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minor change to compound mapping
1 <?xml version="1.0" encoding="UTF-8"?>
2 <vo-dml:model xmlns:vo-dml="http://www.ivoa.net/xml/VODML/v1"
3 xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
4 xsi:schemaLocation="http://www.ivoa.net/xml/VODML/v1 file:///data/vao/staff/mcd/docs/models/dm/vo-dml/xsd/vo-dml-v1.xsd">
5 <name>trans</name>
6 <description>The transform model defines a set of operations which can be used to construct expressions mapping coordinates and other objects defined in one coordinate space to a different coordinate space.
7
8 For many applications, this mapping should work in either direction. One option would be to define entirely separate mapping sequences to describe these two transformations. However, this approach is bulky and requires more maintanence as any change to one object would require equivalent changes be made to the other. Since many operations have a natural inverse, a safer, more compact and flexible approach is to use a single object to describe both transformations. With this approach, a change to the one transform automatically applies to both directions.
9
10 This model defines operations with sufficient information to define both forward and inverse transformations wherever possible. For cases where a natural inverse cannot be defined, we provide a means of explicitly assigning separate operation specifications for the forward and inverse directions.
11
12 In this model, we describe two flavors of operations:
13 * Arithmatic operations performing a particular action
14 * Workflow operations to build and link complex operations
15 - combine operations in parallel or series
16 - combine operations for explicit forward and inverse flow
17 - manage axis sets between steps
18 </description>
19 <uri/>
20 <title>WCS Transform Model</title>
21 <author>Arnold Rots, Mark Cresitello-Dittmar, David Berry, Steven Crawford, Nadia Dencheva, Perry Greenfield, Tim Jenness, Omar Laurino, Stuart Mumford, Erik Tollerud</author>
22 <version>1.0</version>
23 <previousVersion>0.0</previousVersion>
24 <lastModified>2019-09-16T08:14:30</lastModified>
25 <import>
26 <name>ivoa</name>
27 <url>http://www.ivoa.net/xml/VODML/20180519/IVOA-v1.0.vo-dml.xml</url>
28 <documentationURL>http://volute.g-vo.org/svn/trunk/projects/dm/vo-dml/models/ivoa/vo-dml/IVOA-v1.0.html</documentationURL>
29 </import>
30 <enumeration>
31 <vodml-id>InterpolationMethod</vodml-id>
32 <name>InterpolationMethod</name>
33 <description>Enumeration of interpolation methods to control the interpretation of data between known points in operations such as Lookup.</description>
34 <literal>
35 <vodml-id>InterpolationMethod.None</vodml-id>
36 <name>None</name>
37 <description>No interpolation method specified, interpretation between points is undefined.</description>
38 </literal>
39 <literal>
40 <vodml-id>InterpolationMethod.Nearest</vodml-id>
41 <name>Nearest</name>
42 <description>Nearest neighbor is selected</description>
43 </literal>
44 <literal>
45 <vodml-id>InterpolationMethod.Linear</vodml-id>
46 <name>Linear</name>
47 <description>Assume a linear progression between points.</description>
48 </literal>
49 <literal>
50 <vodml-id>InterpolationMethod.Spline</vodml-id>
51 <name>Spline</name>
52 <description>Perform a spline interpolation through the points. 2-dimensional only.</description>
53 </literal>
54 </enumeration>
55
56 <enumeration>
57 <vodml-id>SkyProjectionType</vodml-id>
58 <name>SkyProjectionType</name>
59 <description>Enumeration of non-linear celestial projection algorithm codes as listed in Table 13 of the FITS WCS paper II.</description>
60 <literal>
61 <vodml-id>SkyProjectionType.AZP</vodml-id>
62 <name>AZP</name>
63 <description>Zenithal perspective</description>
64 </literal>
65 <literal>
66 <vodml-id>SkyProjectionType.SZP</vodml-id>
