USOO5774696A United States Patent (19) 11 Patent Number: 5,774,696 Akiyama (45) Date of Patent: Jun. 30, 1998
54) TRIANGLE AND TETRAHEDRON MESH Shigyo et al., “TRIMEDES: A triangular Mesh Device GENERATION METHOD Simulator Linked w/ Topography/Process Simulation”, Trans of IEICE, vol. E71 No. 10, Oct. 88, pp. 992–999. 75 Inventor: Yutaka Akiyama, Tokyo, Japan Machek et al., “A Novel Finite-Element approach to Device Modeling", IEEE Trans on Elec. Dev., vol. ED-30 73 Assignee: NEC Corporation, Tokyo, Japan No. 9, Sep. 1983, pp. 1083–1092. Kójima et al., “Dual Mesh Approach for Semiconductor 21 Appl. No.: 654,190 Device Simulator", IEEE Trans on Magnetics, vol. 25 No. 4, 22 Filed: May 28, 1996 Jul. 1989, pp. 2953-2955. Chou et al., “Tangential Vector Finite Elements for Semi 30 Foreign Application Priority Data conductor Device Simulation', IEEE Trans on CAD, vol. 10 May 29, 1995 JP Japan ...... 7-13O372 No. 9, Sep. 1991, pp. 1193–1200. (51) Int. Cl...... G06F 17/10 (List continued on next page.) 52 U.S. Cl...... 395/500; 395/123; 364/578 58 Field of Search ...... 364/488, 489, Primary Examiner Kevin J. Teska 364/490, 491, 578; 395/500, 920, 123 Assistant Examiner Tyrone V. Walker Attorney, Agent, or Firm-Ostrolenk, Faber, Gerb & Soffen, 56) References Cited LLP U.S. PATENT DOCUMENTS 57 ABSTRACT 4,912,664 3/1990 Weiss et al...... 395/141 A method for eliminating interSections between a Substance 4,933,889 6/1990 Meshkat et al...... 364/578 boundary and triangles (or tetrahedra) of a triangle mesh (or 4.941,114 7/1990 Shigyo et al...... 395/123 tetrahedron mesh) which satisfies a condition of Delaunay 5,214,752 5/1993 Meshkat et al. ... 395/123 partition and is used for a finite difference method. First, 5,315,537 5/1994 Blacker ...... 364/578 triangles interSecting with the Substance boundary are 5,442,569 8/1995 Osano ...... 364/578 5,553,009 9/1996 Meshkat et al...... 364/578 Searched out. One of the vertices of any of the triangles is 5,553,206 9/1996 Meshkat ...... 395/123 Selected as a moving node P and the moving node is 5,579,249 11/1996 Edwards ...... 364/578 projected to the Substance boundary to obtain a projected 5,617,322 4/1997 Yokota ...... 364/578 point P. Processing object triangles which commonly have the moving node and peripheral triangles which are posi FOREIGN PATENT DOCUMENTS tioned around the processing object triangles are listed. 1-106266 4/1989 Japan. Then, checking to detect whether or not the projected point 4-268674 9/1992 Japan. is included in a circumscribed circle about any of the 4-309183 10/1992 Japan. peripheral triangles is performed. When the projected point 7-219977 8/1995 Japan. is included in a circumscribed circle, a node is added at the 7-319947 12/1995 Japan. projected point and triangles are produced using the node. But when the projected point is included in none of circum OTHER PUBLICATIONS Scribed circles, all of the processing object triangles are C.S. Rafferty, et al., “Iterative Methods in Semiconductor deleted, the moving node is shifted to the projected point, Device Simulation', IEEE Transactions on Electron and triangles in a region from which the processing object Devices, vol. ED-32, No. 10, Oct. 1985, pp. 2018-2027. triangles have been removed are reconstructed by using a M.S. Mock, et al., Tetrahadral Elements and the Scharfet maximum included angle method. ter-Gummel Method, Proceeding of the NASECODE IV, 1985, pp. 36–47. 7 Claims, 8 Drawing Sheets
O star ) SEARCH FOR TRAnsle INTERSECTING WITH -- SUBSTANCE BOUNARY Project weRTExp of NTER SECTING TRIANSLE ON SUB STANCE BOUNDARY PolNT P') -- LSTRANGESPROCESSING OBJECT TRANSES).NODE P HAVING - LisT TRANGEs creRipheral TRIANGLES: ARQND --> PROCESSING 08JEC TRIANGLES FINRY cussibois-YESINGLJCE IN CR ANY PERIPHERAL - TREANGLE? s
DELETE PRocessing l---56 OBJECT TRIANGLES MOVE NODE P to P -- 57 53 Reconstruct Transes As NCOE AT PRKJECTED USING MAXIMUM LINCLUDEC): POIN P' AN GEMERATE ANGE METHOD ANGLES
59 - END y 5,774,696 Page 2
OTHER PUBLICATIONS Tanimoto et al., “Discretization Error in MOSFET Device Yuan et al., “A Mesh Generator for Tetrahedral Elements Simulation', IEEE Trans on CAD, vol. 11 No. 7, Jul. 1992, Using Delaone Triangulation', IEEE Trans on Magnetics, pp. 921–925. vol. 29 No. 2, Mar. 1993, pp. 1906–1909. Kumashiro et al., “A Triangular Mesh Generation Method Cianpolini et al., “Efficient 3-D Simulation of Complex Suitable for the Analysis of Complex MOS Device Struc- Structures", IEEE Trans on CAD, vol. 10 No. 9, Sep.1991, tures', NUPAD V, pp. 167–170, 1994. pp. 1141-1149. U.S. Patent Jun. 30, 1998 Sheet 1 of 8 5,774,696
