WO2008012640A1 - Apparatus and method of generating fillets - Google Patents

Apparatus and method of generating fillets Download PDF

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Publication number
WO2008012640A1
WO2008012640A1 PCT/IB2007/002086 IB2007002086W WO2008012640A1 WO 2008012640 A1 WO2008012640 A1 WO 2008012640A1 IB 2007002086 W IB2007002086 W IB 2007002086W WO 2008012640 A1 WO2008012640 A1 WO 2008012640A1
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WO
WIPO (PCT)
Prior art keywords
fillet
generation
vertex
edge lines
fillets
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Application number
PCT/IB2007/002086
Other languages
French (fr)
Inventor
Eisaku Ikeda
Kazuhito Nakano
Original Assignee
Toyota Jidosha Kabushiki Kaisha
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Publication date
Application filed by Toyota Jidosha Kabushiki Kaisha filed Critical Toyota Jidosha Kabushiki Kaisha
Publication of WO2008012640A1 publication Critical patent/WO2008012640A1/en

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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/10Constructive solid geometry [CSG] using solid primitives, e.g. cylinders, cubes
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/20Finite element generation, e.g. wire-frame surface description, tesselation

Definitions

  • the present invention relates to a fillet generation apparatus in a
  • the fillets around the vertex C2 are to be generated next, however, because the fillet of the concave edge line Ll has already been generated, the fillets of the convex edge lines L4 and L5 must be subsequently generated. However, because the radii of the edge lines L4 and L5 are not equal, the corner shape at the vertex C2 it either impossible to generate or will have poor quality. In such cases, the fillets of the edge lines Ll to L3 must be discarded and the fillets must be generated again, in the sequence of edge line L5 ⁇ Ll ⁇ L4 ⁇ L2 ⁇ L3.
  • JP-A-2002-304424 proposes a CAD system that displays a plurality of different corner shape patterns for different generation sequences, and allows the operator select a desired pattern from the displayed corner shape patterns.
  • the present invention provides an apparatus and method that automatically executes fillet processing, even for a complex solid shape.
  • a fillet generation apparatus is a fillet generation apparatus performing fillet processing with respect to a solid shape in a CAD system, having an edge line extraction means for extracting a plurality of edge lines from the solid shape as the targets of fillet generation, a condition inputting means for prompting a user to input a fillet generation conditions with regard to each edge line, a vertex extraction means for extracting a vertex at which a plurality of edge lines converge, a divided edge line generation means for generating divided edge lines by dividing each edge line in two, a synthesis procedure determining means for provisionally generating a fillet at each divided edge line, in accordance with the fillet generation condition, and for determining a synthesis procedure for the fillet at the vertex, based on the correlation between the provisionally generated fillets, with a vertex and a plurality of divided edge lines converging at the vertex taken as a generation unit, and a fillet generation means for
  • a pattern storage means for storing a plurality of pattern types, which define a fillet synthesis procedure at a vertex, may be further provided, wherein the synthesis procedure determining means selects from the plurality of pattern types a synthesis procedure for the generation unit.
  • the synthesis procedure determining means may generate the generation unit as an element that is independent from the constituent elements of the solid shape, and cause procedure information that includes at least the generation condition and synthesis procedure to be held in the generation unit.
  • the synthesis procedure determining means may check for interference between provisionally generated fillets for two divided edge lines belonging to one and the same generation unit as the correlation between the provisionally generated fillets.
  • the synthesis procedure determination means may check for interference between provisionally generated fillets for two divided edge lines belonging to different generation units as the correlation between the provisionally generated fillets.
  • the fillet generation means may execute batch fillet generation and synthesis after the fillet synthesis procedure for all generation units included in the solid shape are determined.
  • the present invention may be understood as a fillet generation apparatus having at least a part of the above-described means, or as a CAD system having such a fillet generation apparatus.
  • the present invention may further be understood as a method for fillet generation having at least a part of the above-described processing, a program for implementing the method, or a storage medium in which the program is stored.
  • Each of the above-described means and processing may be mutually combined as possible to implement the present invention.
  • FIG. 1 is a block diagram showing the configuration of a fillet generation apparatus according to the present invention
  • FIG. 2A is a drawing showing a solid shape (intersection shape) before performing fillet processing
  • FIG. 2B is a drawing showing the solid shape after fillet processing
  • FIG. 3 is a flowchart showing the flow of procedure information generation processing
  • FIG. 4 is a drawing showing an example of a corner shape pattern applicable to a corner at which three convex edge lines converge;
  • FIG. 5 is a drawing showing an example of a generation unit
  • FIG. 6A is a drawing showing a surface-to-surface fillet
  • FIG. 6B is a drawing showing a surface-to-line fillet
  • FIG. 6C is a drawing showing a line-to-line fillet
  • FIG. 7 is a drawing showing the re-calculation of a fillet shape in line passage region
  • FIG. 8 is a drawing showing the fusion at a corner
  • FIG. 9 is a drawing showing an example of interference between branches; and FIG. 10 is a drawing showing a problem arising in convention sequential fillet generation.
  • the constitution of the fillet generation apparatus is shown in block diagram form in FIG. 1.
  • the fillet generation apparatus is typically implemented as one function in a 3-dimensionl CAD system that is used to design 3-dimensional structures, such as vehicles.
  • the fillet generation apparatus is generally formed by an input section 10, a procedure information generation section 11, a procedure information storage section 12, a corner shape pattern database 13 and a automatic fillet generation section 14. These functional elements are implemented by reading a program stored in an auxiliary memory apparatus into a main memory apparatus and executing the program using a central processing unit.
  • the fillet generation apparatus is implemented as a general-purpose computer system.
  • FIG. 2A shows a shape of a solid body (hereinafter "intersection shape") before fillet processing.
  • the fillet generation apparatus reads in an intersection shape designed using a CAD system, and automatically executes fillet processing for elements that make up the intersection shape.
  • FIG. 2B shows the solid shape after fillet processing.
  • fillet size radius value or foot width
  • the method of applying an arc are given as fillet generation conditions via the input section 10. It is extremely difficult to generate all fillets using just this information. This is because, as described above, the shape obtained could differ and it could be impossible to generate a fillet, depending upon the sequence of fillet generation. Another reason is that there are also problems that are not discoverable without actually attempting to generate a fillet (for example, interference between fillets, interference between corners, and interference between a fillet and a corner.
