate surfaces that are not the optimum candidate surfaces among the candidate surfaces of i are discarded. One corresponding surface of i is determined. This does not fix all the faces of the polyhedron. This is because not all of the outer surfaces appear as the surface i of the three-view drawing since the drawing starts from the three-view drawing and not from the six-view drawing.
However, such a surface is parallel to a certain basic surface, and when projected onto the certain basic surface, it always overlaps with a surface close to the basic surface. Since the polyhedron as shown in FIG. 1 is prohibited, the sides of this face have already been determined as the ridgelines of other faces, and the faces can be determined by tracing the ridgelines. In this way, the coordinates of the vertices can be given to all the three-dimensional surfaces. This means that the polyhedron has been restored.

[0222]

EXAMPLE A polyhedron was reconstructed using the method of the present invention with respect to the trihedral view (Example 1) shown in FIG. 2, Example 2 shown in FIG. 10 and Example 3 shown in FIG.

Example 1 is an example in which a polyhedron is reconstructed from a general trihedral view whose data contains an error. This is detailed.

Example 2 is an example in which the number of combinations of candidate surfaces increases due to data error. Example 3 examines the behavior of this method in the case where there is polysemy in the trihedral and the polyhedron from the beginning. In this embodiment, it is assumed that all three views are binarized by 128 × 128. Of course, it may be divided into smaller pixels. Further, the allowable range of the discrepancy between the vertices was set to h = 8.

[0225]

[Table 5]

Table 5 shows the number of iterations t in Example 1 of FIG.
And a corresponding probability P _ik ^t (%) at that time. The first column shows the number i in the three-view drawing, and the second column shows the surface number k in the wire frame model. Correspondence (i,
k), the surface i whose surface is the candidate surface is repeatedly described in the first column.

I = 1 has k = 1 and 2 as candidate surfaces, and i =
2 has k = 3, 4, 5 as candidate surfaces. i = 3 is k =
6, 7, and 8 are candidate surfaces. For i = 4, k = 9 and 10 are candidate surfaces. For i = 5, k = 11 and 12 are candidate surfaces. For i = 6, k = 13, 14, and 15 are candidate surfaces. i
= 7, k = 16 and 17 are candidate surfaces.

The number of iterations of the corresponding probability P _ik ^t is t =
It is from 0 to 8. As described above, the 0th-order probability is determined so as to be proportional to the reciprocal of the sum of the distance between the vertex and the origin (simple plane, compound plane) or the distance between the vertex and the origin.

When (1, 1) corresponds to (1, 2) (P
₁₁ ^t , P ₁₂ ^t ), where i = 1 is a simple plane, and evaluated from the reciprocal of the distance between the vertex and the origin, P ₁₁ ⁰ = 69%, P
In Fu that ₁₂ ⁰ = 31%, have appreciated the corresponding (1,1). Since this is the correct order, the difference in the probability increases due to repetition, and the correspondence (1,
The probability P ₁₁ ¹ of 1) rises to 92%, and the probability P ₁₂ ¹ of (1, 2) falls to 8%. And in the 4 th iteration is made to the probability P ₁₁ ⁴ = 100% of (1,1). This means that i = 1 corresponds to k = 1.

In the case of correspondence of i = 2 and k = 3, 4, 5 (P ₂₃ ^t , P ₂₄ ^t , P ₂₅ ^t ), since i is a simple plane, it is closest to the origin among the three planes. A large initial probability is given to the object k = 3 (P ₂₃ ⁰ = 45, P ₂₄ ⁰ = 35,
P ₂₅ ⁰ = 20%). However, the probability of k = 3 becomes low due to the repeated calculation due to the misalignment with the surrounding surface, and k = 4 becomes large instead.

Such replacement of the maximum probabilities naturally occurs, but since it is not the correct order from the beginning, iterative calculation is required until the correct order is reached. In this case, the order is already correct at t = 1 (P ₂₃ ¹ = 42, ..., P ₂₄ ^1).
= 49, P ₂₅ ¹ = 9%). But the convergence is not fast. At the fourth time, P ₂₅ ⁴ = 0, and it is confirmed that k = 5 is not a corresponding surface of i = 2. The problem is that P ₂₄ ^t is large. At the 8th time, P ₂₄ ⁸ = 100%, and k = 4 becomes i =
It is confirmed that it is the corresponding surface of 2.

