JP2000155857A - Multi-dimensional definition method for object and its device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a modeling technique for realizing the maintenance of the symmetry and validity of a shape including a boundary part. SOLUTION: A shape to be processed is inputted by a shape information inputting part 6. A part to be processed is designated by a part to be processed designating part 8. A sub-space in which cells are constituted as elements in the order starting with lower order is constructed for the designated pat, and the cell information is obtained by a cell information obtaining part 10. A cell information outputting part 14 outputs the obtained cell information to a database 12.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an expression method, an encoding method, or an apparatus capable of defining a phenomenon or an event of any dimension including a three-dimensional shape in a computer.

[0002]

2. Description of the Related Art Shape modeling is a basic technique necessary for handling a solid in a computer. Various modeling methods have been proposed in the past. For example, a method of approximating the surface of a solid by polygon data, a method of dividing the surface of the solid into several parts and pasting a curved surface patch, a combination and collection of basic solids such as spheres, regular triangular pyramids, and cubes called primitives The CSG method of expressing the object three-dimensionally by calculation, the coordinates of the vertices of the solid, the side defined by the combination of vertices, the surface defined by the combination of sides, and the like are specified to specify the shape of the object. The methods themselves, such as the boundary representation method, have no spare time.

[0003] Modeling is not limited to a single shape, and is always performed, whether explicitly or implicitly, when dealing with an arbitrary event or phenomenon on a computer.
For example, the design of a database is based on modeling how to grasp the characteristics of an object, and the act of introducing parameters necessary for a program can also be referred to as modeling that converts the processing contents into numerical concepts using parameters. Furthermore, in the phenomena analysis in the natural sciences, there is a stage of making a model, that is, a modeling assumption, and a stage of verification thereof. In social science, various financial models are actually working. In fact,
It is more difficult to find human thinking and creative activities that do not include the concept of modeling.

[0004]

Now, the story will be returned to the processing of events and phenomena by a computer, and the processing of the shapes therein will be discussed as an example. In particular, whether the shape represented by modeling is "valid" or "invalid" (valid or invalid)
Consider the theme of For example, here we take a solid called a triangular pyramid. Attempting to represent this equilateral triangular pyramid with a well-known wireframe model is actually a big problem from the beginning. In this model, a regular triangular pyramid is formed by six equal wires, and three wires meet at each vertex. Here, if an open wire, that is, a wire that does not include both ends, is used, the vertex itself where the ends of the three wires are gathered is also open, resulting in a model in which the substance of the vertex is missing. If this modeling result is to be displayed on a display, the vertex is already missing at the logical level, so that even at the physical level of mapping to pixels, the vertex may be actually displayed with the vertex missing. In this representation, the shape must be said to be "invalid".

On the other hand, if a closed wire, that is, a wire including both ends, is used as a wire, the three ends of the three wires overlap at the vertex, and the shape is still “invalid”. Essentially, at the top, the ends of the three wires must express the state of "integrating into one point", so to speak, the only "effective" expression is that one wire is closed and the other two are closed. There is only about opening. In this method, the equivalence of the wires is lost and the shape becomes asymmetric, requiring different treatments depending on the direction of the equilateral triangular pyramid.

The essence of the problem is boundary modeling.
odeling). In this method, a regular triangular pyramid is formed by, for example, four congruent regular triangular panels. On the sides of the regular triangular pyramid where two panels meet, if the panel is closed, the sides overlap, and if the panel is open, the sides overlap. Becomes blank, and all shapes are “invalid”. When one panel is closed and the other panel is opened, the shape is also asymmetric, which causes inconvenience. Even in the design of a very simple shape of a regular triangular pyramid, the problem of expressing a valid boundary is unresolved. This problem was recognized by the present inventors more than 30 years ago when they proposed raster graphics with a frame buffer, and while half-expected that any researcher would give an answer. It was not fulfilled.

In view of the above, it is an object of the present invention to provide a modeling method for maintaining the symmetry and validity of a shape including a boundary portion. Preserving the symmetry and validity of a shape leads to the ability to break down the shape into as similar elements as possible and to construct the shape correctly from those elements. Therefore, it becomes easy and useful to construct a database by converting the shape into a part. Therefore, another object of the present invention is to provide a modeling method for expressing the shape of a simple and unified object in a uniform data format, including the steps of disassembly into parts or assembly from parts. On offer. As a result, there is provided a means for achieving one purpose of information science, in which countless design assets designed once are made into parts and reused.

[0008] Still another object is not only a shape described in a three-dimensional range, but also various events and phenomena widely represented by multidimensional data or multivariables, which can be easily made into parts, reused, or analyzed. An object of the present invention is to provide a multidimensional definition technology for an object.