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KXXXXXXXXXX,AAAAAAA2SN/VN F.G. 1 C (PRIOR ART) U.S. Patent Jun. 30, 1998 Sheet 2 of 8 5,774,696
FIG. 2 (PRIOR ART)
(PRIOR ART) U.S. Patent Jun. 30, 1998 Sheet 3 of 8 5,774,696
FG. 4A (PRIOR ART)
U.S. Patent Jun. 30, 1998 Sheet 4 of 8 5,774,696
START
SEARCH FOR TRIANGLE 91 (TRTRAHEDRON) INTERSECTING WITH SUBSTANCE BOUNDARY
PROJECT VERTEX P OF INTER 92 SECTING TRIANGLE (TRTRAHEDRON) ON SUBSTANCE BOUNDARY
93 ADD NODE AT PROJECTED PONT P'
RE-CONSTRUCT TRIANGLES 94 (RTRAHEDRA) USING METHOD OF MOCK F.G. 5 (PRIOR ART)
F.G. 6B (PRIOR ART) U.S. Patent Jun. 30, 1998 Sheet 5 of 8 5,774,696
START
SEARCH FOR TRIANGLE INTERSECTING WITH 51 SUBSTANCE BOUNDARY
PROJECT VERTEX P OF INTER SECTING TRIANGLE ON SUB- 52 STANCE BOUNDARY (POINT P')
LIST TRANGLES (PROCESSING OBJECT TRIANGLES) HAVING 53 NODE P
LIST TRIANGLES (PERIPHERAL TRIANGLES) AROUND 54 PROCESSING OBJECT TRIANGLES
PONT P'
INCLUDED N CR CUMSCRIBEO CRCLE ABOUT YES ANY PERIPHERAL TRIANGLE 2 NO DELETE PROCESSING OBJECT TRIANGLES
MOVE NODE P TO P'
RE-CONSTRUCT TRIANGLES ADD NODE AT PROJECTED USNG MAXIMUM INCLUDED POINT P' AND GENERATE ANGLE METHOD TRIANGLES
END FG. 7 59 U.S. Patent Jun. 30, 1998 Sheet 6 of 8 5,774, 696
7%XX B VNKOY A.FG. 8D FIG. 8BM2, A7 P' /NN/ (3 4&AAAA "YNX P' CY V FG. 8E
U.S. Patent Jun. 30, 1998 Sheet 8 of 8 5,774,696
START
SEARCH FOR TRTRAHEDRON INTERSECTING WITH 61 SUBSANCE BOUNDARY
PROJECT VERTEX P OF INTER SECTING TETRAHEDRON ON SUB- 62 STANCE BOUNDARY (POINT P')
LIST TERAHEDRA (PROCESSING OBJECT TETRA- 63 HEDRA) HAVING NODE P
LIST TETRAHEDRA (PERIPHERAL TETRAHEDRA) AROUND PRO- 64 CESSING OBJECT TETRAHEDRA
POINT P'
RE-CONSTRUCT TETRAHEDRA ADD NODE AT PROJECTED USING MENMUM CIRCUM POINT P' AND GENERATE SCRIBED SPHERE METHOD TETRAHEDRA
END FG 1 O 69 5,774,696 1 2 TRIANGLE AND TETRAHEDRON MESH 2 is connected to a plurality of grid points positioned GENERATION METHOD there around by branches (sides of triangles) indicated by Solid lines in FIG. 2, and the current J is defined on each BACKGROUND OF THE INVENTION: branch. Further, the current J between grid points is inte grated with respect to a croSS Section (indicated by a broken 1. Field of the Invention: line) of a current path covered by each branch. The cross This invention relates to a method of generating a triangle Section of the current path is represented by line Segments mesh or a tetrahedron mesh in a simulation which is based each interconnecting the circumcenters (represented by on a finite difference method or a like method. Small blank triangles) of individual two triangles positioned 2. Description of the Prior Art: 1O on the opposite sides of the current path as a common edge. A device Simulator for a Semiconductor device calculates Accordingly, in order to perform a device Simulation physical quantities in the inside of a Semiconductor device correctly, it is an essential condition that the circumcenters using a computer to calculate electric characteristics Such as of adjacent triangles do not interSect with each other. This is a terminal current and a threshold Voltage of a transistor. because, if the circumcenters of adjacent triangles interSect 15 with each other, then the croSS Section of the current path When it is attempted to optimize transistors in a Semicon with respect to which the current is integrated becomes ductor device represented by an LSI (large Scale integration) negative. Where the condition that the circumcenters of So that the Semiconductor device may exhibit its highest adjacent triangles do not interSect with each other is not electric characteristics, use of the device Simulator can satisfied, as seen in FIG. 3 (cited from the paper of C. S. Significantly reduce both the cost and the term comparing Rafferty et al. mentioned hereinabove), a result of the with an actual production of a prototype of an LSI. Further, analysis yields a physically impossible Voltage Spike at Since the device Simulator calculates physical quantities in the inside of a Semiconductor transistor, it can be investi which the quasifermi potential is 50 V. FIG. 3 is a view gated in what manner electrons or holes behave in the inside showing a result of a simulation by which a distribution of of the Semiconductor. Accordingly, the device Simulator can the quasi-Fermi potential of a device is detected. In order to 25 Satisfy the condition that the circumcenters of adjacent be used to make clear, for example, a cause of an impact triangles do not interSect with each