In this way, the inversion phenomenon occurs between the initial probability and the final probability, in addition to the above, i = 3 and k =
There are cases of correspondence of 6, 7, and 8, and correspondence of plane i = 6 and k = 13, 14, and 15. In the latter case, the correct correspondence (6,14) does not reach 100% after 8 iterations, and
It is 0%, and 10% (6,15) correspondence remains.

Even in the case of a simple plane, in the case of an intermediate surface which is not closest to the basic surface as i = 2, 3, 6 in this way, the probability order is changed in the middle. . However, the probability of face k given the maximum value is 0
The convergence speed of P ₂₃ ^t , P ₃₆ ^t , P ₆₁₅ ^t, etc. becomes slow because the speed of approaching is slow.

Taking the case of correspondence between i = 2 and k = 3, 4, 5 (P ₂₃ ^t , P ₂₄ ^t , P ₂₅ ^t ) as an example, how P
Intuitively explain whether the probability alternation occurs between ₂₃ ^t and P ₂₄ ^t . P ₂₃ ⁰ = 42%, P ₂₄ ⁰ = 35%, and 1
In the calculation of degrees, P ₂₃ ¹ = 42% and P ₂₄ ¹ = 49% are reversed. But the reversal is less powerful.

First, description will be made from the perspective of the first neighboring surface. i =
At 2, its first neighborhood is j = 1. Corresponding surface k for i = 2
= 3 and 4, the first neighboring surface (which is also the corresponding surface of j) is l =
1 and 2. The question is why k = 4 dominates when k = 3 is initially greater than k = 4. l = 1 and k = 3 are on the same plane from FIG. 7, and the matching coefficient r ₂₁₃₁ ^{1 is set} to zero. This is P with a large initial probability
₁₁ is applied min ⁰ = 69%. Since this term disappears, what remains in the max operation is the relationship with the other first neighboring surface 2. Since the initial probabilities P ₁₂ ⁰ = 31% of 2 over a finite compliance coefficient r ₂₁₃₂ ¹ = 2 to 62
To get The numbers in the middle do not include%. This is because the value becomes% at first after being normalized by the expression (12), but it is an intermediate number before that.

Since k = 4 is not on the same plane as the first neighboring surface l = 1, the max operation selects l = 1. Fitness coefficient r ₂₁₄₁
¹ = 2, since P ₁₁ ⁰ = 69%, the contribution to q ₂₄ 1
38. It can be seen that the contribution from the first neighborhood surface significantly increases the probability of k = 4.

Next, description will be given from the perspective of the second neighboring surface. i =
2, the second neighboring surface has h = 3, 4, 6, and 7. We consider the probability alternation between 3 and 4 with candidate plane k = 3,4,5. The candidate surface of h and the second neighboring surface of k are m = 6, 7,
8, 9, 10, 13, 14, 15, 16, and 17.
m = 8, 10, 13, 13, 1 apart from k = 3, 4
6 does not share 2 vertices with k = 3, 4, so r _2hkm ² is 0
And These do not contribute to the calculation.

What is important is m = 9 and 17. Since these surfaces do not share two vertices with k = 3, r _2h3m ² = 0
(I = 2, h = 4,7, k = 3, m = 9,17). However, k = 4 shares two vertices, and the vector drawn from the k vertex of the m-plane vertices has a positive component, so r
_2h4m ² = 2 (i = 2, h = 4,7, k = 4, m = 9,1
7: However, the deviation of the coordinates of the vertices was set to 0, e ₂ = 1). Therefore, the probability of k = 4 is 2 × (P ₄₉ ⁰ + P ₇₁₇ ⁰ ) = 2 ×
It increases by (69 + 69) = 276. This reflects that k = 3 is an imaginary surface and k = 4 is a real surface.

However, it cannot be said that k = 4 is always superior to k = 3 for the remaining second neighboring surface. m = 6 (h = 3), m = 7 (h = 3),
For the four surfaces of m = 14 (h = 6) and m = 15 (h = 6), there is a condition that e ₁ = 0 when the vector is not positive, so r _2h3m ² = 2 for k = 3. (I = 2, h =
3,6, k = 3, m = 6,7,14,15: However, the deviation of the coordinates of the vertices is set to 0, and e ₂ = 1).

