# Patent

## Title
Method for generating progressive solid models based on cellular topology

## Abstract

Disclosed is a method for generating progressive solid models based on a cellular topology. A cellular model generating section 10, if a specific feature-based model is inputted, performs a mapping operation on the input feature-based model with reference to an internal feature library, thereby generating cellular topology models based on feature models. A progressive model initializing section 20 composes cells by use of volume attributes of the cells according to a relationship between the input feature-based model and the cells obtained from the cellular topology model to generate an initial cellular model SM0 which is simplified to generate a progressive solid model, and then searches n delta volumes DVi transiting the initial cellular topology model SM0 by composing and decomposing the cells so as to progressively complement the difference between the initial cellular topology model SM0 and the input feature-based model. A progressive model generating section 30 generates n progressive features PFi defined as a face subset of the delta volume and corresponding attributes from the n delta volumes DVi, and outputs n progressive cellular models PFi and the initial cellular model SM0 as the progressive solid model in the form of {SM0, {PF0, PF1, . . . , PFn−1}}.

## Background
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method and system for generating a solid model of computer graphics, and more particularly, to a method for generating progressive solid models based on a cellular topology according to a feature approach to achieve effective sharing and transmission of the model under a distributed circumstance.
2. Background of the Related Art
Generally, highly detailed geometric models are necessary to satisfy the growing expectation for realism in computer graphics.
In particular, according to conventional modeling systems, detailed models are created by applying versatile modeling operations, such as extrusion, constructive solid geometry, and freeform deformations, to a variety of geometric primitives. In order to efficiently display detailed models, they must be tessellated into meshes such as triangle meshes.
However, the resulting complex meshes are expensive to store, transmit, and render, thus motivating a number of practical solutions: mesh simplification; level-of-detail (LOD); progressive transmission; and mesh compression.
In computer graphics, models are usually represented by use of triangle meshes. However, solid models are widely used in the industry, and are applied to advanced application such as product design and virtual assembly. In addition, since these developing processes are largely proceeded under distributed circumstances, the problem of sharing and interchanging solid models over the network becomes an important issue.
In particular, in order to solve the above problem, it is necessary to generate adequate level-of-details for the solid model depending on the specific application, and to provide the effective transmitting process. The generation of level-of-details and progressive transmission of the solid model is a prerequisite to properly achieve the collaboration for developing the products under the Internet environment. However, current researches are mostly focused on triangular meshes. There are few researches for generating progressive solid models from solid models at present.
For example, several research efforts have addressed how to generate or compress progressive models from triangular meshes, such as a method of a progressive triangular mesh representation and a mesh simplification for maximally maintaining overall appearance defined by scalar attributes as well as shapes of initial mesh model, a method of quickly simplifying polygonal models by progressively applying vertex contractions using a quadric matrix, and a triangular mesh compression method, called as Edgebreaker, for coding the connectivity of arbitrary triangle meshes, which is widely used due to the efficient compressing rate. There are few researches related to the generation of progressive solid models from the solid model or compression or transmission of the solid model.
SUMMARY OF THE INVENTION
Accordingly, the present invention is directed to a method for generating progressive solid models based on a cellular topology according to a feature approach to achieve effective sharing and transmission of the model under a distributed circumstance that substantially obviates one or more problems due to limitations and disadvantages of the related work.
An objective of the present invention is to provide a method for generating progressive solid models based on a cellular topology, in which an input feature-based model is converted into a feature-based cellular model considering feature information and cellular topology, then an initial progressive solid model is extracted from the converted feature-based cellular model, and finally, a set of progressive features are generated by composing and decomposing cells in the feature-based cellular model to progressively convert the initial progressive solid model into the input feature-based model.
To achieve the objective and other advantages, the present invention provides a method for generating progressive solid models based on a cellular topology, which comprises three steps: a cellular model generating section for performing a mapping operation on the input feature-based model with reference to an internal feature library, thereby generating a feature-based cellular model; a progressive model initializing section for composing cells by use of volume attributes of the cells in the feature-based cellular model according to the relationship between the input feature-based model and the cells obtained from the feature-based cellular model to generate an initial cellular model which is simplified to generate the progressive solid model, and searching n delta volumes transiting the initial cellular topology model by composing and decomposing the cells so as to progressively complement a difference between the initial cellular topology model and the input feature-based model; and a progressive model generating section for generating n progressive features defined as a face subset of the delta volumes and corresponding attributes, and finally, outputting n progressive features PFi and the initial cellular model SM0 as a completed progressive solid model.
It is to be understood that both the foregoing general description and the following detailed description of the present invention are exemplary and explanatory and are intended to provide further explanation of the invention as claimed.



BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention. In the drawings:
FIG. 1 is a diagram showing a method for generating progressive solid models based on a cellular topology according to the present invention;
FIG. 2 is a diagram showing a process of generating feature-based models;
FIG. 3 is a diagram showing a process of transiting an initial cellular model generated corresponding to the feature-based models of FIG. 2 to progressive solid models;
FIG. 4a is a diagram showing a process of generating feature-based cellular topology models;
FIG. 4b is a diagram showing the cellular topology of the feature based model of FIG. 4a; 
FIG. 4c is a diagram showing a 3d model of the cellular topology model of FIG. 4b; 
FIG. 5a is a chart showing the relationship between cells and the feature-based models of FIGS. 4a–4c; 
FIG. 5b is a chart showing a cellular model defined as a composition of cells;
FIG. 5c is a diagram showing an initial cellular model and transited feature-based models;
FIG. 6 is a diagram showing a process of generating progressive solid models based on the progressive features; and
FIGS. 7a and 7b show one embodiment of generating progressive solid models from the appearance of an automobile, in the respective steps size of the progressive solid models being compared to each other.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
A preferred embodiment according to the present invention will now be explained with respect to the accompanying drawings.
Referring to FIG. 1, if a specific feature-based model is inputted to a cellular model generating section 10, the section 10 performs a mapping operation on the input feature-based model considering an internal feature library, thereby generating a feature-based cellular topology model.
A progressive model initializing section 20 composes cells by use of volume attributes of the cells according to the relationship between the input feature-based model and the cells obtained from the cellular topology model to generate an initial cellular model SM0 which is simplified to generate a progressive solid model, and further searches n delta volumes DVi transiting the initial cellular topology model SM0 by composing and decomposing the cells so as to progressively complement the difference between the initial cellular topology model SM0 and the input feature-based model.
A progressive model generating section 30 generates n progressive features PFi defined as a face subset of the delta volume and related attributes Ai from the n delta volumes DVi, and outputs the progressive solid model PSM in the form of {SM0, {PF0, PF1, . . . , PFn−1}}.
The respective progressive feature PFi is defined by (Ni, Oi, Ai), where Ai represents attributes such as color, texture, engineering information and so forth.
Ni is a subset of faces of DVi to be added to the model SMi to be transited to SMi+1 and is defined as following Equation 1.




  
    
      
        
          
            N
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          =
          
            
              ∂
              
                DV
                i
              
            
            -
            
              
                ∑
                k
              
              ⁢
              
                f
                k
              
            
          
        
        ,
        
          
            where
            ⁢
            
              
            
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              f
              k
            
          
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                  ∂
                  
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                    i
                  
                
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                and
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                  f
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                  SM
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            ≠
            ∅
          
        
      
    
    
      
        Equation
        ⁢
        
          
        
        ⁢
        1
      
    
  




where ∂SMi represents a set of exterior faces of the model SMi, and fk represents a face of DVi.

Oi is a subset of faces of DVi to be eliminated from the models SMi to be transited to SMi+1 and is defined as following Equation 2.




  
    
      
        
          
            O
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            A
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        ⁢
        
          
            where
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              f
              k
            
          
          ∈
          
            
              
                
                  ∂
                  
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                and
                ⁢
                
                  
                
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                  f
                  k
                
              
              ⋂
              
                ∂
                
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            ≠
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        Equation
        ⁢
        
          
        
        ⁢
        2
      
    
  




where ∂DSMi represents exterior faces of the model SMi, and fk means a face of the delta volumes DVi.