67 <name>SZP</name>
68 <description>Slant zenithal perspective</description>
69 </literal>
70 <literal>
71 <vodml-id>SkyProjectionType.TAN</vodml-id>
72 <name>TAN</name>
73 <description>Gnomonic (Tangent plane projection)</description>
74 </literal>
75 <literal>
76 <vodml-id>SkyProjectionType.STG</vodml-id>
77 <name>STG</name>
78 <description>Stereographic</description>
79 </literal>
80 <literal>
81 <vodml-id>SkyProjectionType.SIN</vodml-id>
82 <name>SIN</name>
83 <description>Slant orthographic (Sine projection)</description>
84 </literal>
85 <literal>
86 <vodml-id>SkyProjectionType.ARC</vodml-id>
87 <name>ARC</name>
88 <description>Zenithal equidistant</description>
89 </literal>
90 <literal>
91 <vodml-id>SkyProjectionType.ZPN</vodml-id>
92 <name>ZPN</name>
93 <description>Zenithal polynomial</description>
94 </literal>
95 <literal>
96 <vodml-id>SkyProjectionType.ZEA</vodml-id>
97 <name>ZEA</name>
98 <description>Zenithal equal-area</description>
99 </literal>
100 <literal>
101 <vodml-id>SkyProjectionType.AIR</vodml-id>
102 <name>AIR</name>
103 <description>Airy</description>
104 </literal>
105 <literal>
106 <vodml-id>SkyProjectionType.CYP</vodml-id>
107 <name>CYP</name>
108 <description>Cylindrical perspective</description>
109 </literal>
110 <literal>
111 <vodml-id>SkyProjectionType.CEA</vodml-id>
112 <name>CEA</name>
113 <description>Cylindrical equal-area</description>
114 </literal>
115 <literal>
116 <vodml-id>SkyProjectionType.CAR</vodml-id>
117 <name>CAR</name>
118 <description>Plate carree</description>
119 </literal>
120 <literal>
121 <vodml-id>SkyProjectionType.MER</vodml-id>
122 <name>MER</name>
123 <description>Mercator</description>
124 </literal>
125 <literal>
126 <vodml-id>SkyProjectionType.SFL</vodml-id>
127 <name>SFL</name>
128 <description>Sanson-Flamsteed</description>
129 </literal>
130 <literal>
131 <vodml-id>SkyProjectionType.PAR</vodml-id>
132 <name>PAR</name>
133 <description>Parabolic</description>
134 </literal>
135 <literal>
136 <vodml-id>SkyProjectionType.MOL</vodml-id>
137 <name>MOL</name>
138 <description>Mollweide</description>
139 </literal>
140 <literal>
141 <vodml-id>SkyProjectionType.AIT</vodml-id>
142 <name>AIT</name>
143 <description>Hammer-Aitoff</description>
144 </literal>
145 <literal>
146 <vodml-id>SkyProjectionType.COP</vodml-id>
147 <name>COP</name>
148 <description>Conic perspective</description>
149 </literal>
150 <literal>
151 <vodml-id>SkyProjectionType.COE</vodml-id>
152 <name>COE</name>
153 <description>Conic equal-area</description>
154 </literal>
155 <literal>
156 <vodml-id>SkyProjectionType.COD</vodml-id>
157 <name>COD</name>
158 <description>Conic equidistant</description>
159 </literal>
160 <literal>
161 <vodml-id>SkyProjectionType.COO</vodml-id>
162 <name>COO</name>
163 <description>Conic orthomorphic</description>
164 </literal>
165 <literal>
166 <vodml-id>SkyProjectionType.BON</vodml-id>
167 <name>BON</name>
168 <description>Bonne equal-area</description>
169 </literal>
170 <literal>
171 <vodml-id>SkyProjectionType.PCO</vodml-id>
172 <name>PCO</name>
173 <description>Polyconic</description>
174 </literal>
175 <literal>
176 <vodml-id>SkyProjectionType.TSC</vodml-id>
177 <name>TSC</name>
178 <description>Tangential spherical cube</description>
179 </literal>
180 <literal>
181 <vodml-id>SkyProjectionType.CSC</vodml-id>
182 <name>CSC</name>
183 <description>COBE Quadrilateralized spherical cube</description>
184 </literal>
185 <literal>
186 <vodml-id>SkyProjectionType.QSC</vodml-id>
187 <name>QSC</name>
188 <description>Quadrilateralized spherical cube</description>
189 </literal>
190 </enumeration>
191
192 <enumeration>
193 <vodml-id>SpectralProjectionType</vodml-id>
194 <name>SpectralProjectionType</name>
195 <description>Enumeration of non-linear spectral projection algorithm codes as listed in Table 2 of the FITS WCS paper III.
