A recently added feature of the SSV2 and CASPA systems is the ability to make use of surface geometry definitions which are not part of the native geometry of the system. The only requirements are that the surfaces are parametric with rectangular patches and that the user is able to provide supporting software in the form of a parametric evaluator capable of evaluating points and derivatives at any point on the surface with parametric value (u,v). The data defining the surface will have been previously created as a data file and must conform to a simple basic format which is meaningful to the parametric evaluator. Once a non-native surface has been defined in this way it can be used in machining and other operations in exactly the same way as any of the native sculptured surfaces of the system. An important advantage of this approach is that surfaces from an external definition system can be machined exactly by the APT system with no approximation errors as occurs in most forms of inter-system surface data transfer.

11.1 Software and Data Requirements

Each new non-native surface type requires two specific routines, one to interpret the data and evaluate points and derivatives on the surface, the other to modify the data when an APT transformation matrix is applied. These subroutines called the evaluator and the transformator must be compiled and linked with the sculptured surfaces system. In the IBM version of the system dynamic loading of the evaluators is possible, with the VAX version a seperate re-linking of the system and evaluators is necessary. A data file for each surface referenced must be available at run time, this has a form similar to that of an LDA and will normally have been created by a program external to the sculptured surfaces system. Parts of the format for these data files is precisely defined and are a system requirement, other parts are dependent upon the surface type and will only be meaningful to the appropriate evaluator. The paragraphs below give the subroutine and data file specifications in detail. Section 11.2 contains an extended example of the creation and use of a non-native surface. Section 11.3 contains details of the VDA-FS Non-native Interface.

11.1.1 Evaluator Specification

This subroutine must have a name ENAME which begins with an E, the remainder of the name 'NAME' being unique for the particular surface type. Each evaluator must have the same parameter list ENAME(U,V,GEO,RESULT,MODE) U,V should be declared as double precision and on input contain the (U,V) parameter values which define the evaluation point P on the selected patch. GEO is a one dimensional double precision array, declared as GEO(*) or more properly as the precise dimension of the patch geometry data, which at run time will contain the patch geometry data as read from the data file, or as modified by TNAME. RESULT(4,8) is a double precision array which returns the coordinates of the point P and the values of the derivatives at this point. The detailed contents of this array on exit from ENAME should be: RESULT(1-4,1) Homogeneous coordinates X,Y,Z,W of the point P. RESULT(1-4,2) Partial derivatives dX/dU, dY/dU, dZ/dU, dW/dU at P. RESULT(1-4,3) Partial derivatives dX/dV, dY/dV etc at P. RESULT(1-4,4) 2nd Partial derivatives d2X/dU2, d2Y/dU2 etc at P. RESULT(1-4,5) 2nd mixed partial derivatives d2X/dUdV,d2Y/dUdV etc at P. RESULT(1-4,6) 2nd Partial derivatives d2X/dV2, d2Y/dV2 etc at P. RESULT(1-3,7) Surface normal dr/du x dr/dv at P. RESULT(1-3,8) Surface unit normal at P. RESULT(4,8) 1.0 if unit normal available, 0.0 otherwise. MODE should be declared as INTEGER, this is an input argument, if MODE=0 on input only the point coordinates are evaluated, if MODE=1 points and derivatives and normals are evaluated. Note: The information contained in RESULT is sufficient for most applications. For example it provides the ability to compute the shortest distance from a point to the surface or to find the curvature of the surface at P.

11.1.2 Transformation Specification

This subroutine must have a name TNAME beginning with T in which 'NAME' is the same as in ENAME. The parameter list is: TNAME(TRANS,GEO) TRANS(4,3) should be declared as a DOUBLE PRECISION (4,3) two dimensional array. On input it contains an APT transformation matrix (See section 3.5) GEO Is a one dimensional DOUBLE PRECISION array declared as in the evaluator subroutine. On input GEO contains the patch geometry data as read from the data file. On exit this is overwritten with the geometry data as modified by the translation and rotation defined by the transformation matrix TRANS.