  • corner shapes “corner shapes,” “inter-branch interference shapes,” and “other interference shapes,” and different processing is used to generate each type of fillet.
  • An inter-element fillet is a fillet generated between two surface elements having an edge line between the two surface elements. Stated in different terms, an inter-element fillet is a fillet generated at an edge line.
  • a corner shape is a shape that is synthesized (by shading) to smoothly connect inter-element fillets generated at a plurality of edge lines that share a vertex.
  • An inter-branch interference shape is a synthesized shape between inter-element fillets that is not a corner shape. For example, a synthesized shape of inter-element fillets that do not share a vertex is an inter-branch interference shape.
  • Other interference shapes are interference shapes other than inter-branch interference shapes, such as interference between a corner shape and a corner shape, and interference between a corner shape and an inter-element fillet.
  • the fillet generation apparatus of this embodiment classifies the imagined corner shapes and creates a database of "corner shape patterns" beforehand (the corner shape pattern database 13).
  • Corner shape patterns can be considered to be macros that define the synthesis procedure for an inter-element fillet at a vertex (that is, the generation sequence and synthesis method (interpolation) for an inter-element fillet, and also the resulting corner shape pattern).
  • the corner shape patterns are classified based on such information as the inter-element fillet generation conditions, the number of edge lines converging at a vertex, the combinations of convex and concave edge lines of these edge lines, the angle of intersection between edge lines, and the angle of intersection between surface elements that sandwich an edge line.
  • the fillet generation apparatus selects the optimal pattern from these corner shape patterns, based on the results of analyzing the intersection shape.
  • shapes of inter-element fillets can generally be determined from the fillet generation conditions.
  • corner shapes, inter-branch interference shapes, and other interference shapes cannot be determined using only information obtained from the intersection shape, and cannot be determined without attempting to actually generate inter-element fillets and corner shapes, for example.
  • the procedure information generation section 11 generates procedure information as described below before the processing for automatic generation and burying of fillets.
  • FIG. 3 is a flowchart showing the flow of procedure information generation processing.
  • the procedure information generation section 11 analyzes the intersection shape model and extracts an "edge line", which is the border line of a surface element. When doing this, the procedure information generation section 11 generates an edge line element that is separate from the intersection shape (refer to FIG. 2A).
  • the procedure information generation section 11 prompts the user to input inter-element fillet generation conditions for each extracted edge line.
  • these values are input at the fillet generation conditions.
  • the procedure information generation section 11 extracts a point (vertex) at which a plurality of edge lines converge (refer to FIG. 2A).
  • the procedure information generation section 11 makes a provisional determination of a corner shape pattern applicable to the vertex, for each extracted vertex. As described above, a plurality of corner shape pattern types are stored in the corner shape database 13.
  • the procedure information generation section 11 selects the optimal pattern for the vertex from the corner shape pattern database 13, based on the information such as the above-described inter-element fillet generation conditions, the number of edge lines converging at a vertex, the combinations of convex and concave edge lines of these edge lines, the angle of intersection between edge lines, and the angle of intersection between surface elements that sandwich an edge line.
  • the determination is a "provisional determination,” and the corner shape pattern provisionally determined is referred to as a "provisional pattern.”
  • FIG. 4 shows an example of a corner shape pattern that can be applied to a vertex at which three convex edge lines converge.
  • the three patterns of "shading,” “priority,” and “convergence” are shown, and the corner shape and inter-element fillet synthesis procedures differ for each pattern.
  • the pattern that is selected may be determined from information such as the angle of intersection between edge lines and the radius value of the inter-element fillet. Also, when the size of the inter-element fillet is specified not as a radius value but rather as a foot width, the approximate radius value may be calculated from the angle between surfaces sandwiching the edge line.
  • the procedure information generation section 11 determines the inter-element fillet generation range based on the provisional pattern. As can be understood from FIG. 4, the type of corner shape pattern that is selected changes the position of the ending point of the inter-element fillet. "Priority" may be selected to apply an inter-element fillet continuously to two edge lines. Thus, the coordinates of the starting point and ending point of each inter-element fillet are calculated taking the provisional pattern selected at step S 13 into consideration. [0046] At step S15, the procedure information generation section 11 divides each edge lines into two parts to generate divided edge lines.
  • the procedure information generation section 11 using the vertex and the plurality of edge lines that converge thereat as a unit of generation, generates "procedure information" for each generation unit.
  • the procedure information is stored as an attribute (or feature) of the generation unit.
  • Procedure information is information defining the shape of an inter-element fillet for each divided edge line belonging to the generation unit and the associated synthesis procedure.
  • the procedure information is information that summarizes the corner shape pattern, the inter-element fillet generation conditions for the edge lines, and the positions of the dividing points of each of the divided edge lines at a vertex.
  • the inter-element fillet generation conditions in addition to the size of the inter-element fillet and the method of applying an arc, also include the generation range determined at step S14, the connection condition, and whether or not there is a line passage location.
  • the connection condition and whether there is a line passage location are checked at steps S18 and S19.
  • FIG. 5 shows an example of a generation unit.
  • indicates a vertex
  • x indicates a connection point.
  • the region surrounded by a broken line is the generation unit.
  • the procedure information generation processing and automatic fillet generation and burying processing are executed for each of these generation units.
  • the determination of the generation sequence for inter-element fillets becomes extremely simple.
  • the fillet generation sequence about the vertex Cl need only consider the relationship of between the divided fillets Ll-I, L2-1, and L3-1, there being absolute no influence from the fillet generation sequence with regard to the area about other vertices, such as the vertices C2, C3, and C4.
  • the procedure information generation section 11 provisionally generates an inter-element fillet for each divided edge line for each generation unit, in accordance with the fillet generation conditions.
  • the inter-element fillets By provisionally generating the inter-element fillets, it is possible to check for problems that otherwise cannot be discovered without actually applying fillets (for example, the connection condition of inter-element fillets, existence of a line passage region, interference between inter-element fillets, interference between inter-element fillets and other elements, the angle of intersection of the curved foot line of an inter-element fillet, and corner fusion).
  • the procedure information generation section 11 checks the inter-element fillet connection condition.