It is still another object of the present invention to provide a multidimensional definition technique of an object which can easily describe the contents of an operation when a predetermined operation is performed on an event or a phenomenon of an arbitrary dimension. With this technology, an object is to realize a common platform for easily and uniformly handling events and phenomena of any dimension in a computer.

[0010]

According to the present invention, the "integration" in the case of "integrating into one point" in the above example is mathematically formulated as "cell adhesion" in the cell structure space. Hereinafter, the term “shape” refers to an event of any dimension,
The phenomenon is only represented by a three-dimensional solid shape,
It should be noted that the scope of the present invention is not limited to “shape”.

According to the method for multidimensionally defining an object of the present invention, an object is decomposed into cells of each dimension in a cell structure space, and a subspace of a predetermined dimension is constructed by a set of cells of a predetermined dimension or less. Describe the relationship between the subspaces of different dimensions in a form in which the subspace of a predetermined dimension is included in the subspace of a dimension exceeding the predetermined dimension, and describe geometric information and topological information about the described subspace of each dimension, and It acquires geometric adhesion information and topological adhesion information defined between the subspaces of the respective dimensions, and encodes the object in a format including the information.

Here, the topological adhesion information describes each subspace constituting the object in such a manner that a higher-order subspace is bonded to a lower-order subspace using a continuous mapping. Information may be included. Further, the continuous mapping may be a surjective mapping, and the surjective mapping may correspond to a subspace of a certain dimension and a higher-order subspace than that. The subspace may be defined as an open set, and the continuous map may have a boundary of the “higher-order subspace” as its domain. Further, the continuous mapping is based on additional information called an element mapping that describes a correspondence between specific elements between subspaces.
It may be more specific, and this element mapping is
The correspondence between geometric feature elements in the subspaces may be described.

On the other hand, the multi-dimensional object definition apparatus of the present invention has an input unit for inputting data describing an object, a specifying unit for specifying a part to be processed in the input data, An acquisition unit that decomposes the part into subspaces of each dimension in the cell structure space, and obtains geometric information and topology information thereof, and geometric adhesion information and topology geometric adhesion information defined between the subspaces of each dimension; including.

A first table for recording topological information relating to cells constituting a predetermined portion of the object in association with each cell; a second table for recording geometric information relating to the cells in association with each cell; A third table that expresses the subspace in the form of a set of cells below that dimension and which cell belongs to which subspace, and associates the adhesion information between subspaces of different dimensions with each subspace And a computer-readable recording device that records the multidimensional definition information of the object, wherein the predetermined portion is configured to be accessible as a component by using the first to fourth tables. A recording medium is also one embodiment of the present invention. The fourth table,
It may include a table for recording geometric adhesion information defined between subspaces and a table for recording topological adhesion information defined between subspaces.

[0015]

DESCRIPTION OF THE PREFERRED EMBODIMENTS First, the present invention
We explain the extended theory of cell structure space theory by the author.
"N-dimensional cell" is an n-dimensional topological open sphere IntBⁿWhen
Defined as topologically homomorphic (in-phase) topological space, eⁿWith
Notation. That is, eⁿ= IntBⁿ  In this specification, "cell" does not include a boundary.
We decide open ball or open set. Here closed ball BⁿIs Bⁿ= ｛X∈Rⁿ, {X} ≦ 1}, and an n-dimensional cell eⁿIn other words, open ball IntBⁿIs IntBⁿ= ｛X∈Rⁿ, {X} <1}. Closed ball BⁿThe boundary ∂BⁿIs ∂Bⁿ= Bⁿ-IntBⁿ= S^n-1Which can be expressed as (Equation 1), which is topologically a (n-1) -dimensional spherical surface
Hit.

A finite or infinite array of cells X ^p can be designed in the phase space X. If Z is an integer,
The space by this array can be expressed as {X ^p | ^p {Z}, and this space is generally called a filtration space. The filtration space X ^p is the topological space X
And is defined as follows:

1. X = a _∪ p∈Z X ^p, 2. X ^p-1 is a subspace of X ^p and is also called a skeleton, and has a relationship of X ⁰ ⊆X ¹ ⊆ ... ⊆X ^p-1 ⊆X ^p ⊆ ... ⊆X (Equation 2).

This filtration space is expressed as ｛X ^p | X ^p
{X, p {Z}, and the cell decomposition (c
ell decomposition) ", or, respectively called split phase space X to the subspace X ^p is a cell (partition). In the filtration space, the phase space X formed by a finite number of cells is particularly a CW space (Closur
It is called e finite Weak topology space.

