曲面数模 (Surface Mathematical Model)

舰艇、汽车、航空、航天的许多产品都具有光滑外形，生产中要大量模型、模线、样板、模具、夹具等，占用空间大、时间长、协调精度差。随着计算机技术的发展，曲面造型已数字化，替代了传统方法。本文介绍切曲线/切曲面（TC/TS）造型方法的曲线曲面数学公式、计算程序、以及和市场常用软件数据格式转换程序。

* 光滑曲面造型-切曲线和切曲面

一个TS曲面片由9个特征网格点定义，曲面片间一阶导数连续。TS曲面片方程为

式中J1(u)，J2(u)，J3(u)是沿u向的3个基函数；J1(w)，J2(w)，J3(w) 是沿w向的3个基函数;V是沿u向和w向特征网格的9个顶奌。

* 利用重顶点技术切曲面造型

* 长空2号（CK-2）超音速无人机切曲面造型

* 切曲线切曲面 Fortran程序

*切曲线/切曲面造型数据格式转换程序

character*12 select

print *,' NOTICE ! < Author: Yisui Jiang>'

print *,' ------- < Machine Vision Lab. U. of M.>'

print *,' This program is used to convert a data file into a'

print *,'.DXF graphics interchange file of AUTOCAD. Formats of'

print *,'2D plane curve, 3D space curve and 3D surface mesh'

print *,'data files are as follows :'

print *,' '

print *,' 1) 2D plane curve '

print *,' x(1) y(1) '

print *,' x(2) y(2) '

print *,' | | '

print *,' x(n) y(n) '

print *,' 2) 3D space curve '

print *,' x(1) y(1) z(1) '

print *,' x(2) y(2) z(2) '

print *,' | | | '

print *,' x(n) y(n) z(n) '

print *,' 3) 3D space surface mesh '

print *,' n m '

print *,' x(1,1) y(1,1) z(1,1) '

print *,' x(1,2) y(1,2) z(1,2) '

print *,' | | | '

print *,' x(m,n) y(m,n) z(m,n) '

pause ' <PRESS ANY KEY TO CONTINUE !>'

print *,' '

print *,'*****************************************'

print *,'* *'

print *,'* MENU *'

print *,'* *'

print *,'* 1) 2D plane curve data *'

print *,'* *'

print *,'* 2) 3D space curve data *'

print *,'* *'

print *,'* 3) 3D space surface mesh *'

print *,'* *'

print *,'* Select 1,2 or 3 *'

print *,'* *'

print *,'*****************************************'

do 5 i=1,10

print *,' '

5 continue

read (*,'(a)') select

if (select.eq.'1') then

call a2dc

elseif (select.eq.'2') then

call a3dc

elseif (select.eq.'3') then

call a3ds

endif

stop

end

subroutine a2dc

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c c

c Program name: dxf2d.for c

c Purpose: This program is used to convert data file into a graphics c

c interchange file .dxf of AUTOCAD. c

c Format of data file: c

c x(1),y(1) /* coordinates of points of curve */ c

c | | c

c x(n),y(n) c

c Date: Nov. 20, 1991. c

c Author: Yisui Jiang, Machine Vision Lab. University of Manitoba. c

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

character*12 name,name1

Print *,' Enter 2D data file name :'

read (*,'(a)') name

print *,' Enter .DXF file name :'

read (*,'(a)') name1

open (6,file=name1)

call sta2c

open (5,file=name)

read (5,*) x,y

x0=x

y0=y

5 read (5,*,err=999) x,y

call lin2c(x0,y0,x,y)

x0=x

y0=y

goto 5

999 call eof2c

close (5)

close (6)

return

end

subroutine sta2c

write (6,'(a)') '0'

write (6,'(a)') 'SECTION'

write (6,'(a)') '2'

write (6,'(a)') 'ENTITIES'

return

end

subroutine eof2c

write (6,'(a)') '0'

write (6,'(a)') 'ENDSEC'

write (6,'(a)') '0'

write (6,'(a)') 'EOF'

return

end

subroutine lin2c(x0,y0,x1,y1)

write (6,'(a)') '0'

write (6,'(a)') 'LINE'

write (6,'(a)') '8'

write (6,'(a)') '0'

write (6,'(a)') '10'

write (6,*) x0

write (6,'(a)') '20'

write (6,*) y0

write (6,'(a)') '11'

write (6,*) x1

write (6,'(a)') '21'

write (6,*) y1

return

end

subroutine a3dc

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c c

c Name of program: DXF3DC.for c

c This program is used to convert a space curve data file into c

c a graphics interchange file .DXF of AUTOCAD. c

c Format of data file: c

c x(1) y(1) z(1) /* coordinates of space points */ c

c | c

c x(n) y(n) z(n) c

c Date: Dec. 12, 1991 c

c Author: Yisui Jiang, Machine Vision Lab. University of Manitoba. c

c cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

character*12 name,name1

print *,'Enter 3D curve data file name:'

read (*,'(a)') name

print *,'Enter .DXF file name:'

read (*,'(a)') name1

open(5,file=name)

open (6,file=name1)

call sta3c

call pol3c

5 read(5,*,end=10) x,y,z

call vetx3c(x,y,z)

goto 5

10 call end3c

close (5)

close (6)

return

end

subroutine sta3c

write(6,'(a)') ' 0'

write(6,'(a)') 'SECTION'

write(6,'(a)') ' 2'

write(6,'(a)') 'ENTITIES'

return

end

subroutine end3c

write(6,'(a)') ' 0'