The method of generating the progressive solid models based on the cellular topology according to the present invention will now be described.
FIGS. 2 and 3 schematically show the input and result of the procedure provided by the present invention. FIG. 2 shows a process of generating the feature-based model to be used in the input, in which P10 is corresponding to the input of the procedure provided by the present invention. FIG. 3 shows the result of the progressive solid model generated from the input P10 according to the procedure provided by the present invention. In other words, the figures show the result of progressive solid model generated by transiting an initial model SM0 to seven delta volumes DV0 to DV6.
First of all, as will be seen from FIG. 4a, if a specific feature-based model P6 for generating the progressive solid model PSM according to the present invention is given to the cellular model generating section 10, the cellular model generating section 10 performs a mapping operation on the input specific feature-based model P6 with reference to the internal feature library, thereby generating the feature-based models P based on the cellular topology as shown in FIG. 4b. 
The input specific feature-based model P6 is generated by adding or subtracting features F1 to F6 to or from the specific base feature-based model P0, as shown in FIG. 4a. The transited feature-based models P1 to P6 are generated by performing Boolean union operation (+*) or Boolean difference operation (−*) on the other feature-based models F1 to F6 relative to the previous feature-based models P1 to P6.
For example, in FIG. 4a, the transited feature-based model P2 is generated by performing the Boolean union operation (+*) on the feature-based model P1 just before the transition to further add the feature-based model F2 indicating a protruded cylinder, the transited feature-based model P5 is generated by performing the Boolean difference operation (−*) on the feature-based model P4 just before the transition to eliminate the feature-based model F5 indicating a sphere, and the input transited feature-based model P6 is generated by performing the Boolean difference operation (−*) on the feature-based model P5 just before the transition to eliminate the feature-based model F6 indicating a polyhedron.
In addition, the feature-based model P based on the cellular topology is modeled as P=F0−*F1+*F2−*F3−*F4−*F5−*F6as shown in FIG. 4b. At that time, F0 denotes a base feature-based model, F1 to F6 denote other features further added or subtracted to or from the base feature-based model F0, and C1 to C10 denote feature cells generated based on criteria such as volume, complexity and so forth.
After the feature-based cellular topology model P is generated by the cellular model generating section 10, the progressive model initializing section 20 generates an initial progressive solid model SM0 by composing all the generated cells except dummy cells which represents an overall shape of the feature-based model P. And then, the section 20 searches n delta volumes DVi transiting the initial cellular Model SM0 by composing and decomposing the cells C1 to C10 generated from the difference of the 3D model shown in FIG. 4c. 
As will be seen from FIG. 4a, the cellular model used in the cellular model generating section 10 is represented by refining a LUMP of the solid model into a region of CELL3D. The CELL3D is represented by a set of CFACE. The CFACE indicates one side, and the FACE is represented by the CFACE and its partner. In addition, the feature information is stored by assigning attributes to the CELL3D and CFACE.
FIG. 5a shows a relationship between the cells C1 to C10 and the feature-based models F1 to F7 in the cellular topology model P shown in FIG. 4, FIG. 5b shows a portion of delta volumes DV0, DV1, and DV2, and FIG. 5c shows the generated 3D initial cellular model SM0 and the transited model SM2.
For example, in FIG. 5a, owner features of C2 are features F0 and F1, and the cells constructing the feature-based model F2 are C3 and C4. FIG. 5b shows the initial cellular model SM0 defined as the composition of the remaining cells (C1, C2, C3, C4, C5, C7, C8 and C9) except for dummy cell defined in FIG. 5a, the delta volume DV0 defined as C2, the delta volume DV1 defined as C5, and the delta volume DV2 defined as C9. In particular, FIG. 5c shows the initial cellular model SM0 and the transited feature-based model SM2 in which a circular hole and a hexahedron are eliminated by performing Boolean difference operation (−*) on the delta volumes DV0 and DV1 defined as C2 and C5 relative to the initial cellular model SM0.
After the initial cellular model SM0 and n delta volumes DVi transiting the initial cellular model SM0 are searched, the progressive model generating section 30 generates n progressive features PFi from n delta volumes DVi, in which PFi is defined as a face subset of the delta volume according to an attribute Ai of n delta volumes DVi and Equations 1 and 2, and outputs n progressive cellular models PFi and the initial cellular model SM0 as the progressive solid model PSM in the form of {SM0, {PF0, PF1, . . . , PFn−1}}.
FIG. 6 shows a process of finally completing and outputting the progressive solid model PSM by generating the initial cellular model SM0 and four progressive features PF0, PF1, PF2 and PF3 from four delta volumes DV0, DV1, DV2 and DV3 searched to transit the initial cellular model SM0. FIG. 7a shows the progressive solid models generated when the method of generating the progressive solid model is applied to an automobile model, and FIG. 7b shows comparative file sizes of the models corresponding to three steps.
Meanwhile, in the method of generating the progressive solid models based on the cellular topology according to the present invention, the reason to use the progressive features PF1 instead of the delta volumes DVi is as the following: the more the transition level interacting between the feature-based models is increased by the use of the delta volumes DVi, the more file size is increased. In the transition process, the Boolean union operation (+*) or Boolean difference operation (−*) requires expensive computational cost. Meanwhile, if the progressive features PFi are utilized, it requires the simple process of composing and eliminating the faces of the models, thereby simplifying the calculation and speeding up the transition process.
In actual, if the solid model is transmitted over the Internet, the transmission of the perfect detailed model requires a lot of time. Therefore, a simplified solid model SM0 is firstly transmitted, and then progressive features PFi are progressively transmitted, so that it is possible to transmit it quickly and effectively. If necessary, it is possible to obtain the level suitable for the application or to allow the user to see only a specific level according to the accessibility of the user.
With the above description of the method for generating the progressive solid models based on the cellular topology according to the present invention, the input feature-based model is represented as an initial progressive solid model SM0 and subsequent progressive features PFi, and thus the progressive solid model representation can be described in the form of {SM0, {PF0, PF2, . . . , PFn−1}}.
The forgoing embodiments are merely exemplary and are not to be construed as limiting the present invention. The present teachings can be readily applied to other types of apparatuses. The description of the present invention is intended to be illustrative, and not to limit the scope of the claims. Many alternatives, modifications, and variations will be apparent to those skilled in the art.