By the following recursive method, a filtration space having the skeleton of Equation 2 can be constructed as a topological space. First, a subspace X ⁰ ⊂X having a zero-dimensional cell e ⁰ as an element is generated. Then, surjectiv
e) By the continuous mapping F ^p , the union 閉_i B ^p _i of the closed sphere B ^p
A direct sum between the phase space X ^p-1 (disjoint union: in union of disjoint, logically equivalent to the exclusive OR) by taking, it is possible to construct a phase space X ^p. This mapping F ^p is given by F ^p : ∪ ^o _i ∂B ^p _i → X ^p-1 (Equation 3) However, in this specification, for convenience of notation,
The direct sum is represented by ∪ ^o . In general, “map f: X → Y is surjective” means that (∃y∈Y) is (∃x∈X) [f
(x) = y]. Further, “map f: X → Y is continuous” means that “{f ⁻¹ (y) | y∈A} is an open set at X, and only when that, the subset A∈X is It becomes an open set. "

Mapping F^pIs an attachment map, adjo
ining map, adjunction map, gluing map, etc.)
The newly generated phase space Y is attached space (attaching sp
ace, adjunction space, adjoining space, etc.)
It is. Equation 3 gives X^p-1To X^pCan compose
Means that. In other words, first,^p-1∪^o(∪
_iB^p _i), X∈∂B^p _iIs a continuous mapping f^p _i, F^p _i= F^p｜ ∂B^p _i: ∂B^p _i → X^p-1  X to f^p _iF and identity while satisfying (x)
Phi, that is, it may be the same. Used here
The | symbol is a restriction (restriction)
That is, the restriction of the mapping is shown. For example, for an arbitrary mapping g such that g: Y → Z, a restriction from g to X is performed.
Is written as g | x = goi: X → Z using i: i → X → Y. i is for inclusion
That is, it means inclusion of a map, and for ∀x∈X, i
(X) = x.

From the above considerations, X ^p is the quotient space (quotient space).
space) ^{next, X p = X p-1} ∪ o (∪ i B p i) / (x~f p i (x) | ∀x∈∂B p i) = X p-1 ∪ f (∪ i IntB ^{Since p} _i ) / x （(the subscript f is f ^p _i (x)), this space obtained by bonding along the mapping f ^p _i is an additional space. Here, “〜” represents an equivalence relationship. The equivalence relation is reflexive "x ~ x", symmetry rule (symme
tric) "If x ~ y then y ~ x", transitive
"X to y if x to y and y to z" is a relation that holds, such as a geometric equivalence relation, a topological equivalence relation, and a homotopy equivalence relation. Geometric equivalence relations include congruence and similarity relations, topological equivalence relations include homeomorphic relations, and homotopy equivalence relations include homotopic equivalents.

When an equivalence class is expressed as x / 〜, it can be written as x / 〜 = {y∈X | x〜y}. In other words, the equivalence class x / 〜 is a set of all elements that have a certain equivalence relationship with x in question.

On the other hand, the quotient space is a set of all equivalence classes, and is generally expressed as X /／ using uppercase letters. Therefore, different equivalent classes are represented by x _{j /／} (j
∈Z), the quotient space X / 〜 is represented by the index “x _j / 〜” of X / 〜 = {x ₁ / 〜, x ₂ / 〜,. Be a set. The quotient map (quotient m
apping) f _Q is defined as f _Q : X → X / 〜. Hereinafter, the discussion will focus on the equivalence relationship of in-phase (topological isomorphism). The present inventor has made it possible to extend the theory and use it in a computer by clearly defining the opening and closing of cells when taking an adhesive map and introducing element mapping to the cell structure space theory. It will be described later in the scene.

Based on the above understanding of the cell structure space related to the present invention, the composition (composition) of the object from the parts using the cell structure space and the decomposition (dec) into reusable parts
omposition) technology. Here, in particular,
Consider a process of converting a three-dimensional object into a part in a cell structure space based on the shape data of the existing three-dimensional object. However, it is naturally possible to describe the solid from the scratch base in the cell structure space.

FIG. 1 is a configuration diagram of a shape definition device 2 using the present invention. The apparatus 2 inputs information on an object to be made into a component, and redefines its shape topologically using a cell structure space. The outline of the processing is, for example, a regular triangular pyramid ABCD shown in FIG. 14 or the like, which is sequentially constructed from 0-dimensional cells in the order shown in FIG. 4 to FIG. 14, and the configuration data is stored in the tables shown in FIG. It will be stored. In the following, when we simply call the equilateral triangular pyramid,
It refers to the equilateral triangular pyramid ABCD shown in FIG.