  • the inter-element fillet connection condition is information representing how and to what element of an intersection shape an inter-element fillet is connected. Specifically, this includes the condition in which an inter-element fillet is connected to a surface element continuous with Cl (known as a surface fillet) and the condition in which a inter-element fillet passes through a line element continuous with CO (known as a line fillet).
  • a surface fillet an inter-element fillet that is tangent to surface elements on both side continuous with Cl is known as a "surface-to-surface" fillet.
  • FIG. 6 A an inter-element fillet that is tangent to surface elements on both side continuous with Cl is known as a "surface-to-surface" fillet.
  • FIG. 6 A an inter-element fillet that is tangent to surface elements on both side continuous with Cl is known as a "surface-to-surface" fill
  • an inter-element fillet that is tangent to a surface element on one side continuous with Cl and that passes through a line element on another side continuous with CO is known as a "surface-to-line” fillet.
  • an inter-element fillet that passes through line elements on both side continuous with CO is known as a "line-to-line” fillet.
  • the procedure information generation section 11 checks for the existence of a line passage region.
  • a line passage region is a region through which an inter-element fillet intersects another line element. As shown in FIG. 7, when the width of a surface element on which surface fillet is generated is very small, the surface fillet might interfere with another line element (edge line). In such cases, additional processing, such as re-calculation of the shape of the fillet in the line passage region, is required. For example, under some circumstances a surface-to-surface fillet in the region is re-generated as a surface-to-line fillet. [0053] In the processing of steps S18 and S19, once the connection condition and existence of a line passage region have been checked, the associated information is added to the fillet generation conditions of the procedure information.
  • the procedure information generation section 11 checks for the existence of an inter-branch interference shape. Specifically, the procedure information generation section 11 checks for an interference condition between inter-element fillets belonging to different generation units (for example, position and range of interference locations and angle of intersection between inter-element fillets). [0055] At step S21, the procedure information generation section 11 checks for the existence of corner fusion. Corner fusion is the condition in which there is interference between the corner shapes of two generation units. Specifically, a check is made of whether the range of the inter-branch interference shape obtained at step S20 overlaps with a vertex, or with the range of a corner shape established by a provisional pattern. For example, as shown in FIG.
  • the procedure information generation section 11 establishes the corner shape pattern based on not only the information used in determining the provisional pattern, but also on the correlation between provisionally generated inter-element fillets.
  • the correlation between the inter-element fillets includes information regarding the angle between and point of intersection between curved foot lines of the inter-element fillets, and the inter-branch interference shape and corner conversion obtained at step S20 and step S21.
  • the procedure information is updated to include the determined corner shape pattern (hereinafter "established pattern").
  • the procedure information generation section 11 calculates the range of the corner shape at the vertex of each generation unit from the established patterns, and checks for the existence of other interference shapes (that is, interference between corner shapes, and interference between a corner shape and an inter-element fillet). With regard to other interference shapes, after generating and burying one corner shape or inter-element fillet, because another corner shape or inter-element fillet can be generated and buried, it is sufficient at this point to determine only the generation sequence between generation units. The procedure information is then updated to include this information.
  • other interference shapes that is, interference between corner shapes, and interference between a corner shape and an inter-element fillet.
  • the procedure information generation section 11 moves the edge line connection point (dividing point) to a position other than the interference range or corner shape range, based on information obtained at steps S 18 to S21. If the connection point is moved, the procedure information for the corresponding generation unit is updated accordingly.
  • the procedure information generation section 11 determines the pattern of inter-branch interference shape. For example, if the inter-branch interference shape such as shown in FIG. 9 exists, if an inter-element fillet having a small radius value is generated first, warpage and the like may occur in the ultimately obtained synthesized form of the fillet, resulting in poor surface quality. Given this situation, the generation sequence between two generation units is determined, based on the correlation between interfering inter-element fillets.
  • the generation sequence and synthesized shape in the inter-branch interference shape are determined, in accordance with the information regarding the inter-branch interference shape, the combination of convex and concave edge lines and distance between edge lines, and the inter-branch interference shape generation sequence and pattern determining rule that are set beforehand. If complex synthesis processing is not required with regard to inter-branch interference shapes, it is sufficient to determine only the generation sequence between generation units. The procedure information is then updated based on the information determined at this point.
  • the procedure information generation section 11 references all the procedure information to set the generation sequence between each task unit. However, in the generation sequence between task units, because a problem only occurs when an inter-branch interference shape or other interference shape exists, as described above, the determination of the task sequence is not particularly difficult at this point.
  • the automatic fillet generation section 14 executes batch generation, synthesis, and burying of fillets for the intersection shape. At this time as well, the processing is performed in task units. By doing this, it is possible to automatically generate fillets (by batch processing).
  • the present invention achieves the following effect.
  • a conventional apparatus because inter-element fillet synthesis occurs at both ends of an edge line, it is necessary to determine the optimal solution for the fillet generation sequence for the overall solid shape. Consequently, it is extremely difficult to determine the generation sequence of inter-element fillet, and automation of the fillet processing is hindered.
  • the fillet generation apparatus of this embodiment of the present invention adopts generation units formed by vertices and divided edge lines, it is sufficient to consider the synthesis at only one end of an inter-element fillet (the vertex end of a divided edge line). That is, it is sufficient to determine the optimal solution for the closed range within one task unit, without looking at the overall solid shape. Thus, even for a complex solid shape made of many edge lines, it is possible to determine the generation sequence for fillets simply, and to automate the fillet processing.
  • fillet shapes are classified into inter-element fillets, corner shapes, inter-branch interference shapes, and other interference shapes, and forming patterns of corner shapes, it is not only easy to perform processing to determine the synthesis procedure, but also possible to synthesize fillet shapes of consistent accuracy and quality.
  • information for fillet generation conditions and the like is generally held in an edge line element that is the target of fillet generation.
  • edge line elements are replaced by fillets, the information such as fillet generation conditions is lost.
  • the procedure information is stored as attributes (or features) of the generation unit that are elements independent from the intersection shape, even after fillet processing the generation units and procedure information remain as is.
  • the procedure information is stored as attributes (or features) of the generation unit that are elements independent from the intersection shape, even after fillet processing the generation units and procedure information remain as is.