## Claims

1. A method for generating progressive solid models based on a cellular topology, the method comprising the following steps:
a cellular model generating section, if a specific feature-based model is inputted, for performing a mapping operation on the input feature-based model with reference to an internal feature library, thereby generating cellular topology models based on feature models;
a progressive model initializing section for composing cells by use of volume attributes of the cells according to a relationship between the input feature-based model and the cells obtained from the cellular topology model to generate an initial cellular model which is simplified to generate the progressive solid model, and searching n delta volumes transiting the initial cellular topology model by composing and decomposing the cells so as to progressively complement a difference between the initial cellular topology model and the input feature-based model; and
a progressive model generating section for generating n progressive features defined as a face subset of the n delta volumes and corresponding attributes, and outputting n progressive features PF1, and the initial cellular model SM0 as a completed progressive solid model representation PSM={SM0, {PF0, PF1, . . . , PFn}}.

2. The method as claimed in claim 1, wherein n progressive features generated in the progressive model generating section are represented as a subset of faces of n delta volumes generated in the progressive model initializing section and related attributes.

3. The method as claimed in claim 2, wherein the subset (Ni) of faces of delta volumes, which is contained in n progressive features generated in the progressive model generating section, are those to be added to SMi to be progressively transited to SMi+1, and is defined in the following equation.




  
    
      N
      i
    
    =
    
      
        ∂
        
          DV
          i
        
      
      -
      
        
          ∑
          k
        
        ⁢
        
          f
          k
        
      
    
  
  ,
  
    
      where
      ⁢
      
        
      
      ⁢
      
        f
        k
      
    
    ∈
    
      
        
          
            ∂
            
              DV
              i
            
          
          ⁢
          
            
          
          ⁢
          and
          ⁢
          
            
          
          ⁢
          
            f
            k
          
        
        ⋂
        
          ∂
          
            SM
            i
          
        
      
      ≠
      ∅
    
  



where ∂SMi means a set of exterior faces of the feature cells, and fk means a face of DVi.

4. The method as claimed in claim 2, wherein the subset (Oi) of faces of delta volumes, which is contained in n progressive features generated in the progressive model generating section, are those to be removed from SMi to be progressively transited to SMi+1, and is defined in the following equation:




  
    
      O
      i
    
    =
    
      A
      ⁢
      
        
      
      ⁢
      set
      ⁢
      
        
      
      ⁢
      of
      ⁢
      
        
      
      ⁢
      faceIds
      ⁢
      
        
      
      ⁢
      of
      ⁢
      
        
      
      ⁢
      
        
          ∑
          k
        
        ⁢
        
          f
          k
        
      
    
  
  ,
  
    
      where
      ⁢
      
        
      
      ⁢
      
        f
        k
      
    
    ∈
    
      
        
          
            ∂
            
              DV
              i
            
          
          ⁢
          
            
          
          ⁢
          and
          ⁢
          
            
          
          ⁢
          
            f
            k
          
        
        ⋂
        
          ∂
          
            SM
            i
          
        
      
      ≠
      ∅
    
  



where ∂SMi means exterior faces of the transited model SMi, and fk means a face of delta volumes DVi.