On the contrary, for k = 4, r _2h4m ²
= 0 (i = 2, h = 3,6, k = 4, m = 6,7,1
4, 15). For this reason, the probability of k = 4 is 2 ×
^{_{(P 36 0 + P 37 0}} + P 614 0 + P 615 0) = 2 × (46 + 3
4 + 25 + 62) = 334 increases. In the end, it becomes 396 for k = 3 and 414 for k = 4.

[0241] For k = 5, the contribution from the second neighboring side is 0, the contribution from the first near surface, 2 × P ₁₁ ⁰ = 2
X69 = 138. If these three values are corrected to%, k
= 3, 4, 5, the probability of the first t = 1 is obtained. P ₂₃
¹ = 41%, P ₂₄ ¹ = 44%, P ₂₅ ¹ = 15%.
The probabilities for k = 3 and 4 are slightly reversed. This is because there is a discrepancy with the results in Table 5, but Table 5 shows the case where there is discrepancy in the vertex coordinates, and the one described here is the case where there is no discrepancy in the vertex coordinates.

As described above, in the case of a complicated simple plane i, the 0th-order correspondence probability with the actual corresponding surface k is lower than the 0th-order probability than the imaginary surface k ′ closer to the basic surface, but this is repeated repeatedly. It turns out that it is reversed by. We also see that this reversal is slow. This is because the second neighboring surface does not always work effectively for the determination. r
_In the definition of _ihkm ² = e ₁ × e _{2, since} the definition of e _{1 has} the condition that the vector direction is positive (simple plane, compound plane) and negative (dividing plane), r _{ihkm of an} imaginary surface close to the basic surface
² becomes bigger.

In order to avoid this, the condition regarding the vector may be removed and the condition may be changed so that two vertices are shared. In this case, the second from the surface far from the basic surface
The near surface contribution comes out. However, this should be dropped because the contribution of the first neighboring surface is originally small.

FIG. 12 shows the restored polyhedron of Examples 1 and 2, and FIG. 13 shows the restored polyhedron of Example 3. Example 2 is one in which two thin square poles are mounted on a flat flat plate. FIG. 14 is a wire frame model of this. Since the distance between the vertices is small, the upper surface of the rectangular prism may also select the adjacent surface as a correspondence candidate.

In this case, if the rule is not appropriate and the combination method is used, an imaginary surface generated by intersecting the adjacent plane is generated in addition to the original solution, as shown in FIG. Three imaginary solutions (a), (b), including such a surface,
(C) may occur. According to the method of the present invention, in which the probability calculation is performed on the second neighboring surface, it is possible to prevent the occurrence of such a false solution.

The imaginary solution (a) is a solution in which the side surfaces of the columns are separated from each other and have no thickness, and the top surface of the columns is floating above the top surface. The imaginary solution (b) is a figure in which there are pillars having only two side surfaces, and the top surface floats at a position deviated from these top surfaces. In the case of imaginary solution (c), the pillar is 4
Rather than being a face piece, non-thick surfaces are present separately.

(D) given by the present invention is a correct solution.
Since the present invention obtains the probability using the second neighboring surface, such an isolated plane does not appear. Therefore, such a false solution does not occur. The present invention is also excellent in the sense that such a false solution can be excluded.

Next, the calculation amount of Example 1 and Example 2 will be considered. The number of plane views (plan view, front view, right side view) corresponding to each plane is a, b, and c, respectively. In Example 1,
The calculation amount when using the round-robin method according to the rules is O (a.
b ・ c). However, using the method of the present invention,
The sum of the number of planes corresponding to each plan is multiplied by the number of iterations to obtain O (a +
b + c) · T. Here, T is the number of iterations of the relaxation matching method.

In Example 2, the calculation amount when the brute force method is used is O (a.b.c + d). In the method of the present invention, the calculation amount is O (a + b + c) · T. Here, d is a calculation amount for removing a false solution caused in the polyhedron due to an error.

As can be seen from these results, the more complex the three-view drawing, the better the method of the present invention. It is possible to obtain a solution with a smaller amount of calculation as compared with the brute force method according to the rule. Further, in Example 2, since the present invention stochastically removes the imaginary solution using the adaptation coefficient, the calculation amount is the same as in Example 1.