write(6,'(a)') 'SEQEND'

write(6,'(a)') ' 8'

write(6,'(a)') '0'

write(6,'(a)') ' 0'

write(6,'(a)') 'ENDSEC'

write(6,'(a)') ' 0'

write(6,'(a)') 'EOF'

return

end

subroutine pol3c

write(6,'(a)') ' 0'

write(6,'(a)') 'POLYLINE'

write(6,'(a)') ' 8'

write(6,'(a)') '0'

write(6,'(a)') '66'

write(6,'(a)') ' 1'

write(6,'(a)') '10'

write(6,'(a)') '0.0'

write(6,'(a)') '20'

write(6,'(a)') '0.0'

write(6,'(a)') '30'

write(6,'(a)') '0.0'

write(6,'(a)') '70'

write(6,'(a)') ' 8'

return

end

subroutine vetx3c(x,y,z)

write(6,'(a)') ' 0'

write(6,'(a)') 'VERTEX'

write(6,'(a)') ' 8'

write(6,'(a)') '0'

write(6,'(a)') '10'

write(6,*) x

write(6,'(a)') '20'

write(6,*) y

write(6,'(a)') '30'

write(6,*) z

write(6,'(a)') '70'

write(6,'(a)') ' 32'

return

end

subroutine a3ds

cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

c c

c Name of program: DXF3DS.for c

c Purpose of the program: c

c This program is used to convert multi-surface data c

c files into graphics interchange file .DXF of AUTOCAD. c

c Format of data file c

c n /* the size of points in direction first read in. */ c

c m /* the size of points in direction secondly read in. */ c

c x(1,1) y(1,1) z(1,1) c

c x(1,2) y(1,2) z(1,2) c

c | | | c

c x(m,n) y(m,n) z(m,n) c

c Date: Dec. 1, 1991 c

c Author: Yisui Jiang, Machine Vision Lab. University of Manitoba c

c c

ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

character*12 name,name1,anser

dimension x(200,200),y(200,200),z(200,200)

print *,'Enter .DXF file name:'

read (*,'(a)') name1

open (5,file=name1)

1 print *,'Enter surface data file name:'

read(*,'(a)') name

open(7,file=name)

read(7,*) n,m

do 5 i=0,m-1

do 5 j=0,n-1

read(7,*) x(i,j),y(i,j),z(i,j)

5 continue

close(7)

call sta3s

call pol3s(m,n)

do 20 i=0,m-1

do 20 j=0,n-1

call vetx3s(x(i,j),y(i,j),z(i,j))

20 continue

call eof3s

print *,'Is there any other data file to enter (y/n) ?'

read (*,'(a)') anser

if (anser.eq.'y') then

goto 1

else

endif

call end3s

close(5)

return

end

subroutine sta3s

write(5,'(a)')' 0'

write(5,'(a)')'SECTION'

write(5,'(a)')' 2'

write(5,'(a)')'ENTITIES'

return

end

subroutine eof3s

write(5,'(a)')' 0'

write(5,'(a)')'SEQEND'

write(5,'(a)')' 0'

write(5,'(a)')'ENDSEC'

return

end

subroutine end3s

write(5,'(a)')' 0'

write(5,'(a)')'EOF'

return

end

subroutine poit3s(x,y,z)

write(5,'(a)')' 0'

write(5,'(a)')'POINT'

write(5,'(a)')' 8'

write(5,'(a)')'POINTS'

write(5,'(a)')' 10'

write(5,*) x

write(5,'(a)')' 20'

write(5,*) y

write(5,'(a)')' 30'

write(5,*) z

return

end

subroutine pol3s(m,n)

write(5,'(a)')' 0'

write(5,'(a)')'POLYLINE'

write(5,'(a)')' 8'

write(5,'(a)')'SMOOTH-1'

write(5,'(a)')' 66'

write(5,'(a)')' 1'

write(5,'(a)')' 10'

write(5,'(a)')'0.0'

write(5,'(a)')' 20'

write(5,'(a)')'0.0'

write(5,'(a)')' 30'

write(5,'(a)')'0.0'

write(5,'(a)')' 70'

write(5,'(a)')' 16'

write(5,'(a)')' 71'

write(5,'(i6)') m

write(5,'(a)')' 72'

write(5,'(i6)') n

return

end

subroutine vetx3s(x,y,z)

write(5,'(a)')' 0'

write(5,'(a)')'VERTEX'

write(5,'(a)')' 8'

write(5,'(a)')'SMOOTH-1'

write(5,'(a)')' 10'

write(5,*) x

write(5,'(a)')' 20'

write(5,*) y

write(5,'(a)')' 30'

write(5,*) z

write(5,'(a)')' 70'

write(5,'(a)')' 64'

return

end

* TC Curves and TS Surfaces and Their Applications in CAD/CAM

Yisui Jiang and R.P.S. Han

* 3D MEASUREMENT AND GEOMETRY MODELLING FOR CURFACED SURFACE

Yisui Jiang, Craig Muller, Hui Wang, Doug Strong

jajemasehere

博联社：Jiangyisui（871348）

《美国航天》

编译：江怡穗 (Yisui Jiang)
电子信箱:yisuijiang@163.com
网站:jsdy2k.jimdo.com

当今，在航天领域，美国无疑是世界的排头兵，中国是最强有力的新兴和挑战力量。了解美国航天事业的发展和决策背景，对中国航天事业爱好者，参与者和决策者都很重要。经过几年的翻译和整理，出版了《太空探索和开发》，欢迎交流指正。

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