The shape definition device 2 includes a shape information input unit 6 for inputting shape data of a solid, for example, a car or various machines designed by CAD, or other objects related to a design from the shape database 4, Part of the shape for which the shape should be actually redefined
), And obtains information on a cell (hereinafter, “cell information” is simply referred to as “cell information”) input by the user with respect to the target portion, or outputs shape data of the target portion. A cell information acquisition unit 10 for automatically extracting the cell information based on the cell information, a cell information output unit 14 for storing the acquired cell information in a cell database 12, and a user interface for receiving an instruction necessary for a series of processes from a user It comprises a unit 16 and a display control unit 20 for controlling the display device 18. Each of these functional parts may be implemented in any form of hardware or software, and may be constructed based on, for example, a personal computer.

FIG. 2 and FIG. 3 are flowcharts showing the processing procedure by the shape definition device 2. First, the user
An object is specified via the user interface unit 16 (S2). Here, it is assumed that a target object that includes a regular triangular pyramid as a target portion is specified. The shape information input unit 6 reads the shape data of the specified object from the shape database 4 into the device 2 (S4). The read shape data is displayed on the display device 18 via the display control unit 20 (S6). Although not shown, an object including a regular triangular pyramid is displayed on the display device 18 at this time.

Subsequently, the user designates a regular triangular pyramid as a target portion via the processing portion designation section 8 (S8). Thereafter, the user constructs this equilateral triangular pyramid in the order of FIG. 4 to FIG.
0 (S10). The acquired cell information is transmitted to the cell database 1 by the cell information output unit 14.
2 (S12). Thereafter, the user is inquired whether there is a target portion other than the regular triangular pyramid (S1).
4) If the target portion remains, the process is repeated from the designation of the target portion (Y in S14). If there is no target portion (N in S14), the process ends.

FIG. 3 shows a procedure for obtaining cell information (S10). In the present invention, a regular triangular pyramid is constructed in order from the lowest dimension constituting the regular triangular pyramid. That is, first to build a subspace X ⁰ by zero dimension cell (S20), the subspace X ¹ by a one-dimensional cell in the form that contains this subspace X ⁰
Constructs a (S22), to construct a subspace X ² by two-dimensional cell in the form that contains this subspace X ¹ (S24), finally the subspace X ³ by a three-dimensional cell in the form that includes a subspace X ² It is constructed (S26).

FIG. 4 shows a subspace X by a zero-dimensional cell.⁰of
It is a figure showing construction. A regular triangular pyramid has four vertices
A, B, C, D
And four topologically corresponding zero-dimensional cells e⁰To
Place them at positions that correspond geometrically to these vertices. here
Are in order of vertices AD to distinguish the four cells
e ⁰ ₁, E⁰ _Two, E⁰ _Three, E⁰ _FourNotation. This process is performed by the user
May be performed manually, or the cell information acquisition unit 10
May be automatically executed with reference to the shape data of the above. For example, positive
If the original data of the triangular pyramid contains vertex data, the cell information
The information acquisition unit 10 extracts the vertex data, and
Information, that is, in this case, the coordinate data is stored while
What is necessary is just to replace it with a dimension cell. The same applies to the following processing
In addition, using the characteristic geometric information of the cell of each dimension as a clue
By extracting cells of each dimension, the cell information acquisition unit 1
0 means that cell information is acquired. In addition, zero order
Former cell e ⁰ ₁, E⁰ _Two, E⁰ _Three, E⁰ _FourIs the same as open ball
Both are open sets because they are phases. Any of the following
Dimensional cells are also open sets.

Subsequently, a subspace X ¹ by one-dimensional one-dimensional cell is constructed (S22). 5-8 shows the construction procedure of the subspace X ¹ by one-dimensional cell, FIG. 5
Shows a state of bonding the one-dimensional cell, 6-8 already constructed subspace X ⁰ and one dimensional cells needed to build.

The regular triangular pyramid has six sides AB, AC, AD, B
It has D, BC, and CD. Therefore, the cell information acquisition unit 10
Is a one-dimensional cell e that corresponds topologically to these edges
¹ ₁, E ¹ _Two, E¹ _Three, E¹ _Four, E¹ _Five, E¹ ₆The order of those
We will correspond to the sides. At this time, the geometrical
Information, that is, the coordinates of the start and end points of each side
From the data source. As a result, it is necessary to construct a regular triangular pyramid.
Six important one-dimensional cells will come out (Fig. 5). In addition, primary
If the source cell is generally a curve, the curve
Get the display expression of.