Example 3 is an examination of the case where the input trihedral and the polyhedron do not have uniqueness. In the xy view of the trihedral view, it is not possible to decide only by what direction the second and third triangles face when viewed from the xy plane. There can be three solutions. By using the method of the present invention for such a three-view drawing, one of the optimal solutions in the sense that the simple plane is close to the viewpoint in the drawing and the division plane is far from the viewpoint can be obtained.

Table 6 lists the number of planes, the number of candidate planes, and the number of corresponding planes of the three-view drawing in the example.

[0253]

[Table 6]

It has already been explained that in Example 1, the number of planes in the three views is seven. It is also clearly shown in FIG. 7 that the number of candidate surfaces is 17. There are seven corresponding surfaces because they correspond to the planes of the three-view drawing.

In Example 2, the number of planes in the three views is 9,
It can be seen from FIG. This wire frame model is shown in Fig. 1.
4 shows. There are 28 candidate surfaces for this. Corresponding number of faces is 9
Is.

In Example 3, the number of planes in the three-view drawing is 14. There are 42 candidate surfaces in the wire frame model. The number of corresponding surfaces is 11. In this case, the initial response,
Excludes surfaces that do not correspond.

In the present invention, the relaxation method is performed by setting the error allowable range h and narrowing down the correspondence candidates in advance. When h is increased, the convergence of the solution is improved, but the number of candidate surfaces is increased.
The calculation amount increases with the increase amount of the candidate surface.

[0258]

INDUSTRIAL APPLICABILITY The present invention can restore a three-dimensional drawing from the drawings given as three views. The method of the present invention is
In the wire frame model produced by back-projecting the three views, the first neighborhood surface j and the second neighborhood surface h are defined for each plane i of the three views, and the plane i of the three views corresponds to two faces. When several candidate surfaces k having the same dimensional coordinates are designated and the corresponding surfaces l and m of j and h are the original first and second neighboring surfaces of k, the correspondence between i and k is obtained. This is to increase the probability of (i, k).

The probability of the correspondence (i, k) between i in the three-view drawing and k in the wire frame model is determined by utilizing the property that two types of neighboring surfaces are in common, so the amount of calculation is small. Become. If the total number of faces is used, the amount of calculation increases in proportion to the square or cube of the number of faces when the number of faces is large. However, the method of the present invention only increases substantially in proportion to the number of faces, and thus is particularly effective when the number of faces is large.

This method can also be applied to the case where the coordinate value of the vertex includes an error. Even if the coordinate values are separated to some extent, they are regarded as the same point and the number of candidate surfaces is not increased.
However, if the total contact method is applied to a drawing having an error, the number of candidate surfaces increases abnormally due to the error, and the amount of calculation explosively increases. The present invention can prevent the calculation amount from exploding due to such an error.

Furthermore, the present invention can prevent the occurrence of a false solution including an isolated surface. Only significant solutions can be found. If a false answer is obtained, it must be judged whether this is a false answer, and the calculation time is wasted.

[Brief description of drawings]

FIG. 1 is a perspective view of a cylindrical polygon that cannot be handled by the present invention.

FIG. 2 is a trihedral view showing an example for facilitating the description of the present invention.

FIG. 3 is a view showing that each surface is numbered in an example including a division plane.

FIG. 4 is an example showing labeling of a plane in the example of the three-view drawing of FIG. 2;

5 is an example of a wire frame model composed of the three views shown in FIG.

FIG. 6 is a perspective view showing an example of a surface that appears in different views and is labeled with two labels because it is tilted with respect to the basic plane of coordinates.

FIG. 7 is a perspective view showing the coordinates of the vertices of the surface with the surfaces labeled in the wire frame model shown in FIG.

FIG. 8 is a diagram for explaining the meaning of a first matching coefficient that is determined by the relationship between the first neighboring surfaces.

FIG. 9 is a diagram showing a polyhedron restoration method of the present invention.

FIG. 10 is a trihedral view showing an example (Example 2) of a polyhedron in which a space between vertices is narrow and an adjacent plane may be selected as a candidate surface.

