1.矢量

矢量是一个对方向的数学描述方式，矢量用I、J、K来定义它的方向，I、J、K分别代表了该矢 量与X、Y、Z轴空间夹角的余弦值，取值范围是从1到-1，且满足条件I×I+J×J+K×K=1。 例如：

 X正向矢量的I、J、K为1，0，0 X负向矢量的I、J、K为-1，0，0 Y正向矢量的I、J、K为0，1，0 Y负向矢量的I、J、K为0，-1，0 Z正向矢量的I、J、K为0，0，1 Z负向矢量的I、J、K为0，0，-1 

讯享网
在三维直角坐标系中的点，除了有位置外，还要有方向—矢量

图中点P天量方向I,J.K，分别为与X,Y,Z三根轴夹角的余弦值

I=COS（α）
J=COS（β）
K=COS（γ）

最终点P在三维直角坐标系中表示为：P=(X,Y,Z,I,J,K)

X,Y,Z代表位置，I,J,K代表方向

1.1平面元素/空间元素

平面元素：可以用两个坐标来描述的元素。如点、直线、圆、椭圆、方槽和圆槽。

空间元素：必须用三个坐标来描述的元素。如平面、圆柱、圆锥和球。

1.2点元素/矢量元素

点元素包括点、圆、椭圆、球、方槽、圆槽、圆环，只表达元素的尺寸和空间位置。

矢量元素包括直线、平面、圆柱和圆锥，既要表达元素的空间方向同时也可能表达元素的尺寸和空间位置。

矢量元素矢量方向的规定：向实体外的平面法线方向规定为该平面的矢量方向；圆锥方向从锥底指向锥顶；圆柱方向从第一层截面圆指向最后一层截面圆；直线方向从第一个测点指向最后一个测点。

2.矢量的应用场合

2.1标准球的方向——球杆指向球心的方向

在测头校验时，可用工具列表中需要设置标准球的支撑矢量。对于常规垂直向上的标准球，IJK则分别要设置成001。当用到星型针时，有时需要把标准球装到侧边（多方向底座），几个不同方向对应的IJK分别是：X+ 1、0、0；Y+ 0、1、0；X+ -1、0、0；Y- 0、-1、0。对于NETDMIS可以选择不用手动输入具体数值!

2.2零件坐标系的建立：

找正——把一个三维特征的矢量作为零件坐标系的第一轴方向

旋转——把一个特征的矢量作为零件坐标系的第二轴方向

2.3自动特征的IJK——特征的矢量方向

手动测量点的补偿是单轴补偿的。比如说，测针往Z-方向打点，最终点的坐标值是通过获取红宝石中心的坐标再加上测针的补偿半径，从而得到准确的Z坐标。如果测针斜着打点，就会根据测针的反弹反向与哪个坐标轴的夹角最小，则会沿着该坐标轴进行半径的补偿。所以我们在测斜面和曲面时，则要求导入数模，通过软件的自动矢量点获取模型的理论矢量，从而在测量时根据该矢量（IJK）进行三轴的同时补偿。虽然该补偿方式不是最完美的，但也是目前最合适的补偿方式。

讯享网F(点3)=FEAT/POINT,CART,111.8012,40.7703,0,0,0,1.00000000 CALL/EXTERN,DMIS,M(NETDMIS_AUTO_POINT_1007),AUTOFIGURE,F(点3),POINT,CART,DME,111.8012,40.7703,0,0,0,1.00000000,$ 0,0,0,FALSE,FALSE,FALSE,10.0000,"CUR",TRUE,FALSE,0,FA(VECBLD),10.0000,2.5000,3,XYPLAN,"","EXT1","EXT2",$ "EXT3",ENDCAL F(点4)=FEAT/POINT,CART,208.0548,102.4514,-6.9929,0,-0.0,0. CALL/EXTERN,DMIS,M(NETDMIS_AUTO_POINT_1007),AUTOFIGURE,F(点4),POINT,CART,DME,208.0548,102.4514,-6.9929,$ 0,-0.0,0.,0,0,0,FALSE,FALSE,FALSE,10.0000,"CUR",TRUE,FALSE,0,FA(VECBLD),10.0000,2.5000,$ 3,XYPLAN,"","EXT1","EXT2","EXT3",ENDCAL 