Next, the already existing subspace X⁰And one
Dimensional cell e¹ ₁~ E¹ ₆Are connected by cell bonding. FIG.
Indicates the state of cell bonding, and the partial space X⁰And one-dimensional
Cell e¹ ₁~ E¹ ₆, For example, e⁰ ₁And e¹ ₁,
e¹ _Two, E¹ _ThreeThe part corresponding to one end of is bonded. FIG.
Is the subspace X⁰A certain one-dimensional cell e¹ _iExpand the state of bonding
It shows much. From equation 1 described above, one-dimensional cell e¹ _iTo
A one-dimensional closed sphere in the form of a closed set is B¹ _iAnd write
If B¹ _i= E¹ _i+ ∂B¹ _i  It is. Now, the projection F
Is F¹: ∂B¹ ₁∪^o∂B¹ _Two∪^o∂B¹ _Three∪^o∂B¹ _Four∪^o∂B¹ _Five∪^o
∂B¹ ₆→ X⁰  The mapping f considered for each one-dimensional cell¹ _iAnd f¹ _i= F¹｜ ∂B¹ _i: ∂B¹ _i → X⁰  Decide to be Mapping F¹When using, X¹= X⁰∪^o _F(∪^o _{i = 1,… 6}B¹ _i) = X⁰∪^o(∪^o _{i = 1,… 6}
e¹ _i) (Where F is F¹Is shown).

Mapping F¹Is the boundary ∂B including the cell¹From
Subspace X⁰To a certain dimension
A higher-order subspace is defined based on the subspace of
Good. At this time, the domain of the mapping ∂B¹And range X⁰Have the same dimensions
In other words, the one-dimensional cell is once (Z
(1D cell + 1D cell)
X-dimensional cell constructed subspace X⁰Included in
Note that it adheres to the zero-dimensional cell.
Mapping F determined in this way¹Is a mapping table (see later figure)
Entered in 18). Note that the mapping F¹Is the algebraic continuous function
It may be defined by a mathematical formula, or by some typical correspondence
May be specified. The situation is an individual mapping f ¹ _iAbout
The same is true.

In the present embodiment, as an example of the latter rule, an element mapping (element m) that specifies the contents of the mapping F ¹ more is described.
apping). The element mapping specifies correspondence between specific elements included in the domain and the range. Figure 8 is out of action of the elements mapping with the mapping F ¹ shown in FIG. 7 (collectively referred to as f _e ^1), shows the two corresponding. In the figure, e ⁰ ₁ (corresponding to vertex A of regular triangular pyramid ABCD), e ⁰ ₂ (corresponding to vertex B) belonging to subspace X ⁰ ,
And the correspondence between e ¹ ₁ (corresponding to the side connecting vertices A and B) that should belong to the subspace X ¹ . Both ends of .differential.B ¹ surrounding the e ¹ ₁ is here indicated as P ₁₁ s and P ₁₁ t, these points correspond to a vertex A, B in this order. Note that points A, B, C, and D are also four points corresponding to the zero-dimensional cell, and will be referred to as P ₀₀ , P ₀₁ , P ₀₂ ,
Notated as _P03 .

When combined with the element mapping, ΔB ¹
Acts as a pointer to the correspondence between elements. That is,
While defining all the cells to be glued open to avoid overlapping of the glued points, the element mapping supports by defining ∂B, which is the boundary when the cell is closed, as the domain. Has the advantage of not leaving ambiguity in the description. This advantage is not found in conventional modeling methods such as boundary representation.

[0037] More specifically, two of the corresponding element mapping f _e ¹ is a _{P 00 → P 11 s P 01} → P 11 t. Such correspondence is with other vertices belonging to the subspace X ^0, also between the other side should belong to the subspace X ¹ is defined, it is indicated as comprehensive element mapping f _e ¹ the entire element mapping table ( This is written in FIG. 18 described later. Figure 9 is thus in the finished subspace X ^1, in the form of so-called wire frame.

Next, to construct a subspace X ² (S24 in FIG. 3). 10 Upon construction of this space represent the four 2-cell e ² ₁ to e ² ₄ to be used anew. All of these cells are in phase with a two-dimensional open ball, with a regular triangular pyramid AB
A panel that constitutes the four sides of the CD.

FIG. 11 shows an already constructed wire frame.
Subspace X¹Four four-dimensional cells e^Two ₁~ E^Two _FourConnect
The state of wearing is shown in part. Again subspace
X¹Following the construction of the two-dimensional cell e^Two _iOf the closed set
One closed two-dimensional ball is B^Two _iIf you write^Two _i= E^Two _i+ ∂B^Two _i  It is. Now, the projection F
^TwoIs F^Two: ∂B^Two ₁∪^o∂B^Two _Two∪^o∂B^Two _Three∪^o∂B^Two _Four→ X¹  The mapping f for each two-dimensional cell^Two _iAnd f^Two _i= F^Two｜ ∂B^Two _i: ∂B^Two _i → X¹  Decide to be Mapping F^TwoWhen using, X^Two= X¹∪^o _F(∪^o _{i = 1,… 4}B^Two _i) = X¹∪^o(∪^o _{i = 1,… 4}
e^Two _i) (Where F is F^TwoIs shown).