11.1.3 Data File Specification

Each data file is normally produced by an external formatter routine FNAME where 'NAME' is shared with ENAME and TNAME for this particular surface type. In simple cases, as in section 11.2 FNAME will actually define the surface and generate the data, in other cases it is a routine which re-formats data which has been produced by another geometric definition system. The data file produced must have the same general format as an APT surface and consists of a surface header block, a header block and geometry block for each patch and, finally, a block of topology data. The layout of the header blocks and the topology block are rigidly specified by the sculptured surfaces system but the patch geometry block layouts and interpretation are completely dependent upon surface type. The surface header block consists of precisely 10 DOUBLE PRECISION numbers, these are: SHEAD(1) = APT RECORD NO. (Assigned by system) SHEAD(2) = Total length of geometry data SHEAD(3) = Total length of topology data SHEAD(4) = Number of patches SHEAD(5) = 2.0 SHEAD(6) = 1.0 SHEAD(7) = Sign of surface normal (1.0 or -1.0) SHEAD(8) = Total length of data SHEAD(9) = Number of splines SHEAD(10) = Number of cross splines The surface header block is followed, patch by patch, by the patch header blocks. For each patch this block consists of a fixed length header block of 6 DOUBLE PRECISION numbers. These must be PHEAD(1) = Index of start of patch geometry data in file. PHEAD(2) = 0.0 PHEAD(3) = 0.0 PHEAD(4) = 0.0 PHEAD(5) = Coded version of surface type 'NAME'. PHEAD(6) = Index of start of patch topology data. The set of patch header blocks is followed patch by patch by the geometric data for each patch. This can be of any length provided it can be correctly interpreted by the evaluator and transformator routines. The detailed contents of this geometric data is not specified in any way and will depend upon the type of non-native surface being used. After the last block of geometric data comes the topology table. For each patch this table takes the same format as a standard surface canonical form and consists of 4 consecutive real numbers which give in turn the number of the patch adjacent to each boundary. The boundaries are ordered as v=0, u=0, u=1, v=1, 0.0 is stored as the adjacent patch number for any patch boundary coinciding with the edge of the surface.

11.2 Torus Example

A simple example of non-native geometry definition and evaluation has been included with the SSV2 system release tape. The relevant subroutines are program FTORUS, which is an interactive routine external to the system and enables the user to define a parametric surface which forms part of a torus (or doughnut). The data created is then evaluated by the routine ETORUS and, if necessary can be rotated or translated by the routine TTORUS. ETORUS and TTORUS are linked and loaded with the SSV2 system. A torus of major radius R and minor radius r has a parametric vector equation: r(u,v) = c + rsinua + cosv(R + rcosu)b - sinv(R + rcosu)d where c is the position vector of the centre, a is a unit vector in the direction of the axis of symmetry, b, d are mutually perpendicular unit vectors in the plane perpendicular to a. The program FTORUS constructs a parametric surface of this type which consists of precisely 4 patches, two in the u-direction and two in the v-direction. The user is able to specify interactively the basic dimensions, position and orientation of the surface and how much of the torus is to be represented. FTORUS has two subsidiary routines DEFTOR and PUNTOR which are responsible respectively for the actual geometric definition and for storing the data generated in APT4 LDA format to APTLIB. When running FTORUS the user receives a number of prompts for input data, these together with possible responses are illustrated in section 11.2.1 .

11.2.1 Creation of a Torus

Before running the program FTORUS the user should create a sub-directory ›.APTLIB!, if it does not already exist. In the example below screen prompts are shown in upper case, user responses are enclosed in › ! and explanatory notes are in lower case text. The initial command RUN FTORUS produces the informative response THIS PROGRAM SETS UP THE CANONICAL FORM OF A TORUS AS 4 PATCHES AND CREATES AN APT4 LDA EXTERNAL FILE IN APTLIB INPUT MAJOR AND MINOR RADII OF TORUS ›30.0,10.0! The user defines the major radius as 30, the minor as 10. AXIS OF SYMMETRY VECTOR? ›0.0,0.0,1.0! The OZ axis has been chosen as the direction of the axis of symmetry. Any 3 vector components are permissible, the user need not supply a unit vector. CENTRE OF TORUS? ›0.0,0.0,0.0! The origin has been selected here as the centre C, any 3 coordinates are permissible. REF POINT (START OF PARAMETERISATION, I.E. U=0, V=0)? ›1.0,0.0,0.0! The user is asked to supply a point P such that CP is in the direction of the edge of the toroidal section and is normal to the axis. If P is incorrectly defined the system projects CP onto the central plane of the torus in order to find a reference point. In this case OX has been chosen as the direction of the reference point. UMAX, VMAX (IN RADIANS)? NOTE: U-MINOR RADIUS DIRECTION V-MAJOR RADIUS DIRECTION ›3.1416,3.1416! UMAX and VMAX define the total extent of the surface. For a complete torus UMAX=VMAX=2p. In this case half a torus is being defined with a semi-circular section. After definition those parameters are re-scaled so that the final surface has parametric range 0 < u < 2, 0 < v < 2. APT SURFACE NAME (MAX 6 CHARACTERS)? ›TOR1! The user has chosen TOR1 as his name for this particular surface. The data will be defined in APTLIB file TOR1.LDA .