FIG. 11 is a trihedral view showing an example (example 3) of a figure whose shape cannot be determined only by the trihedral view.

FIG. 12 is a diagram showing a polyhedron restored in Examples 1 and 2;

FIG. 13 is a diagram showing a polyhedron restored in Example 3;

14 is a wire frame model for Example 2. FIG.

FIG. 15 is a candidate solution of Example 2 generated by the combination method.

FIG. 16 is a complete expression of expressions (1) to (7) that cannot be expressed in JIS.

FIG. 17 is expressions (8) to (13) that cannot be expressed in JIS.
Full expression of.

Claims (3)

[Claims] 1. A polyhedron composed of planes orthogonal to each other 3
A method of restoring an original polyhedron from a trihedral drawing that includes only a solid line showing an outline and a broken line showing a hidden line, which is projected on two planes and includes an error, and assigns a number i to the plane of the trihedral drawing,
The vertex coordinates (x _im , y _im , z _im ) of each surface i, a simple plane surrounded by solid lines (w = 0), a division plane surrounded by solid lines and broken lines (w = 1), and a simple plane. To which of the three types of planes the composite plane (w = 2) that integrates the division plane belongs, and in the case of a simple plane or a composite plane, the adjacent planes via solid lines or broken lines or this includes The first neighborhood surface {E _ij ¹ } is defined as a dividing plane and, in the case of a dividing plane, is defined as the surface including this, and the error h of the line segment that constitutes the surface of each plan is projected on the principal axis. A feature amount list consisting of the second neighboring surface {E _ij ² } defined as a surface having a line segment corresponding to one to one in the range is created for each surface i, and the three views are back-projected to create the three views. It has three-dimensional coordinates obtained by adding the coordinates determined from the line segment coordinates of another surface to the two-dimensional coordinates of the surface i. Composed of the surface Waiyafure - Create Mumoderu, numbered k to all candidate surface corresponding to the surface i, the surface k vertex coordinates _{(x kl ', y kl'} ,
z _im ′) and a surface adjacent to another surface or a line segment that overlaps when projected onto the basic surface of the coordinate system, a surface included therein, or a first neighboring surface {E defined as a surface included therein.
_kl ¹ ′} and the second neighboring surface {E _kl ² ′} defined as the surface where the line segments match within the error h when projected onto the coordinate axis
A feature amount list consisting of and is created, and a plurality of candidate planes k of the wire frame model are associated with the plane i of the three-view drawing,
The correspondence (i, k) between the surface i and the candidate surface k is created, and the probability P _ik ^t indicating the certainty of k corresponding to i is obtained by iterative calculation while increasing the order t of the certainty.
The initial probability P _ik ⁰ is determined from the property of the surface k itself, and the order t
When seeking more the probability P _ik ^{t + 1} of higher from the probability P _ik ^t, the first near surface of the surface i j, the candidate face surface j as l,
The first matching coefficient r _ijkl ¹ is defined as being large when the surfaces k and l are separated from each other and non-parallel, and small when they are parallel and close to each other. If m is a candidate surface of h and i is a simple plane or a compound plane,
In the wire frame model, the surfaces k and l share two vertices within the range of the allowable error h, and the surface m is more stable than the surface k.
When the distance is larger than the existing basic surface, it is large, and when it is not, it becomes small, and when i is a division plane, the surfaces k and l share two vertices in the range of the allowable error h in the wire frame model, The first fitting when the surface m is larger than the surface k when the surface i extends near the existing basic surface, and the second fitting coefficient r _ihkm ² that becomes smaller when the surface i does not grow is defined and l is changed The sum of j obtained by multiplying the maximum value of the coefficient r _ijkl ¹ by the t-th probability P _jl ^t corresponding to j of l that gives this, and the second matching coefficient r when m is changed
_The coefficient q _ik ^t is calculated by adding the maximum value of _ihkm ² and the t-th probability P _hm ^t corresponding to h of m that gives this, and the coefficient q _ik ^t is obtained. The probability P _ik ^t multiplied by the probability of probability is normalized to obtain a higher-order probability P _ik ^{t + 1,} and k which gives the maximum probability after a certain number of calculations is determined to be the optimal corresponding surface of the surface i. A method for restoring polyhedrons from three views by the relaxation matching method. 2. A polyhedron composed of planes orthogonal to each other 3