The mapping F ² is a mapping from the boundary ∂B ^{2 including the} cell to the subspace X ¹ , and is also entered in the mapping table (FIG. 18 described later). At this time, the two-dimensional cell once decomposed in the form of (2-cell + one dimensional cells), thus the same dimensions of the cells included obtained one-dimensional cells in the pre-built subspace X ^1, i.e. the primary It will be adhered to the original cell.

Next, an element mapping for more specifically specifying the mapping F ² will be introduced. 12 and a portion corresponding to the side AB belonging to the subspace X ¹ (denoted which _{L 11 (P 11 s, P} 11 t) and), it bonded is to e ² ₁ (corresponding to the surface ABC) One side constituting the circumference of ∂B ² is shown. The both ends of this side are P ₂₁₁ u and P ₂₁₁ v, and this side itself is described as L ₂₁₁ (P ₂₁₁ u, P ₂₁₁ v).

Under this condition, the element mapping f_e ^TwoOne of
The correspondence of L₁₁→ L₂₁₁  Becomes Such correspondence is represented by the subspace X¹Belongs to other
Edge and subspace X^TwoAnd the edges of the four panels that belong to
Are defined between the other sides, and the whole is collectively an element map f
_e ^TwoAnd written in the element mapping table (FIG. 19 described later).
Be included. FIG. 13 shows the completed subspace X^Twoso,
It has the shape of a hollow triangular pyramid.

Subsequently, the subspace X^Three(Figure 3)
S26). Fig. 14 shows the construction of this space.
3D cell to be used e^ThreeAnd already constructed subspace
X^TwoIs shown. Three-dimensional cell e^ThreeIs in phase with a three-dimensional open ball
Thus, the content becomes a solid triangular pyramid ABCD. Same figure
Then, the already constructed panel-shaped subspace X^TwoTertiary
Former cell e^ThreeAre shown. Three-dimensional cell e^Three
A three-dimensional closed sphere in the form of a closed set^ThreeWrite
If so, B^Three _i= E^Three _i+ ∂B^Three _i  It is. Now, the projection F
^TwoIs F^Three: ∂B^Three→ X^Two The mapping f for each 3D cell^Three _iAnd f^Three _i= F^Three｜ ∂B^Three _i: ∂B^Three _i → X^Two  Decide to be However, in this case, i = 1 only
No.

[0044] When using the mapping ^{F 3, X 3 = X 2} ∪ o F B 3 = X 2 ∪ o e 3 (F in the formula have F ³⁾ and can be formulated. The mapping F ³ are also noted in the mapping table (described later Figure 18).

Next, an element mapping for further specifying the mapping F ³ will be introduced. As an example in Figure 14, one apex portion corresponding to A in the plane ABC belonging subspace X ^2, that is, P _{0 0,} the point P ₃ a one included in .differential.B ³ to be bonded thereto is shown ing. Therefore, one correspondence of the element mapping f _e ³ is P ₀₀ → P ₃ a. The entire element including the specific correspondence relationship other than the above is described as an element mapping f _e ^3, and an element mapping table (FIG.
9) is written. By the above process, the subspace X ³
Is completed, and finally a solid regular triangular pyramid ABCD is constructed.

It should be noted here that a corresponding example of the element mapping f _e ³ is described between points. In other words, in the process of bonding three-dimensional cells that we are currently considering, this three-dimensional cell is first implicitly decomposed into (three-dimensional cell + two-dimensional cell), and the two-dimensional cell obtained in this way is implicitly decomposed. It is decomposed into (two-dimensional cell + one-dimensional cell), and this one-dimensional cell is further implicitly decomposed into (one-dimensional cell + zero-dimensional cell). Acquisition, that is, acquisition of the correspondence between points is possible. That is, the method of implicit decomposition of a cell into lower cells is defined by the dimensions of the elements of the element mapping. That is, even if it is a three-dimensional solid, if a certain side (this is a one-dimensional cell) is noticed, the place is decomposed into a one-dimensional cell, and if a certain point (this is a zero-dimensional cell) is noticed, the place is The process of decomposing into zero-dimensional cells is implicit. Even if it is only necessary to pay attention to a certain side, if a certain point on the side is to be treated specially, the above-mentioned point becomes a zero-dimensional cell (one-dimensional cell + zero-dimensional cell). It is broken down into That is, it can be said that the intention of the design is reflected in the operation of the cell.