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Abstract

A fillet generation apparatus has an edge line extraction means (S11) for extracting a plurality of edge lines from the solid shape as fillet generation targets, a condition inputting means (10) for prompting a user to input a fillet generation condition with regard to each edge line, a vertex extraction means (S12) for extracting a vertex at which a plurality of edge lines converge, a divided edge line generation means (S15) for generating divided edge lines by dividing each edge line into two, a synthesis procedure determining means (S26) for provisionally generating a fillet at each divided edge line, in accordance with the fillet generation condition, and for determining a synthesis procedure for a fillet at the vertex, based on the correlation between the provisionally generated fillets, with a vertex and a plurality of divided edge lines converging at the vertex taken as a generation unit.

Description

APPARATUS AND METHOD OF GENERATING FILLETS
BACKGROUND OF THE INVENTION
1. Field of the Invention [0001] The present invention relates to a fillet generation apparatus in a
3-dimensional CAD system.
2. Description of the Related Art
[0002] In a 3-dimensionl CAD system, input commands are given of conditions for generating a fillet in units of edges, with the fillet being generated and buried one line at a time. Hereinafter, this will be referred to as "sequential generation."
[0003] In the sequential generation of fillets, however, because the shaped obtained (in particular the corner shape at a vertex at which a plurality of edge lines converge) depends upon the sequence of fillet generation, variation occurs in the final shaped of the part, which is dependent upon operator skill and the sequence of operations performed.
[0004] If the specification of sequence is poor, the fillet itself could be impossible to generate, it could be impossible to obtain the desired corner shape, and a poor quality corner shape can result. Taking the vertex Cl in the solid shape shown in FIG. 10 of the accompany drawings, for example, we see that one convex edge line, Ll, and two concave edge lines, L2 and L3, converge at the vertex Cl. If the convex edge line Ll fillet is generated first and then the fillets of the concave edge lines L2 and L3 are continuously generated, it is possible to generate the fillets around the vertex Cl without a problem. If the fillets around the vertex C2 are to be generated next, however, because the fillet of the concave edge line Ll has already been generated, the fillets of the convex edge lines L4 and L5 must be subsequently generated. However, because the radii of the edge lines L4 and L5 are not equal, the corner shape at the vertex C2 it either impossible to generate or will have poor quality. In such cases, the fillets of the edge lines Ll to L3 must be discarded and the fillets must be generated again, in the sequence of edge line L5 → Ll → L4 → L2 → L3. [0005] As can be understood from the above, in determining the sequence of generating fillets, it is insufficient to consider the area around only one vertex, and it is necessary to understand and analyze the makeup of the edge lines of the overall part. That said, because a single part usually includes dozens or hundreds of edge lines, the determination of the optimal solution for the generation sequence is not easy. Given this situation, in addition to the need for the operator to have a high level of skill and knowledge, problems arise because of the great amount of trial-and-error that is required to arrive at the appropriate generation sequence and generation conditions.
[0006] Given the above, there have been attempts made to simplify and automate fillet generation. For example, the Japanese Patent Application Publication No.
JP-A-2002-304424 proposes a CAD system that displays a plurality of different corner shape patterns for different generation sequences, and allows the operator select a desired pattern from the displayed corner shape patterns.
[0007] The foregoing system, however, still generates fillets in units of edge lines, and does not solve the problem illustrated in FIG. 10. That is, although the operator can give commands in the sequence of vertex C2 and then Cl to perform proper fillet processing, if the vertex Cl command is done first, because the fillet of the edge line Ll is generated first, a problem arises in the generation of the fillet around the vertex C2, the result being that it is necessary to re-perform the generation. [0008] Thus, in the conventional method, the determination of the fillet generation sequence about one vertex might be influenced by the fillet generation sequence about another vertex. As a result, it is extremely difficult to automate fillet processing for a complex solid shape made up of many edge lines.
SUMMARY OF THE INVENTION
[0009] The present invention provides an apparatus and method that automatically executes fillet processing, even for a complex solid shape.
[0010] A fillet generation apparatus according to an aspect of the present invention is a fillet generation apparatus performing fillet processing with respect to a solid shape in a CAD system, having an edge line extraction means for extracting a plurality of edge lines from the solid shape as the targets of fillet generation, a condition inputting means for prompting a user to input a fillet generation conditions with regard to each edge line, a vertex extraction means for extracting a vertex at which a plurality of edge lines converge, a divided edge line generation means for generating divided edge lines by dividing each edge line in two, a synthesis procedure determining means for provisionally generating a fillet at each divided edge line, in accordance with the fillet generation condition, and for determining a synthesis procedure for the fillet at the vertex, based on the correlation between the provisionally generated fillets, with a vertex and a plurality of divided edge lines converging at the vertex taken as a generation unit, and a fillet generation means for executing generation and synthesis of a fillet for each generation unit, in accordance with the fillet generation conditions and synthesis procedure.
[0011] In a conventional apparatus, because fillet synthesis occurs at both ends of an edge line, it is necessary to determine the optimal solution for the fillet generation sequence for the overall solid shape. Given this, it is extremely difficult to determine the fillet generation procedure, which hinders the automation of the fillet processing. In contrast, in this aspect of the present invention it is sufficient to consider only the synthesis at one side (the vertex side) of the fillet, because divided lines are used. That is, it is sufficient to determine the optimal solution over a closed range within one task unit, without considering the overall solid shape. Even for a complex solid shape made up of a large number of edge lines, therefore, it is possible to simply determine the fillet generation sequence and automate the fillet processing. Furthermore, in the aspect of the present invention, because provisional fillets are generated and the correlation between the fillets is checked, problems that are not detectable without actually generating fillets (such as interference between fillets) are solved, and it is possible to generate fillets with high accuracy and high quality.
[0012] In a fillet generation apparatus according to an aspect of the present invention, a pattern storage means for storing a plurality of pattern types, which define a fillet synthesis procedure at a vertex, may be further provided, wherein the synthesis procedure determining means selects from the plurality of pattern types a synthesis procedure for the generation unit.
[0013] By setting up patterns of fillet synthesis procedures beforehand in this manner, not only is the processing to determine the synthesis procedure facilitated, but also it is possible to synthesize fillets of consistent accuracy and quality.
[0014] In this aspect of the present invention, the synthesis procedure determining means may generate the generation unit as an element that is independent from the constituent elements of the solid shape, and cause procedure information that includes at least the generation condition and synthesis procedure to be held in the generation unit.