196 NOTE: We exclude the TAB code from this list, that type is handled by the Lookup operation in this model.
197 </description>
198 <literal>
199 <vodml-id>SpectralProjectionType.F2W</vodml-id>
200 <name>F2W</name>
201 <description>Frequency - Wavelength</description>
202 </literal>
203 <literal>
204 <vodml-id>SpectralProjectionType.F2V</vodml-id>
205 <name>F2V</name>
206 <description>Frequency - Apparent radial velocity</description>
207 </literal>
208 <literal>
209 <vodml-id>SpectralProjectionType.F2A</vodml-id>
210 <name>F2A</name>
211 <description>Frequency - Air wavelength</description>
212 </literal>
213 <literal>
214 <vodml-id>SpectralProjectionType.W2F</vodml-id>
215 <name>W2F</name>
216 <description>Wavelength - Frequency</description>
217 </literal>
218 <literal>
219 <vodml-id>SpectralProjectionType.W2V</vodml-id>
220 <name>W2V</name>
221 <description>Wavelength - Apparent radial velocity</description>
222 </literal>
223 <literal>
224 <vodml-id>SpectralProjectionType.W2A</vodml-id>
225 <name>W2A</name>
226 <description>Wavelength - Air wavelength</description>
227 </literal>
228 <literal>
229 <vodml-id>SpectralProjectionType.V2F</vodml-id>
230 <name>V2F</name>
231 <description>Apparent radial velocity - Frequency</description>
232 </literal>
233 <literal>
234 <vodml-id>SpectralProjectionType.V2W</vodml-id>
235 <name>V2W</name>
236 <description>Apparent radial velocity - Wavelength</description>
237 </literal>
238 <literal>
239 <vodml-id>SpectralProjectionType.V2A</vodml-id>
240 <name>V2A</name>
241 <description>Apparent radial velocity - Air wavelength</description>
242 </literal>
243 <literal>
244 <vodml-id>SpectralProjectionType.A2F</vodml-id>
245 <name>A2F</name>
246 <description>Air wavelength - Frequency</description>
247 </literal>
248 <literal>
249 <vodml-id>SpectralProjectionType.A2W</vodml-id>
250 <name>A2W</name>
251 <description>Air wavelength - Wavelength</description>
252 </literal>
253 <literal>
254 <vodml-id>SpectralProjectionType.A2V</vodml-id>
255 <name>A2V</name>
256 <description>Air wavelength - Apparent radial velocity</description>
257 </literal>
258 <literal>
259 <vodml-id>SpectralProjectionType.LOG</vodml-id>
260 <name>LOG</name>
261 <description>Logarithm</description>
262 </literal>
263 <literal>
264 <vodml-id>SpectralProjectionType.GRI</vodml-id>
265 <name>GRI</name>
266 <description>Grism</description>
267 </literal>
268 <literal>
269 <vodml-id>SpectralProjectionType.GRA</vodml-id>
270 <name>GRA</name>
271 <description>Grism in air</description>
272 </literal>
273 </enumeration>
274
275 <enumeration>
276 <vodml-id>SpectralCoordType</vodml-id>
277 <name>SpectralCoordType</name>
278 <description>Enumeration of spectral coordinate types as listed in Table 1 of the FITS WCS paper III.</description>
279 <literal>
280 <vodml-id>SpectralCoordType.FREQ</vodml-id>
281 <name>FREQ</name>
282 <description>Frequency</description>
283 </literal>
284 <literal>
285 <vodml-id>SpectralCoordType.ENER</vodml-id>
286 <name>ENER</name>
287 <description>Energy</description>
288 </literal>
289 <literal>
290 <vodml-id>SpectralCoordType.WAVN</vodml-id>
291 <name>WAVN</name>
292 <description>Wavenumber</description>
293 </literal>
294 <literal>
295 <vodml-id>SpectralCoordType.VRAD</vodml-id>
296 <name>VRAD</name>
297 <description>Radio velocity</description>
298 </literal>
299 <literal>
300 <vodml-id>SpectralCoordType.WAVE</vodml-id>
301 <name>WAVE</name>
302 <description>Vacuum wavelength</description>
303 </literal>
304 <literal>
305 <vodml-id>SpectralCoordType.VOPT</vodml-id>
306 <name>VOPT</name>
307 <description>Optical velocity</description>
308 </literal>
309 <literal>
310 <vodml-id>SpectralCoordType.ZOPT</vodml-id>
311 <name>ZOPT</name>
312 <description>Redshift</description>
313 </literal>
314 <literal>
315 <vodml-id>SpectralCoordType.AWAV</vodml-id>
316 <name>AWAV</name>
317 <description>Air wavelength</description>
318 </literal>
319 <literal>
320 <vodml-id>SpectralCoordType.VELO</vodml-id>
321 <name>VELO</name>
322 <description>Apparent radial velocity</description>
323 </literal>
324 <literal>
325 <vodml-id>SpectralCoordType.BETA</vodml-id>
326 <name>BETA</name>
327 <description>Beta factor (v/c)</description>
328 </literal>
329 </enumeration>
330
331 <objectType abstract="true">
332 <vodml-id>TMapping</vodml-id>
333 <name>TMapping</name>
334 <description>Bi-directional mapping, contains the forward and inverse transform operation specifications. Many operations, such as a shift, rotation, and many matrix operations, have a natural inverse. For these cases, it is not necessary to define and propogate both the forward and inverse operations since the inverse can be easily derived from the forward. In other cases, an explicit inverse specification may be needed.