FIGS. 15 to 19 show various information tables obtained by the above series of processing. Figure 15 is a topological cell table storing topological information of all the cells constituting the equilateral pyramid, the element ID is expressed in the form of e ⁱ _j
And the dimensions of each element, and whether each element is open (0 as data) / closed (1 as well). In the present embodiment, all cells are defined as open, so that the open / close columns are all “0”.

FIG. 16 shows a geo that stores geometric information of each cell.
Metrical cell table, e for zero-dimensional cells
⁰ ₁P corresponding to₀₁(X₀₁, y₀₁, z₀₁) Etc.
E for a one-dimensional cell¹ ₁Line corresponding to the side AB corresponding to
Min L₁₁(P₁₁s, P₁₁t) etc. are displayed in two-dimensional cells
About e^Two ₁Triangle indicating the three vertices of the surface ABC corresponding to
Shape display Tr_{twenty one}(P_{twenty one}u, P_{twenty one}v, P_{twenty one}Surface display such as w)
And for three-dimensional cells e^Three3D ABCD corresponding to
Polyhedral display Te showing the above four elements_Three(P_Threea, P _Threeb,
P_Threec, P_Threed) etc. are included.
Topological cell table and geometric cell table
The necessary information about the cell is provided by the file.

FIG. 17 shows parts of a regular triangular pyramid ABCD.
Is a table and the subspace X of each dimensionⁱTo build
Classification of required element dimensions and actual components
I do. That is, the subspace X⁰Zero dimension to construct
Cell e⁰ ₁~ E⁰ _FourIs required, and the subspace X¹To build
Subspace X⁰And one-dimensional cell e¹ ₁~ E¹ ₆Required, partially empty
Interval X^TwoTo construct a subspace X¹And the two-dimensional cell e^Two ₁~ E
^Two _FourIs required, and the subspace X ^ThreeTo construct a subspace X^TwoWhen
Three-dimensional cell e^ThreeAre described, respectively.

FIG. 18 shows a mapping table, which is necessary when a (i + 1) -dimensional subspace is formed by bonding an (i + 1) -dimensional cell higher by one to the i-dimensional subspace. Domain of F ^{(i + 1)} ∂B ^{(i + 1)} and range X ⁱ
Is entered. The mapping table may be referred to as a table that records adhesion information between subspaces of different dimensions in association with each subspace.

FIG. 19 shows the coordinates or algebra of real points, line segments, surfaces, etc., which are the domain and range of the element mapping f _e ^{(i + 1)} further specifying the mapping F ^{(i + 1)} of FIG. It is an element mapping table in which a combination of display is entered. In FIG. 19, for the correspondences other than the correspondences already exemplified, for example, _fe ² : L ₂₁₂ (P ₂₁₂ u, P ₂₁₂ v) → L ₁₂ (P ₁₂ s, P ₁₂
As in t), symbols are given and displayed according to the same rule. It should be noted that the element mapping table may be incorporated in the mapping table of FIG. 18, and in this case, the mapping table records the geometric adhesion information defined between the subspaces (FIG. 1).
9) and a portion for recording topological adhesion information (corresponding to FIG. 18) defined between the subspaces.

According to the present embodiment, the above-mentioned problem relating to shape modeling is solved. The internal structures of the various tables shown in FIGS. 15 to 19 are highly versatile, and any shape data can be basically expressed in a unified manner in the format of these tables. For this reason, the present embodiment is most suitable for constructing a shape database, and it is easy to configure a processing target portion and its components as accessible parts, contributing to reuse and sharing of shapes. it can. Here, the shape is taken as an example, but the present invention can of course be widely used for events beyond three dimensions. At this time, if the number of parameters defining the event is n, generally a 0 to n-dimensional subspace may be constructed in order from the bottom, and even in such a case, the format of various tables in the present embodiment has versatility. .

The above-mentioned table may of course be recorded as a special data structure on a hard disk, floppy disk or other computer-readable recording medium.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of a shape definition device according to an embodiment.

FIG. 2 is a flowchart showing a process performed by the shape definition device.

FIG. 3 is a flowchart showing a procedure of acquiring cell information (S10).

FIG. 4 is a diagram showing a set of zero-dimensional cells for forming a regular triangular pyramid.

FIG. 5 is a diagram showing a set of one-dimensional cells for forming a regular triangular pyramid.

FIG. 6 is a diagram showing a state in which a zero-dimensional cell and a one-dimensional cell are bonded to form a regular triangular pyramid.