[0015] In a conventional apparatus, information for fillet generation conditions and the like is generally held in an edge line element that is the target of fillet generation. However, with such a form of holding, when fillet processing is executed and edge line elements are replaced by fillets, the information such as fillet generation conditions is lost. Because of this, if a shape change occurs because of a change in the solid shape after fillet processing, it is necessary to perform troublesome re-inputting of fillet generation conditions and the like.
[0016] In contrast, in the holding method of this aspect of the present invention, because the generation unit and procedure information remain even after fillet processing, even if a shape change occurs, it is only necessary to update the procedure information for the generation units affected by the shape change, thus, accommodation of the change is facilitated.
[0017] Also, because the information required in the execution of fillet processing with respect to one generation unit is summarized in the form of procedure information, handing of the procedure information is facilitated. For example, it also possible to re-use procedure information for another solid shape or generation unit having a similar or the same shape.
[0018] The synthesis procedure determining means may check for interference between provisionally generated fillets for two divided edge lines belonging to one and the same generation unit as the correlation between the provisionally generated fillets.
[0019] Doing this enables optimization, for example, of the fillet generation shape at a vertex for the generation unit and the synthesis range (position of starting interpolation), and enables fillet generation with high accuracy and high quality. [0020] The synthesis procedure determination means may check for interference between provisionally generated fillets for two divided edge lines belonging to different generation units as the correlation between the provisionally generated fillets.
[0021] This is because, for example, in the case of two vertices in mutual proximity, it is sometimes more desirable to determine the fillet synthesis shape and synthesis range as one vertex (one generation unit), as opposed to treating these vertices as separate vertices. This is also because, when fillets belonging to different generation units interfere with one another, there are cases in which the fillet generation sequence between the generation units should be considered.
[0022] The fillet generation means may execute batch fillet generation and synthesis after the fillet synthesis procedure for all generation units included in the solid shape are determined.
[0023] By doing this, automatic fillet generation processing is executed in batch mode after inputting only the fillet generation conditions.
[0024] The present invention may be understood as a fillet generation apparatus having at least a part of the above-described means, or as a CAD system having such a fillet generation apparatus. The present invention may further be understood as a method for fillet generation having at least a part of the above-described processing, a program for implementing the method, or a storage medium in which the program is stored. Each of the above-described means and processing may be mutually combined as possible to implement the present invention.
BRIEF DESCRIPTION OF THE DRAWINGS
[0025] The foregoing and further features and advantages of the invention will become apparent from the following description of example embodiments with reference to the accompanying drawings, wherein like numerals are used to represent like elements, and wherein:
FIG. 1 is a block diagram showing the configuration of a fillet generation apparatus according to the present invention; FIG. 2A is a drawing showing a solid shape (intersection shape) before performing fillet processing;
FIG. 2B is a drawing showing the solid shape after fillet processing;
FIG. 3 is a flowchart showing the flow of procedure information generation processing; FIG. 4 is a drawing showing an example of a corner shape pattern applicable to a corner at which three convex edge lines converge;
FIG. 5 is a drawing showing an example of a generation unit;
FIG. 6A is a drawing showing a surface-to-surface fillet;
FIG. 6B is a drawing showing a surface-to-line fillet; FIG. 6C is a drawing showing a line-to-line fillet;
FIG. 7 is a drawing showing the re-calculation of a fillet shape in line passage region;
FIG. 8 is a drawing showing the fusion at a corner;
FIG. 9 is a drawing showing an example of interference between branches; and FIG. 10 is a drawing showing a problem arising in convention sequential fillet generation.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS [0026] Example embodiments of the present invention are described below, with reference made to accompanying drawings.
[0027] The constitution of the fillet generation apparatus according to an embodiment of the present invention is shown in block diagram form in FIG. 1. The fillet generation apparatus is typically implemented as one function in a 3-dimensionl CAD system that is used to design 3-dimensional structures, such as vehicles. [0028] As shown in FIG. 1, the fillet generation apparatus is generally formed by an input section 10, a procedure information generation section 11, a procedure information storage section 12, a corner shape pattern database 13 and a automatic fillet generation section 14. These functional elements are implemented by reading a program stored in an auxiliary memory apparatus into a main memory apparatus and executing the program using a central processing unit. At the hardware level, the fillet generation apparatus is implemented as a general-purpose computer system.
[0029] FIG. 2A shows a shape of a solid body (hereinafter "intersection shape") before fillet processing. The fillet generation apparatus reads in an intersection shape designed using a CAD system, and automatically executes fillet processing for elements that make up the intersection shape. FIG. 2B shows the solid shape after fillet processing.
[0030] When performing fillet processing, usually only the fillet size (radius value or foot width) generated at edge lines and the method of applying an arc are given as fillet generation conditions via the input section 10. It is extremely difficult to generate all fillets using just this information. This is because, as described above, the shape obtained could differ and it could be impossible to generate a fillet, depending upon the sequence of fillet generation. Another reason is that there are also problems that are not discoverable without actually attempting to generate a fillet (for example, interference between fillets, interference between corners, and interference between a fillet and a corner.
[0031] Given this, the fillet generation apparatus of this embodiment adopts the approach described below, thereby eliminating causes that hinder the automation of fillet generation. [0032] Fillets can be internally classified into four types: "inter-element fillets,"
"corner shapes," "inter-branch interference shapes," and "other interference shapes," and different processing is used to generate each type of fillet.
[0033] An inter-element fillet is a fillet generated between two surface elements having an edge line between the two surface elements. Stated in different terms, an inter-element fillet is a fillet generated at an edge line. A corner shape is a shape that is synthesized (by shading) to smoothly connect inter-element fillets generated at a plurality of edge lines that share a vertex. An inter-branch interference shape is a synthesized shape between inter-element fillets that is not a corner shape. For example, a synthesized shape of inter-element fillets that do not share a vertex is an inter-branch interference shape. Other interference shapes are interference shapes other than inter-branch interference shapes, such as interference between a corner shape and a corner shape, and interference between a corner shape and an inter-element fillet.
[0034] With regard to corner shape patterns, a large number of patterns exist, and a great deal characteristic methodology and knowledge is related to each of the patterns. In conventional systems, the operator made use of the ability of CAD to render points, lines, and surfaces in the generation of a corner shape thought to be optimal. For this reason, variation occurs between operators, and there was no logical guarantee of accuracy. Additionally, even if automatic calculations are performed by a computer, because of an excessive degree of freedom, there was in the same manner the problem of no guarantee of accuracy or surface quality.