other, the Delaunay ionization phenomenon which becomes an issue with regard partition wherein a circumscribed circle about a triangle to a fine MOSFET (metal-oxide-semiconductor field effect does not have a vertex of another triangle in the inside transistor). thereof should be assured. In order to obtain physical quantities in the inside of a By the way, as integration of LSIS proceeds and the device Semiconductor transistor, the device Simulator Solves a Pois Size decreases, a narrow channel effect and like effects of a Son's equation which represents a relationship between the MOSFET become progressively apparent, and it is neces potential and the carrier concentration or a partial differen tial equation of an current continuity equation or a like Sary to execute a device Simulation taking also the depthwise equation. As a method of Solving a partial differential shape of a transistor into consideration. In order to Subdivide 35 an arbitrary shape accurately in Such a three-dimensional equation, there is a method wherein a Semiconductor device problem, using a tetrahedron as a dividing element, a is divided into Small regions and a partial differential equa tion is discretized and calculated as disclosed in Ryo Dan three-dimensional Semiconductor device Shape should be ed., “Process Device Simulation Technology', Sangyo represented as a Set of tetrahedral elements. In this instance, Tosho, pp.90-122. current is defined on an edge of a tetrahedron, and the croSS 40 Section of a current path is represented by a face defined by On the other hand, where an analysis of a Semiconductor line Segments interconnecting the circumcenters of tetrahe device having a complicated Structure Such as a trench dra which commonly have the edge. Also in a three Structure is performed using a device Simulator, in order to dimensional problem, Similarly as in the two-dimensional represent the shape or the Structure of the Semiconductor problem described above, the division into tetrahedra must device accurately, the device shape is Subdivided using a 45 be the Delaunay partition wherein a circumscribed sphere of triangle to discretize it as disclosed in C. S. Rafferty et al., the tetrahedron does not have a vertex of another tetrahedron "Iterative methods in semiconductor device simulation', in the inside thereof as disclosed in M. S. Mock, “Tetrahe IEEE Trans. On Electron Devices, Vol. ED-32, No. 10, dral elements and the Scharfetter-Gummel method’, Pro pp.2018-2027, Oct. 1985. ceeding of the NASECODE IV, pp.36–47, 1985. FIGS. 1A, 1B and 1C are cited from the paper of C. S. 50 A method of Delaunay partition of a shape to be analyzed Rafferty et al. mentioned above and Show a detailed example with tetrahedral elements is disclosed in the document of M. of a manner in which a trench isolated CMOS S. Mock mentioned above. Here, for simplified description, (Complementary MOS) device is discretized using triangu the Delaunay partition of a two dimensional region with lar elements. A Semiconductor device having Such a Sec triangular elements is described. The method by Mock adds tional shape as shown in FIG. 1A is represented as Such a Set 55 a point on a Substance boundary or a new node required to of triangular elements as shown in FIG. 1B. Further, in an improve the accuracy in calculation one by one into a area around a boundary between a player and p+ layer or a triangle Set already Delaunay-partitioned. The method is boundary between a player and an in layer, the Semicon illustrated in FIGS. 4A, 4B and 4.C. ductor device is divided into finer or Smaller triangular When to add a new node P' to a triangle set already elements as seen in FIG. 1C. Since the shape of the semi 60 Delaunay-partitioned, as shown in FIG. 4A, a triangle which conductor device is represented as a Set of triangular includes the new node P' in the inside of a circumscribed elements, the trench Structure can be represented accurately. circle thereabout is searched for. In FIG. 4A, each broken FIG. 2 shows, in an enlarged Scale, part of the Set of line indicates a circumscribed circle, and a Slanting line triangular elements obtained in this manner. In the Solution region indicates triangles Searched out. Thereafter, the of a partial differential equation based on a finite difference 65 Searched out triangles are deleted as Seen in FIG. 4B, and method which uses triangular elements, each grid point sides (indicated by broken lines in FIG. 4B) of an outermost (vertex of a triangle) indicated by a solid circle mark in FIG. hull defined by the