$$ NET_DMIS_ $$ MADE IN DE 2023-2-9 12:59:58 INCLUD/DMIS,'NET_DMIS_DEFINES.DMI' INCLUD/DMIS,'VARDEFINE' DMESW/COMAND,'PROBE_VAL/INIT' UNITS/MM,ANGDEC D(MACHINE)=DATSET/MCS DMESW/COMAND,'COORDSYS/ALIGN' WKPLAN/XYPLAN PRCOMP/ON PRCOMP/ON FEDRAT/POSVEL,MMPS,300.0000 ACLRAT/POSACL,MMPSS,100.0000 FEDRAT/MESVEL,MMPS,20.0000 ACLRAT/MESACL,MMPSS,100.0000 SNSET/RETRCT,1.0000 SNSET/SEARCH,5.0000 SNSET/APPRCH,1.0000 DMESW/COMAND,'SNSET/MANRETRCT,2' DMESW/COMAND,'REPORT/CLEAR' MODE/MAN DID(D2L40)=DEVICE/STOR,'D2L40' OPEN/DID(D2L40),SNS S(A0B0)=SNSDEF/PROBE,INDEX,POL,0.0,0.0,0.0000,0.0000,1.0000,189.6500,2.0000 SNSLCT/SA(A0B0) DMESW/COMAND,'SNSET/MANRETRCT,2.0000' GEOALG/PLANE,LSTSQR F(平面1)=FEAT/PLANE,CART,76.0287,192.8169,0,0,0,1.00000000 MEAS/PLANE,F(平面1),3 PTMEAS/CART,7.5414,47.7680,0,0,0,1.00000000 PTMEAS/CART,8.1091,263.3654,0,0,0,1.00000000 PTMEAS/CART,212.4357,267.3174,0,0,0,1.00000000 ENDMES SNSET/DEPTH,0 DMESW/COMAND,'CONST/SET_PROJ_VEC,FA(平面1),1' F(直线1)=FEAT/LINE,UNBND,CART,34.3779,0,-3.3053,0.,0,-0.00,0,-1.00000000,0 MEAS/LINE,F(直线1),2 PTMEAS/CART,34.3779,0,-3.4570,0,-1.00000000,0 PTMEAS/CART,150.4931,0,-3.4570,0,-1.00000000,0 ENDMES F(点1)=FEAT/POINT,CART,0,23.5265,-6.5252,-1.00000000,0,0 MEAS/POINT,COMP,DME,F(点1),1 PTMEAS/CART,0,23.5265,-6.5252,-1.00000000,0,0 ENDMES DATDEF/F(平面1),DAT(A_平面1) D(坐标系1_S)=DATSET/DAT(A_平面1),ZDIR D(坐标系1_R)=ROTATE/ZAXIS,FA(直线1),XDIR D(坐标系1_T)=TRANS/ZORIG,FA(平面1) D(坐标系1_T)=TRANS/YORIG,FA(直线1) D(坐标系1_T)=TRANS/XORIG,FA(点1) DMESW/COMAND,'COORDSYS/CAD=PART' SAVE/DA(坐标系1) MODE/AUTO,PROG,MAN SNSET/RETRCT,1.0000 SNSET/APPRCH,1.0000 DMESW/COMAND,'CLEARP/ZDIR,16.3500,ZDIR,16.3500,ON' F(平面2)=FEAT/PLANE,CART,115.4396,164.0308,0,0,0,1.00000000 CALL/EXTERN,DMIS,M(NETDMIS_AUTO_PLANEPOINTS_1006),AUTOFIGURE,F(平面2),PLANE,CART,LSTSQR,115.4396,164.0308,$ 0,0,0,1.00000000,FALSE,FALSE,FALSE,10.0000,"CUR",TRUE,FALSE,POINTS,'15,7.2047,41.9974,0,0,0,1.00000000,$ 4.8898,132.0474,0,0,0,1.00000000,4.1513,196.1882,0,0,0,1.00000000,3.2635,268.1064,0,0,0,1.00000000,97.9666,$ 267.2889,0,0,0,1.00000000,117.9679,299.7366,0,0,0,1.00000000,180.4967,301.2118,0,0,0,1.00000000,218.8148,$ 301.9191,0,0,0,1.00000000,250.7712,255.6899,0,0,0,1.00000000,130.4285,199.4061,0,0,0,1.00000000,129.0168,$ 