[0035] Given the above, the fillet generation apparatus of this embodiment classifies the imagined corner shapes and creates a database of "corner shape patterns" beforehand (the corner shape pattern database 13). Corner shape patterns can be considered to be macros that define the synthesis procedure for an inter-element fillet at a vertex (that is, the generation sequence and synthesis method (interpolation) for an inter-element fillet, and also the resulting corner shape pattern). The corner shape patterns are classified based on such information as the inter-element fillet generation conditions, the number of edge lines converging at a vertex, the combinations of convex and concave edge lines of these edge lines, the angle of intersection between edge lines, and the angle of intersection between surface elements that sandwich an edge line. The fillet generation apparatus selects the optimal pattern from these corner shape patterns, based on the results of analyzing the intersection shape.
[0036] By setting up patterns of the fillet synthesis procedures beforehand in this manner, the processing for determining the synthesis procedure is facilitated, and it is possible to synthesize fillets of consistent accuracy and quality.
[0037] In generating procedure information, of the above-described fillet shapes, shapes of inter-element fillets can generally be determined from the fillet generation conditions. In contrast, corner shapes, inter-branch interference shapes, and other interference shapes cannot be determined using only information obtained from the intersection shape, and cannot be determined without attempting to actually generate inter-element fillets and corner shapes, for example.
[0038] Given this, the procedure information generation section 11 generates procedure information as described below before the processing for automatic generation and burying of fillets.
[0039] FIG. 3 is a flowchart showing the flow of procedure information generation processing.
[0040] At step SlO, the procedure information generation section 11 analyzes the intersection shape model and extracts an "edge line", which is the border line of a surface element. When doing this, the procedure information generation section 11 generates an edge line element that is separate from the intersection shape (refer to FIG. 2A).
[0041] At step SIl, the procedure information generation section 11 prompts the user to input inter-element fillet generation conditions for each extracted edge line. At this stage, because only the size (radius value or foot width) of the fillet and the method of applying an arc are known, these values are input at the fillet generation conditions.
[0042] At step S 12, the procedure information generation section 11 extracts a point (vertex) at which a plurality of edge lines converge (refer to FIG. 2A). [0043] At step S 13, the procedure information generation section 11 makes a provisional determination of a corner shape pattern applicable to the vertex, for each extracted vertex. As described above, a plurality of corner shape pattern types are stored in the corner shape database 13. The procedure information generation section 11 selects the optimal pattern for the vertex from the corner shape pattern database 13, based on the information such as the above-described inter-element fillet generation conditions, the number of edge lines converging at a vertex, the combinations of convex and concave edge lines of these edge lines, the angle of intersection between edge lines, and the angle of intersection between surface elements that sandwich an edge line. However, because it might be not possible to determine whether or not application of a corner shape is possible without actually attempting to apply a fillet, at this stage the determination is a "provisional determination," and the corner shape pattern provisionally determined is referred to as a "provisional pattern."
[0044] FIG. 4 shows an example of a corner shape pattern that can be applied to a vertex at which three convex edge lines converge. In this example, the three patterns of "shading," "priority," and "convergence" are shown, and the corner shape and inter-element fillet synthesis procedures differ for each pattern. The pattern that is selected may be determined from information such as the angle of intersection between edge lines and the radius value of the inter-element fillet. Also, when the size of the inter-element fillet is specified not as a radius value but rather as a foot width, the approximate radius value may be calculated from the angle between surfaces sandwiching the edge line.
[0045] At step S 14, the procedure information generation section 11 determines the inter-element fillet generation range based on the provisional pattern. As can be understood from FIG. 4, the type of corner shape pattern that is selected changes the position of the ending point of the inter-element fillet. "Priority" may be selected to apply an inter-element fillet continuously to two edge lines. Thus, the coordinates of the starting point and ending point of each inter-element fillet are calculated taking the provisional pattern selected at step S 13 into consideration. [0046] At step S15, the procedure information generation section 11 divides each edge lines into two parts to generate divided edge lines. Although the position of the point of division (also called the connection point) may be established anywhere on the edge line, the dividing point in this case will be taken to be at the center of the edge line. [0047] At step S16, the procedure information generation section 11, using the vertex and the plurality of edge lines that converge thereat as a unit of generation, generates "procedure information" for each generation unit. The procedure information is stored as an attribute (or feature) of the generation unit.
[0048] Procedure information is information defining the shape of an inter-element fillet for each divided edge line belonging to the generation unit and the associated synthesis procedure. Specifically, the procedure information is information that summarizes the corner shape pattern, the inter-element fillet generation conditions for the edge lines, and the positions of the dividing points of each of the divided edge lines at a vertex. The inter-element fillet generation conditions, in addition to the size of the inter-element fillet and the method of applying an arc, also include the generation range determined at step S14, the connection condition, and whether or not there is a line passage location. The connection condition and whether there is a line passage location are checked at steps S18 and S19.
[0049] FIG. 5 shows an example of a generation unit. In FIG. 5, • indicates a vertex, and x indicates a connection point. The region surrounded by a broken line is the generation unit. The procedure information generation processing and automatic fillet generation and burying processing are executed for each of these generation units. By adopting such a generation unit, the determination of the generation sequence for inter-element fillets becomes extremely simple. The reason for this is that the fillet generation sequence about the vertex Cl need only consider the relationship of between the divided fillets Ll-I, L2-1, and L3-1, there being absolute no influence from the fillet generation sequence with regard to the area about other vertices, such as the vertices C2, C3, and C4. In this case, the fillet processing by these generation units will be called "branch-divided fillet processing." [0050] At step S 17, the procedure information generation section 11 provisionally generates an inter-element fillet for each divided edge line for each generation unit, in accordance with the fillet generation conditions. By provisionally generating the inter-element fillets, it is possible to check for problems that otherwise cannot be discovered without actually applying fillets (for example, the connection condition of inter-element fillets, existence of a line passage region, interference between inter-element fillets, interference between inter-element fillets and other elements, the angle of intersection of the curved foot line of an inter-element fillet, and corner fusion).