deleted triangles are found out. Then, the 5,774,696 3 4 sides of the outermost hull and the new node P' are con Application No. Hei7-319947 (JP, A, 7-319947). FIG. 5 is nected to each other to produce new triangles as shown in a flow chart illustrating a procedure of the method disclosed FIG. 4C. In FIG. 4C, the triangles newly produced are in JP, A, 7-319947. According to the method, a triangle (or indicated by Slanting lines. Here, also the Set of triangles tetrahedron) which intersects with a shape boundary is produced newly Satisfies a condition of Delaunay partition. searched for first (step 91), and a vertex P of the intersecting While the two-dimensional Delaunay partition based on the triangle (tetrahedron) is projected on the shape boundary to method of Mock is described above, also the three obtain a projected point P' (step 92). A node is added at the dimensional Delaunay partition is executed in a similar procedure. projected point P' (Step 93), and triangles (tetrahedra) are In Japanese Patent Laid-Open Application No. Hei reproduced using the method of Mock described above (step 7-219977 (JP, A, 7-219977), a method of deleting a node 94). from within a region for which the Delaunay partition has been performed, while the condition of Delaunay partition (Method 2) remains Satisfied is disclosed. According to the method, in Japanese Patent Laid-Open Application No. Hei 4-309183 order to delete a node in a two-dimensional plane, triangles (JP, A, 4-309183) discloses a method wherein intersections are re-constructed using a maximum included angle method. 15 are eliminated by addition of a node Similarly as in the In particular, a node (mesh point) to be deleted and mesh method of JP, A, 7-319947. However, a node to be added is edges (sides of triangles) connecting to the node are deleted not determined by projection on a shape boundary. and, from among Sides of a polygon which remains around the deleted node, a Side which has not been processed as yet (Method 3) is selected. Thereafter, a vertex of the polygon with which Japanese Patent Laid-Open Application No. Hei 1-106226 the angle of the Side included thereat exhibits a maximum value and by which a triangle can be defined together with (JP, A, 1-106266) discloses a technique wherein it is checked the Side is Selected and a new triangle is produced with the to detect whether or not a tetrahedron and a shape boundary Selected Side and the Selected vertex. The Sequence of (shape Surface) intersect with each other and, where they operations just described is performed for all sides of the 25 interSect with each other, a vertex of the tetrahedron is polygon. In order to delete a node in a three-dimensional moved to a position on the shape Surface to eliminate the Space, tetrahedra are re-constructed using a minimum cir intersection. FIGS. 6A and 6B are diagrammatic views cumscribed Sphere method. In particular, a node and mesh illustrating the method. In those figures, an ellipse shown edges (sides of tetrahedra) connecting to the node are represents a shape Surface. AS shown in FIG. 6A, a vertex of deleted first. Since a polyhedron whose faces are triangles a tetrahedron (which is shown in triangular shape in FIG. remains around the deleted node, from among the triangles 6A) which intersects with a shape boundary is moved to a of the faces of the polyhedron, a triangle which has not been position on the Solid shape to eliminate the intersection. processed as yet is Selected, and a vertex of the polyhedron with which the circumscribed sphere about the tetrahedron (Method 4) formed by the triangle and the vertex of the polyhedron Japanese Patent Laid-Open Application No. Hei 4-268674 exhibits the Smallest size and by which a tetrahedron can be 35 defined together with the face is Selected. Then, a new (JP, A, 4-268674) discloses elimination of an intersection not tetrahedron is produced with the Selected triangle and the of a tetrahedron but of a hexahedron (Square grid) by Selected vertex. The Sequence of operations just described is movement of a node. Where the position of a node of a grid performed for all faces, that is, for all triangles, of the is moved by optimization, an interSection between the polyhedron. 