11.2.2 Use of Non Native Geometry

Once the non-native torus geometry has been created it can be accessed and used by an APT part program. This usage can include transforming it to create new surfaces, use as drive part or check surface in machining, or data extraction via the INTOF facility described in Chapter 9. An example of such a part program is: PARTNO/'TESTOR' REMARK/'TOR1 HAS BEEN PREVIOUSLY CREATED BY FTORUS' PRINT/SSTEST,ON READ/1,TOR1 M1=MATRIX/TRANSL,10,20,30 TOR2=SSURF/COMBIN,TOR1,TRFORM,M1 M2=MATRIX/XYROT,90 TOR3=SSURF/COMBIN,TOR1,TRFORM,M2 P1=POINT/INTOF,TOR1,PARAM,0.5,0.5,1 P2=POINT/INTOF,TOR2,PARAM,0.5,0.5,1 P3=POINT/INTOF,TOR3,PARAM,0.5,0.5,1 V3=VECTOR/INTOF,TOR3,PARAM,0.5,0.5,1,NORMAL,UNIT PRINT/3,ALL FINI In this part program the original torus TOR1 as defined in 11.2.1 is read in from APTLIB. This is then translated to take the centre to point(10,20,30) in order to create TOR2. TOR3 is created by rotating TOR1 through 90 degrees about the Z axis which is in fact its axis of symmetry. P1, P2, P3 are then defined repectively as the points with parameter u=0.5, v=0.5 (i.e. the mid point) of the first patch of each surface. V3 is the unit tangent vector dr/du at P3. The results should be: P1=(26.213,-26.213,7.071) P2=(36.213,-6.213,37.071) P3=(26.213,26.213,7.071) V3=(-0.5,-0.5,0.7071) Note that P2 is the result of displacing P1 by (10,20,30) and that P3 can be obtained by rotating P1 through 90 degrees about OZ.

11.3 VDA-FS Non-Native Interface

VDA-FS is a German National (DIN) Standard originally developed by the German motor manufacturers for the transfer of surface data. the basic file format is compatible with IGES and consists of 80 character ASCII records with sequence numbers permitted in columns 73-80. The file always commences with a file or part name followed by a human readable file header and is terminated by <name>=END where <name> is the file or part name. Entities in the file are either: POINT PSET (sequence of points) MDI (master dimension or point, vector sequence) CURVE (piecewise parametric curve) or SURF (patched bi=parametric surface) Comment lines are permissable at any point in the file and always start with $$ . Surfaces in the file may be of arbitrary degree and are communicated via their explicit polynominal coefficients. All multi-patch surfaces must have a simple rectangular topology but patches may differ in their degrees. All surfaces and other entities are named with a maximum of 8 characters for the name.

11.3.1 VDA-FS Formatter, FVDAFS

The VDA-FS Formatter, FVDAFS and its associated subroutines, which are initiated by the RUN FVDAFS command, will read a standard VDA-FS file and format all surface data in a form suitable for the evaluator EVDAFS and the transformator TVDAFS. In reading the VDA-FS file all comments and all POINT,PSET,MDI and CURVE entities are ignored. When running FVDAFS the user has the option of creating either a single file containing all surfaces on the VDA-FS file or of creating a seperate file for each surface. For use with the SSV2 system a seperate file must be used for each surface but CASPA permits more than one surface per file. As far as possible the VDA-FS surface name is used for the corresponding APT surface but where the original name exceeds 6 characters the user is prompted for a new surface name. A similar prompt appears if the surface name is duplicated. Where the option of seperate files is chosen the file names will be surface_name.LDA for each surface on the VDA tape. A further difference in requirements between SSV2 and CASPA when using FVDAFS is that for SSV2 all files created must be single surface files of type .LDA and contained in subdirectory ›.APTLIB! whereas for CASPA any file name and subdirectory can be chosen. After the LDA files have been created by FVDAFS they can be read into CASPA by the instruction READ/LDA,'Filename'›,list of surface names! ›,ALL! (Default value ALL) or into SSV2 by the instruction READ/1,surface_name

11.3.2 VDA-FS Evaluator and Transformator

For LDA files produced by FVDAFS the corresponding evaluator and transformator are EVDAFS and TVDAFS. These are capable of an exact evaluation and coordinate transformation of any parametric surfaces obtained from VDA-FS files subject to a maximum degree of 24 in either u or v. In practice this limitation is sufficient for all known surface design systems with VDA-FS pre-processors.