[0051] At step S 18, the procedure information generation section 11 checks the inter-element fillet connection condition. The inter-element fillet connection condition is information representing how and to what element of an intersection shape an inter-element fillet is connected. Specifically, this includes the condition in which an inter-element fillet is connected to a surface element continuous with Cl (known as a surface fillet) and the condition in which a inter-element fillet passes through a line element continuous with CO (known as a line fillet). As shown in FIG. 6 A, an inter-element fillet that is tangent to surface elements on both side continuous with Cl is known as a "surface-to-surface" fillet. In contrast, as shown in FIG. 6B, an inter-element fillet that is tangent to a surface element on one side continuous with Cl and that passes through a line element on another side continuous with CO is known as a "surface-to-line" fillet. As shown in FIG. 6C, an inter-element fillet that passes through line elements on both side continuous with CO is known as a "line-to-line" fillet.
[0052] At step S 19, the procedure information generation section 11 checks for the existence of a line passage region. A line passage region is a region through which an inter-element fillet intersects another line element. As shown in FIG. 7, when the width of a surface element on which surface fillet is generated is very small, the surface fillet might interfere with another line element (edge line). In such cases, additional processing, such as re-calculation of the shape of the fillet in the line passage region, is required. For example, under some circumstances a surface-to-surface fillet in the region is re-generated as a surface-to-line fillet. [0053] In the processing of steps S18 and S19, once the connection condition and existence of a line passage region have been checked, the associated information is added to the fillet generation conditions of the procedure information.
[0054] At step S20, the procedure information generation section 11 checks for the existence of an inter-branch interference shape. Specifically, the procedure information generation section 11 checks for an interference condition between inter-element fillets belonging to different generation units (for example, position and range of interference locations and angle of intersection between inter-element fillets). [0055] At step S21, the procedure information generation section 11 checks for the existence of corner fusion. Corner fusion is the condition in which there is interference between the corner shapes of two generation units. Specifically, a check is made of whether the range of the inter-branch interference shape obtained at step S20 overlaps with a vertex, or with the range of a corner shape established by a provisional pattern. For example, as shown in FIG. 8, in the case, for example, in which the vertices C4 and C5 are in mutual proximity, fusion of corners can occur. If corner fusion is discovered, the edge line L4 that vanishes at the fusion (known as an invalid edge line) is detected, and the procedure information is then updated with the associated information. In subsequent processing, a divided edge line that converges with the vertices C4 and C5 is treated as converging at a single vertex (known as a fused vertex). [0056] At step S22, the procedure information generation section 11 establishes the corner shape pattern based on not only the information used in determining the provisional pattern, but also on the correlation between provisionally generated inter-element fillets. Specifically, the correlation between the inter-element fillets includes information regarding the angle between and point of intersection between curved foot lines of the inter-element fillets, and the inter-branch interference shape and corner conversion obtained at step S20 and step S21. In this manner, by considering not only the information obtained from constituent elements of the intersection shape (for example, edge lines, surfaces), but also the correlation between provisionally generated inter-element fillets, it is possible to determine the optimal corner shape. The procedure information is updated to include the determined corner shape pattern (hereinafter "established pattern").
[0057] At step S23, the procedure information generation section 11 calculates the range of the corner shape at the vertex of each generation unit from the established patterns, and checks for the existence of other interference shapes (that is, interference between corner shapes, and interference between a corner shape and an inter-element fillet). With regard to other interference shapes, after generating and burying one corner shape or inter-element fillet, because another corner shape or inter-element fillet can be generated and buried, it is sufficient at this point to determine only the generation sequence between generation units. The procedure information is then updated to include this information.
[0058] At step S24, the procedure information generation section 11 moves the edge line connection point (dividing point) to a position other than the interference range or corner shape range, based on information obtained at steps S 18 to S21. If the connection point is moved, the procedure information for the corresponding generation unit is updated accordingly.
[0059] At step S25, the procedure information generation section 11 determines the pattern of inter-branch interference shape. For example, if the inter-branch interference shape such as shown in FIG. 9 exists, if an inter-element fillet having a small radius value is generated first, warpage and the like may occur in the ultimately obtained synthesized form of the fillet, resulting in poor surface quality. Given this situation, the generation sequence between two generation units is determined, based on the correlation between interfering inter-element fillets. Specifically, the generation sequence and synthesized shape in the inter-branch interference shape are determined, in accordance with the information regarding the inter-branch interference shape, the combination of convex and concave edge lines and distance between edge lines, and the inter-branch interference shape generation sequence and pattern determining rule that are set beforehand. If complex synthesis processing is not required with regard to inter-branch interference shapes, it is sufficient to determine only the generation sequence between generation units. The procedure information is then updated based on the information determined at this point.
[0060] At step S26, the procedure information generation section 11 references all the procedure information to set the generation sequence between each task unit. However, in the generation sequence between task units, because a problem only occurs when an inter-branch interference shape or other interference shape exists, as described above, the determination of the task sequence is not particularly difficult at this point.
[0061] By going through the foregoing process, the information required for fillet processing is collected in the procedure information. Furthermore, all factors hindering the automation of the fillet processing are eliminated.
[0062] With regard to automatic generation and burying of fillets, after generating procedure information for all generation units included in the intersection shapes, the automatic fillet generation section 14 executes batch generation, synthesis, and burying of fillets for the intersection shape. At this time as well, the processing is performed in task units. By doing this, it is possible to automatically generate fillets (by batch processing).
[0063] The present invention achieves the following effect. In a conventional apparatus, because inter-element fillet synthesis occurs at both ends of an edge line, it is necessary to determine the optimal solution for the fillet generation sequence for the overall solid shape. Consequently, it is extremely difficult to determine the generation sequence of inter-element fillet, and automation of the fillet processing is hindered.