40 Square grid and a shape boundary is created. However, in JP, By the way, while, in the method which involves the A, 4-268674, the intersection between the shape and the grid Delaunay partition described above, triangles (or tetrahedra) is eliminated by correcting the node moved using a shape are updated by addition or deletion of a node, it Sometimes function to a position on the Solid shape. occurs that a triangle (or tetrahedron) and a Substance shape However, the conventional methods described above boundary interSect with each other. Here, the Substance 45 which eliminate an interSection between a triangle or tetra shape boundary Signifies, with regard to a Semiconductor hedron and a Solid shape have the following problems. In device, an interface between a wiring layer and a Semicon particular, with the method 1 and the method 2, although the ductor layer, an interface between a Semiconductor layer and Delaunay partition is assured, Since an interSection is elimi an insulator, a pnjunction plane in a Semiconductor layer, or nated adding a node, there is a problem that an increase in an interface between regions which are different in impurity 50 number of nodes and an increase in analysis time cannot be concentration. In a Semiconductor device Simulator, Since avoided. Meanwhile, with the method 3 and the method 4, the shape of a wiring layer, insulator layer and Semiconduc even though the Delaunay partition is assured before elimi tor layer is represented as a Set of triangles for an analysis nation of an interSection, Since a node is moved upon in two dimensions or as a set of tetrahedra for an analysis in three dimensions, if a triangle (or tetrahedron) is produced elimination of an interSection, the shape of a triangle acroSS a Substance shape boundary plane, then it becomes 55 (tetrahedron) changes, resulting in another problem that the impossible to represent the shapes of different portions Delaunay partition cannot necessarily be assured after elimi accurately, resulting in failure to perform an accurate analy nation of an interSection. Sis. Therefore, newly produced triangles (or tetrahedra) are SUMMARY OF THE INVENTION checked to detect whether or not they interSect with any Substance shape boundary, and where Some triangle (or 60 It is an object of the present invention to provide a mesh tetrahedron) intersects with a Substance shape boundary, the generation method by which, upon elimination of an inter interSection must be eliminated. The following methods are Section between a shape boundary and a triangle (or available to eliminate an interSection. tetrahedron), the Delaunay partition is assured after elimi nation of an interSection by Suppressing out an increase in (Method 1) 65 number of nodes. The inventor of the present invention proposed an inter The object of the present invention is achieved by a Section elimination method in Japanese Patent Laid-Open triangle mesh generation method wherein, from a triangle 5,774,696 S 6 mesh which Satisfies a condition of Delaunay partition, moving node is not shifted but the projected point is added interSections between triangles constructing the triangle as a node. Consequently, the Delaunay partition is assured mesh and a Substance boundary are eliminated, the method and an increase in number of nodes can be Suppressed to a comprising Steps of Searching for triangles which are necessary minimum level. included in the triangle mesh and interSect with the Sub stance boundary; Selecting one of Vertices of any of the Generally, where a Substance boundary and a triangle triangles interSecting with the Substance boundary as a (tetrahedron) intersect each other, the number of Such inter moving node, the one of Vertices being not on the Substance Secting triangles (tetrahedra) is a plural number, and also the boundary and projecting the moving node on the Substance number of Vertices which can be Selected as a moving node boundary to obtain a projected point, listing triangles which is a plural number. Since it is considered that the probability commonly have the moving node as processing object that the Delaunay partition is maintained when a moving triangles and listing triangles which are positioned around node is moved to a Substance boundary increases as the the processing object triangles as peripheral triangles, and distance between the moving node and the Substance bound ary decreases, in order to prevent an increase in number of checking to detect whether or not the projected point is nodes, it is effective to Select, as a moving node, that one of included in a circumscribed circle about any of the periph 15 eral triangles and, when the projected point is included in a vertices of triangles (tetrahedra) intersecting with the Sub circumscribed circle, adding a node at the projected point stance boundary which exhibits the smallest (but not