A method of restoring an original polyhedron from a trihedral drawing that includes only a solid line showing an outline and a broken line showing a hidden line, which is projected on two planes and includes an error, and assigns a number i to the plane of the trihedral drawing,
The vertex coordinates (x _im , y _im , z _im ) of each surface i, a simple plane surrounded by solid lines (w = 0), a division plane surrounded by solid lines and broken lines (w = 1), and a simple plane. To which of the three types of planes the composite plane (w = 2) that integrates the division plane belongs, and in the case of a simple plane or a composite plane, the adjacent planes via solid lines or broken lines or this includes The first neighborhood surface {E _ij ¹ } is defined as a dividing plane and, in the case of a dividing plane, is defined as the surface including this, and the error h of the line segment that constitutes the surface of each plan is projected on the principal axis. A feature amount list consisting of the second neighboring surface {E _ij ² } defined as a surface having a line segment corresponding to one to one in the range is created for each surface i, and the three views are back-projected to create the three views. It has three-dimensional coordinates obtained by adding the coordinates determined from the line segment coordinates of another surface to the two-dimensional coordinates of the surface i. Composed of the surface Waiyafure - Create Mumoderu, numbered k to all candidate surface corresponding to the surface i, the surface k vertex coordinates _{(x kl ', y kl'} ,
z _im ′) and a surface adjacent to another surface or a line segment that overlaps when projected onto the basic surface of the coordinate system, a surface included therein, or a first neighboring surface {E defined as a surface included therein.
_kl ¹ ′} and the second neighboring surface {E _kl ² ′} defined as the surface where the line segments match within the error h when projected onto the coordinate axis
A feature amount list consisting of and is created, and a plurality of candidate planes k of the wire frame model are associated with the plane i of the three-view drawing,
The correspondence (i, k) between the surface i and the candidate surface k is created, and the probability P _ik ^t indicating the certainty of k corresponding to i is obtained by iterative calculation while increasing the order t of the certainty.
The initial probability P _ik ⁰ is determined to be approximately inversely proportional to the distance from the origin when the surface k is a simple plane or a compound plane, and is approximately proportional to the distance from the origin when the surface k is a division plane. , Probability P _ik ^{t of} degree t to higher probability P _ik
To obtain ^{t + 1} , let j be the first neighboring surface of the surface i and l be the candidate surface of the surface j, and let n _k and n _{l be} normal vectors of the surfaces k and l,
With a _k and a _l as vertices of the surfaces k and l, the first matching coefficient r _ijkl ¹ is large when the surfaces k and l are separated from each other and non-parallel, and is large when they are parallel and close to each other. , R _ijkl ¹ = min [2 {1- | n _k · n _l | / | n _k |
| N _l |} + | n _k · (a _k −a _l ) | / h, 2], where h is the second neighboring surface of the surface i and m is the candidate surface of the surface h, and i is a simple plane. Alternatively, in the case of a compound plane, in the wire frame model, the surfaces k and l share two vertices within the allowable error h, and the surface m extends farther than the basic surface of the surface i than the surface k. The second matching coefficient r _ihkm ² that is larger than the above, and is smaller otherwise is r _ihkm ² = e ₁ × e ₂ e ₁ = 2: two adjacent vertices of the surface k and the surface 1 are _equal to each other within a corresponding allowable range. However, among the vectors connecting these vertices to the other vertices of the plane l, there is a vector that is positive with respect to the axial direction that is not represented in the plan view including i. = 0: Others e ₂ = 1- (sum of distances between vertices of k and l that are supposed to be the same) / 2h, and when i is a division plane, the faces k and l in the wire frame model are defined. Is within the allowable error h of 2
The second matching coefficient r _ihkm ² is r _ijkl ² = e ₁ × e ₂ which is larger when the surface m shares the vertices and which is larger than the surface k when the surface i extends near the existing basic surface, and which is small when the surface i does not e ₁ = 2: An axis which is not represented in a plan including i among the vectors connecting two adjacent vertices of the surface k and the surface l within the corresponding allowable range and connecting the other vertices of the plane l from their contact points There is a vector that is negative with respect to direction. = 0: Others e ₂ = 1− (sum of distances between vertices of k and l that are supposed to be the same) / 2h, and the first matching coefficient r when l is changed