FIG. 7 is an enlarged view showing a map for bonding a one-dimensional subspace to a zero-dimensional subspace.

FIG. 8 is an enlarged view showing an element mapping for bonding a one-dimensional subspace to a zero-dimensional subspace.

FIG. 9 is a diagram showing a constructed one-dimensional subspace.

FIG. 10 is a diagram showing a set of two-dimensional cells for forming a regular triangular pyramid.

FIG. 11 is a diagram conceptually showing a mapping for bonding a two-dimensional subspace to a one-dimensional subspace.

FIG. 12 is an enlarged view showing an element mapping for bonding a two-dimensional subspace to a one-dimensional subspace.

FIG. 13 is a diagram showing a constructed two-dimensional subspace.

FIG. 14 is a diagram showing a procedure for constructing a three-dimensional subspace for a regular triangular pyramid ABCD.

FIG. 15 is a diagram showing a topological (topological) cell table introduced in the embodiment.

FIG. 16 is a diagram showing a geometrical (geometric) cell table introduced in the embodiment.

FIG. 17 is a diagram showing a parts table introduced in the embodiment.

FIG. 18 is a diagram showing a mapping table introduced in the embodiment.

FIG. 19 is a diagram showing an element mapping table introduced in the embodiment.

[Explanation of symbols]

2 shape definition device, 4 shape database, 6 shape information input unit, 8 processing part designation unit, 10 cell information acquisition unit, 12 cell database, 14 cell information output unit,
16 user interface unit, 18 display device, 20
Display control unit.

Claims (14)

[Claims] 1. An object is decomposed into cells of each dimension in a cell structure space, a subspace of a predetermined dimension is constructed by a set of cells of a predetermined dimension or less, and the subspace of the predetermined dimension exceeds the predetermined dimension. Describes the relationship between the subspaces of different dimensions in a form encompassed by the subspaces of the dimensions, and defines geometric information and topological information about the described subspaces of each dimension, and is defined between the subspaces of each dimension. A multi-dimensional definition method for an object, comprising acquiring geometric adhesion information and topological adhesion information to be encoded and encoding the object in a format including the information. 2. The topological adhesion information describes each subspace constituting the object in such a manner that a higher-order subspace is bonded to a lower-order subspace using a continuous mapping. The method according to claim 1, comprising the information of: 3. The method according to claim 2, wherein said continuous mapping is a surjective mapping. 4. The method according to claim 3, wherein said surjective mapping associates a subspace of a certain dimension with a higher-order subspace. 5. The subspace is defined as an open set,
3. The method of claim 2, wherein the continuous mapping has its higher-order subspace boundary as its domain. 6. The method according to claim 5, wherein the continuous mapping is further specified by an element mapping that describes correspondence between specific elements between subspaces. 7. The method of claim 6, wherein the element mapping describes correspondence between geometric features between subspaces. 8. The geometric information includes, for a zero-dimensional cell included in any one of the subspaces, coordinate information corresponding to the cell, for a one-dimensional cell, a curve display corresponding to the cell, 2. The method according to claim 1, wherein the two-dimensional cell includes a curved surface display corresponding to the cell, and the three-dimensional cell includes a three-dimensional display corresponding to the cell. 9. Reading existing data representing an object,
The method according to claim 1, wherein cells of each dimension are extracted from the data using geometric information characteristic of the cells of each dimension as a clue, and an object is decomposed into cells of each dimension. 10. When a predetermined operation is performed on an object, a part related to the operation in the object is specified, and this part is decomposed into lower-order cells. The method according to claim 1, wherein the method is described in a format including adhesion information. 11. The method of claim 1, wherein the object is decomposed into cells of each dimension according to a design intent for the object. 12. An input unit for inputting data describing an object, a specifying unit for specifying a portion to be processed in the input data, and decomposing the specified portion into a subspace of each dimension in a cell structure space. An acquisition unit for acquiring the geometric information and the topological information, and the geometric adhesion information and the topological adhesion information defined between the subspaces of the respective dimensions. Dimensional definition device. 13. A first table for recording topological information relating to a cell constituting a predetermined portion of an object in association with each cell, a second table for recording geometric information relating to the cell in association with each cell, The subspace of a dimension is represented as a set of cells below that dimension,
And a third table that represents in which form each cell belongs, and a fourth table that records adhesion information between subspaces of different dimensions in association with each subspace. A computer-readable recording medium on which multi-dimensional definition information of an object is recorded, wherein the predetermined portion is configured to be accessible as a component by a fourth table. 14. The fourth table includes a table for recording geometric adhesion information defined between subspaces, and a table for recording topological adhesion information defined between subspaces. A recording medium according to claim 1.