zero) and producing triangles using the node, but when the pro distance from the Substance boundary. jected point is not included in a circumscribed circle about Application of the present invention significantly reduces any one of the peripheral triangles, deleting all of the the calculation time of the finite difference method. processing object triangles, shifting the moving node to the The above and other objects, features, and advantages of projected point and re-constructing triangles in a region, the present invention will become apparent from the fol from which the processing object triangles have been lowing description based on the accompanying drawings removed, using a maximum included angle method. which illustrate an example of a preferred embodiment of The object of the present invention is achieved also by a 25 the present invention. tetrahedron mesh generation method wherein, from a tetra hedron mesh which Satisfies a condition of Delaunay BRIEF DESCRIPTION OF THE DRAWINGS partition, interSections between tetrahedra constructing the FIG. 1A is a Sectional view of an example of a Semicon tetrahedron mesh and a Substance boundary are eliminated, ductor device; the method comprising Steps of Searching for tetrahedra FIGS. 1B and 1C are diagrammatic views showing an which are included in the tetrahedron mesh and interSect example of a triangular mesh produced from the Semicon with the Substance boundary; Selecting one of vertices of any ductor device shown in FIG. 1A; of the tetrahedra interSecting with the Substance boundary as FIG. 2 is a diagrammatic view illustrating electric cur a moving node, the one of Vertices being not on the rents of a triangle mesh and an integration region thereof; Substance boundary, and projecting the moving node on the 35 Substance boundary to obtain a projected point, listing FIG. 3 is a diagrammatic view showing an example of a tetrahedra which commonly have the moving node as pro result of a simulation and illustrating that an interSection of cessing object tetrahedra and listing tetrahedra which are circumcenters causes an inappropriate simulation result; positioned around the processing object tetrahedra as periph FIGS. 4A, 4B and 4C are diagrammatic views illustrating eral tetrahedra, and checking to detect whether or not the 40 a method of the Delaunay partition in two dimensions, projected point is included in a circumscribed sphere about FIG. 5 is a flow chart illustrating an example of a any of the peripheral tetrahedra and, when the projected conventional technique for eliminating an interSection point is included in a circumscribed Sphere, adding a node between a triangle and a Substance boundary; at the projected point and producing tetrahedra using the FIGS. 6A and 6B are diagrammatic views illustrating node, but when the projected point is not included in a 45 another conventional technique for eliminating an interSec circumscribed Sphere about any one of the peripheral tion between a triangle and a Substance boundary; tetrahedra, deleting all of the processing object tetrahedra, FIG. 7 is a flow chart illustrating processing by a triangle shifting the moving node to the projected point and generation method of a first embodiment of the present re-constructing tetrahedra in a region, from which the pro invention; cessing object tetrahedra have been removed, using a mini 50 mum circumscribed circle method. FIGS. 8A, 8B, 8C, 8D and 8E are diagrammatic views In the present invention, preferably, one of Vertices of illustrating a concrete example of generation of a triangle those triangles (tetrahedra) intersecting with the Substance mesh in the first embodiment; boundary which is spaced by the Smallest distance from the FIG. 9 is a diagrammatic view showing a structure of data to be used for elimination of an interSection with a Substance Substance boundary is Selected as the moving node. 55 According to the present invention, one of Vertices of boundary; and Some triangle (tetrahedron) intersecting with a Substance FIG. 10 is a flow chart illustrating processing by a boundary is Selected as a moving node under the condition tetrahedron generation method of a Second embodiment of that the vertex is not on the Substance boundary, and it is the present invention. discriminated whether or not the condition of the Delaunay 60 partition is still Satisfied if the moving node is shifted to a DESCRIPTION OF THE PREFERRED projected point obtained by projecting the moving node on EMBODIMENTS the Substance boundary. Then, when the condition of the <