_The sum of j multiplied by the maximum value of _ijkl ¹ and the t-th probability P _jl ^t corresponding to j of l that gives it, and the maximum value of the second matching coefficient r _ihkm ² when m is changed. The coefficient q _ik ^t is calculated by adding the ^t-th probability P _hm ^t corresponding to h of m and the sum related to h, and the probability P _ik of the probability of correspondence between i and k at the previous time is calculated. A relaxation matching method characterized by normalizing a product of ^t to obtain a higher-order probability P _ik ^{t + 1,} and _obtaining k that gives the maximum probability after a certain number of times of calculation, and making k the optimum corresponding surface of the surface i. Method for recovering polyhedron from trihedral drawing. 3. A polyhedron composed of planes orthogonal to each other 3
A method of restoring an original polyhedron from a trihedral drawing that includes only a solid line showing an outline and a broken line showing a hidden line, which is projected on two planes and includes an error, and assigns a number i to the plane of the trihedral drawing,
The vertex coordinates (x _im , y _im , z _im ) of each surface i, a simple plane surrounded by solid lines (w = 0), a division plane surrounded by solid lines and broken lines (w = 1), and a simple plane. To which of the three types of planes the composite plane (w = 2) that integrates the division plane belongs, and in the case of a simple plane or a composite plane, the adjacent planes via solid lines or broken lines or this includes The first neighborhood surface {E _ij ¹ } is defined as a dividing plane and, in the case of a dividing plane, is defined as the surface including this, and the error h of the line segment that constitutes the surface of each plan is projected on the principal axis. A feature amount list consisting of the second neighboring surface {E _ij ² } defined as a surface having a line segment corresponding to one to one in the range is created for each surface i, and the three views are back-projected to create the three views. It has three-dimensional coordinates obtained by adding the coordinates determined from the line segment coordinates of another surface to the two-dimensional coordinates of the surface i. Composed of the surface Waiyafure - Create Mumoderu, numbered k to all candidate surface corresponding to the surface i, the surface k vertex coordinates _{(x kl ', y kl'} ,
z _im ′) and a surface adjacent to another surface or a line segment that overlaps when projected onto the basic surface of the coordinate system, a surface included therein, or a first neighboring surface {E defined as a surface included therein.
_kl ¹ ′} and the second neighboring surface {E _kl ² ′} defined as the surface where the line segments match within the error h when projected onto the coordinate axis
A feature amount list consisting of and is created, and a plurality of candidate planes k of the wire frame model are associated with the plane i of the three-view drawing,
The correspondence (i, k) between the surface i and the candidate surface k is created, and the probability P _ik ^t indicating the certainty of k corresponding to i is obtained by iterative calculation while increasing the order t of the certainty.
The initial probability P _ik ⁰ is determined from the property of the surface k itself, and the order t
When seeking more the probability P _ik ^{t + 1} of higher from the probability P _ik ^t, the first near surface of the surface i j, the candidate face surface j as l,
The first matching coefficient r _ijkl ¹ is defined as being large when the surfaces k and l are separated from each other and non-parallel, and small when they are parallel and close to each other. If the candidate surface of h is m, and whether i is a simple plane, a compound plane, or a division plane, the surface k in the wire frame model
The second matching coefficient r _ihkm that is large when the two vertices and l share two vertices within the range of the allowable error h and is small _otherwise
First definition coefficient r _ijkl ¹ when ² is defined and l is changed
And the probability p of the t-th order corresponding to j of l that gives it
_The sum of _jl ^t multiplied by j, the maximum value of the second matching coefficient r _ihkm ² when m is changed, and the t-th probability P _hm ^t corresponding to h of m which gives this value are multiplied. The coefficient q _ik ^t is obtained by adding the sum of the thing and h, and is multiplied by the probability P _ik ^t of the probability of the correspondence between i and k at the previous time to be normalized to obtain a higher-order probability P _ik ^{t + 1.} A method for restoring a polyhedron from a trihedral diagram by a relaxation matching method, which is characterized by obtaining k which gives a maximum probability after a certain number of times of calculation and using it as an optimal corresponding surface of the surface i.