[0064] In contrast, because the fillet generation apparatus of this embodiment of the present invention adopts generation units formed by vertices and divided edge lines, it is sufficient to consider the synthesis at only one end of an inter-element fillet (the vertex end of a divided edge line). That is, it is sufficient to determine the optimal solution for the closed range within one task unit, without looking at the overall solid shape. Thus, even for a complex solid shape made of many edge lines, it is possible to determine the generation sequence for fillets simply, and to automate the fillet processing. [0065] Also, by classifying fillet shapes into inter-element fillets, corner shapes, inter-branch interference shapes, and other interference shapes, and forming patterns of corner shapes, it is not only easy to perform processing to determine the synthesis procedure, but also possible to synthesize fillet shapes of consistent accuracy and quality. [0066] In a conventional CAD system, information for fillet generation conditions and the like is generally held in an edge line element that is the target of fillet generation. However, with such a form of holding, when fillet processing is executed and edge line elements are replaced by fillets, the information such as fillet generation conditions is lost. Thus, if a shape change occurs because of a change in the solid shape after fillet processing, it is necessary to re-input the fillet generation conditions and the like, which may be troublesome. Also, in a parametric CAD system in which there is a high affinity with change history, geometry, and phase, if the phase of the intersection shape changes by a change in shape, it is not possible to reproduce the fillets, making it necessary to reperform the task.
[0067] In contrast to the above, in this embodiment because the procedure information is stored as attributes (or features) of the generation unit that are elements independent from the intersection shape, even after fillet processing the generation units and procedure information remain as is. Thus, even if a shape change occurs, because it is only necessary to update the procedure information for the generation units affected by the shape change, accommodation of the change is facilitated.
[0068] Also, because the information required in the execution of fillet processing with respect to one generation unit is summarized in the form of procedure information, handing of the procedure information is facilitated. For example, it also possible to re-use procedure information for another solid shape or generation unit having a similar or the same shape.
[0069] While the invention has been described with reference to an example embodiment thereof, it is to be understood that the invention is not limited to the described embodiment or constructions. To the contrary, the invention is intended to cover various modifications and equivalent arrangements. In addition, while the various elements of the example embodiment are shown in various combinations and configuration, other combinations and configurations, including more, fewer, or only a single element, are also within the spirit and scope of the invention.

Claims

1. A fillet generation apparatus in a CAD system that performs fillet processing with respect to a solid shape, comprising: edge line extraction means for extracting a plurality of edge lines from the solid shape as fillet generation targets; condition inputting means for prompting a user to input a fillet generation condition for each edge line of the plurality of edge lines; vertex extraction means for extracting a vertex at which the plurality of edge lines converges; divided edge line generation means for generating divided edge lines by dividing each edge line of the plurality of edge lines in two; synthesis procedure determining means for provisionally generating a fillet at each divided edge line, in accordance with the fillet generation condition, and for determining a synthesis procedure for the fillet at the vertex, based on the correlation between the provisionally generated fillets, with the vertex and a plurality of the divided edge lines converging at the vertex taken as a generation unit; and fillet generation means for executing generation and synthesis of the fillet for each generation unit, in accordance with the fillet generation conditions and synthesis procedure.
2. The fillet generation apparatus according to claim 1, further comprising: pattern storage means for storing a plurality of types of patterns that define a synthesis procedure of fillet at a vertex, wherein the synthesis procedure determining means selects from the plurality of types of patterns a synthesis procedure for application to the generation unit.
3. The fillet generation apparatus according to claim 1 or 2, wherein the synthesis procedure determining means generates the generation unit as an element that is independent from the constituent elements of the solid shape, and causes procedure information that includes at least the generation condition and synthesis procedure to be held in the generation unit.
4. The fillet generation apparatus according to any one of claims 1 to 3, wherein the synthesis procedure determining means checks for interference between provisionally generated fillets for two divided edge lines belonging to one and the same generation unit as the correlation between the provisionally generated fillets.
5. The fillet generation apparatus according to any one of claims 1 to 4, wherein the synthesis procedure determining means checks interference between provisionally generated fillets for two divided edge lines belonging to different generation units as the correlation between the provisionally generated fillets.
6. The fillet generation apparatus according to any one of claims 1 to 5, wherein the fillet generation means executes batch fillet generation and synthesis after the fillet synthesis procedure for all generation units included in the solid shape are determined.
7. A method for fillet generation in a CAD system that performs fillet processing with respect to a solid shape, comprising: extracting a plurality of edge lines from the solid shape as fillet generation targets; prompting a user to input a fillet generation condition with regard to each edge line; extracting a vertex at which the plurality of edge lines converge; generating divided edge lines by dividing each edge line of the plurality of edge lines in two; provisionally generating a fillet at each divided edge line, in accordance with the fillet generation condition, and determining a synthesis procedure for a fillet at the vertex, based on the correlation between the provisionally generated fillets, with the vertex and the plurality of divided edge lines converging at the vertex taken as a generation unit; and executing generation and synthesis of the fillet for each generation unit, in accordance with the fillet generation conditions and synthesis procedure.
8. A program for executing fillet processing with respect to a solid shape in a CAD system, comprising causing a computer to execute: a process to extract of a plurality of edge lines from the solid shape as fillet generation targets; a process to prompt a user to input a fillet generation condition with regard to each edge line; a process to extract a vertex at which the plurality of edge lines converge; a process to generate a divided edge lines by dividing each edge line of the plurality of edge lines in two; a process to provisionally generate a fillet at each divided edge line, in accordance with the fillet generation condition, and to determine a synthesis procedure for a fillet at the vertex, based on the correlation between the provisionally generated fillets, with the vertex and the plurality of divided edge lines converging at the vertex taken as a generation unit; and a process to generate and synthesize the fillet for each generation unit, in accordance with the fillet generation conditions and synthesis procedure.
9. A computer-readable storage medium storing the program according to claim 8.
10. A fillet generation apparatus in a CAD system that performs fillet processing with respect to a solid shape, comprising: an edge line extraction portion that extracts a plurality of edge lines from the solid shape as fillet generation targets; a condition inputting portion that prompts a user to input a fillet generation condition for each edge line of the plurality of edge lines; a vertex extraction portion that extracts a vertex at which the plurality of edge lines converges; a divided edge line generation portion that generates divided edge lines by dividing each edge line of the plurality of edge lines in two; a synthesis procedure determining portion that provisionally generates a fillet at each divided edge line, in accordance with the fillet generation condition, and determines a synthesis procedure for the fillet at the vertex, based on the correlation between the provisionally generated fillets, with the vertex and a plurality of the divided edge lines converging at the vertex taken as a generation unit; and a fillet generation portion that executes generation and synthesis of the fillet for each generation unit, in accordance with the fillet generation conditions and synthesis procedure.
PCT/IB2007/002086 2006-07-26 2007-07-23 Apparatus and method of generating fillets WO2008012640A1 (en)

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