106.3228,0,0,0,1.00000000,244.2170,41.5178,0,0,0,1.00000000,160.6365,37.3103,0,0,0,1.00000000,146.2703,$ 4.5891,0,0,0,1.00000000,35.4984,7.1308,0,0,0,1.00000000',TOUCH,0.3000,XYPLAN F(直线2)=FEAT/LINE,BND,CART,23.1238,0,-10.0000,226.3325,0,-10.0000,0,-1.00000000,0 CALL/EXTERN,DMIS,M(NETDMIS_AUTO_LINE_1007),AUTOFIGURE,F(直线2),LINE_BND,CART,23.1238,0,-10.0000,1.00000000,$ 0,0,203.2087,FALSE,FALSE,FALSE,10.0000,"CUR",TRUE,FALSE,0,-1.00000000,0,4,0,0,0,TOUCH,0.3000,XYPLAN,0,$ 0,LINE,"","","EXT1","EXT2","EXT3",ENDCAL F(直线3)=FEAT/LINE,BND,CART,0,23.9537,-10.0000,0,268.3748,-10.0000,-1.00000000,0,0 CALL/EXTERN,DMIS,M(NETDMIS_AUTO_LINE_1007),AUTOFIGURE,F(直线3),LINE_BND,CART,0,23.9537,-10.0000,0,1.00000000,$ 0,244.4211,FALSE,FALSE,FALSE,10.0000,"CUR",TRUE,FALSE,-1.00000000,0,0,4,0,0,0,TOUCH,0.3000,XYPLAN,0,0,$ LINE,"","","EXT1","EXT2","EXT3",ENDCAL F(点2)=FEAT/POINT,CART,0,0,-10.0000,0,0,-1.00000000 CONST/POINT,F(点2),INTOF,FA(直线2),FA(直线3) DATDEF/F(平面2),DAT(A_平面2) D(坐标系2_S)=DATSET/DAT(A_平面2),ZDIR D(坐标系2_R)=ROTATE/ZAXIS,FA(直线2),XDIR D(坐标系2_T)=TRANS/XORIG,FA(点2),YORIG,FA(点2) D(坐标系2_T)=TRANS/ZORIG,FA(平面2) SAVE/DA(坐标系2) F(圆1)=FEAT/CIRCLE,INNER,CART,57.1500,81.2800,0,0,0,1.00000000,50.8000 CALL/EXTERN,DMIS,M(NETDMIS_AUTO_CIRCLE_1007),AUTOFIGURE,F(圆1),CIRCLE,INNER,CART,LSTSQR,57.1500,81.2800,$ 0,0,0,1.00000000,50.8000,0.,-0.,0,5,-3.0000,0,0,0,0,360.0000,TOUCH,CIRCLE,0.3000,0,FALSE,$ FALSE,FALSE,10.0000,"CUR",TRUE,FALSE,0,FA(VECBLD),10.0000,2.5000,3,XYPLAN,"",'7,0,0,0,0,3.0000,0,10',$ '0,1,0,5.0000',"EXT3",ENDCAL DMESW/COMAND,'MOVE/CLEARPLANE' F(点3)=FEAT/POINT,CART,111.8012,40.7703,0,0,0,1.00000000 CALL/EXTERN,DMIS,M(NETDMIS_AUTO_POINT_1007),AUTOFIGURE,F(点3),POINT,CART,DME,111.8012,40.7703,0,0,0,1.00000000,$ 0,0,0,FALSE,FALSE,FALSE,10.0000,"CUR",TRUE,FALSE,0,FA(VECBLD),10.0000,2.5000,3,XYPLAN,"","EXT1","EXT2",$ "EXT3",ENDCAL F(点4)=FEAT/POINT,CART,208.0548,102.4514,-6.9929,0,-0.0,0. CALL/EXTERN,DMIS,M(NETDMIS_AUTO_POINT_1007),AUTOFIGURE,F(点4),POINT,CART,DME,208.0548,102.4514,-6.9929,$ 0,-0.0,0.,0,0,0,FALSE,FALSE,FALSE,10.0000,"CUR",TRUE,FALSE,0,FA(VECBLD),10.0000,2.5000,$ 3,XYPLAN,"","EXT1","EXT2","EXT3",ENDCAL