335
336 This class serves as the building block, from which arbitrarily complex operations can be built.</description>
337 <attribute>
338 <vodml-id>TMapping.invert</vodml-id>
339 <name>invert</name>
340 <description>Boolean flag indicating that the inverse operation should be applied. If missing, it is assumed to be "False".
341
342 For many operations, the inverse transformation can be directly derived from the forward transform. For instance, the inverse of a transform that simply adds a constant to each input is a transform of the same type, with a negated constant. However, there are potentially operations for which this cannot be done. For instance, a transform that maps 3D Cartesian coodinates to spherical coordinates cannot be re-written to represent its inverse. This flag indicates that it should be used in its inverse sense.
343
344 In addition, the invert flag allows a complex compound transformation to be be inverted simply by toggling its invert flag. Without such a flag each component would need to be re-written to represent its inverse (if possible), and the order of serial transformations would need to be reversed - a much more complex and error prone process.
345 </description>
346 <datatype>
347 <vodml-ref>ivoa:boolean</vodml-ref>
348 </datatype>
349 <multiplicity>
350 <minOccurs>0</minOccurs>
351 <maxOccurs>1</maxOccurs>
352 </multiplicity>
353 </attribute>
354 </objectType>
355
356 <objectType>
357 <vodml-id>TAtomic</vodml-id>
358 <name>TAtomic</name>
359 <description>Single stage bi-directional mapping.</description>
360 <extends>
361 <vodml-ref>trans:TMapping</vodml-ref>
362 </extends>
363 <composition>
364 <vodml-id>TAtomic.forward</vodml-id>
365 <name>forward</name>
366 <description>The forward transform operation specification.</description>
367 <datatype>
368 <vodml-ref>trans:TForward</vodml-ref>
369 </datatype>
370 <multiplicity>
371 <minOccurs>1</minOccurs>
372 <maxOccurs>1</maxOccurs>
373 </multiplicity>
374 </composition>
375 <composition>
376 <vodml-id>TAtomic.inverse</vodml-id>
377 <name>inverse</name>
378 <description>The inverse transform operation specification.</description>
379 <datatype>
380 <vodml-ref>trans:TInverse</vodml-ref>
381 </datatype>
382 <multiplicity>
383 <minOccurs>0</minOccurs>
384 <maxOccurs>1</maxOccurs>
385 </multiplicity>
386 </composition>
387 </objectType>
388
389 <objectType abstract="true">
390 <vodml-id>TCompound</vodml-id>
391 <name>TCompound</name>
392 <description>Abstract class to facilitate the combination of Mappings in various ways.
393 </description>
394 <extends>
395 <vodml-ref>trans:TMapping</vodml-ref>
396 </extends>
397 <composition>
398 <vodml-id>TCompound.map</vodml-id>
399 <name>map</name>
400 <description>Components of the complex operation. Depending on how the operations are combined, the interpretation of the components will change.</description>
401 <datatype>
402 <vodml-ref>trans:TMapping</vodml-ref>
403 </datatype>
404 <multiplicity>
405 <minOccurs>1</minOccurs>
406 <maxOccurs>-1</maxOccurs>
407 </multiplicity>
408 <isOrdered>true</isOrdered>
409 </composition>
410 </objectType>
411
412 <objectType>
413 <vodml-id>TCompose</vodml-id>
414 <name>TCompose</name>
415 <description>A complex operation which executes the component maps in sequence.
416 This allows the building of multi-stage transforms such as a Matrix operation followed by a WCS Projection.</description>
417 <extends>
418 <vodml-ref>trans:TCompound</vodml-ref>
419 </extends>
420 </objectType>
421
422 <objectType>
423 <vodml-id>TConcatenate</vodml-id>
424 <name>TConcatenate</name>
425 <description>Combines operations in parallel. This class enables the building of an operation which covers the full dimension space of the input. Axes are distributed to the component operations in order. For example, to perform a shift on a 2-dimensional coordinate (x,y), one would join two Shift operations giving the offset in x and y respectively. Since this class is an operation itself, it can be used as a component in other complex operations.</description>
426 <extends>
427 <vodml-ref>trans:TCompound</vodml-ref>
428 </extends>
429 </objectType>
430
431 <objectType abstract="true">
432 <vodml-id>TOperation</vodml-id>
433 <name>TOperation</name>
434 <description>Uni-directional transform operation, executes the contained function.</description>
435 <composition>
436 <vodml-id>TOperation.operation</vodml-id>
437 <name>operation</name>
438 <description>Transform operation specification.</description>
439 <datatype>
440 <vodml-ref>trans:TFunction</vodml-ref>
441 </datatype>
442 <multiplicity>
443 <minOccurs>1</minOccurs>
444 <maxOccurs>1</maxOccurs>
445 </multiplicity>
446 </composition>
447 </objectType>
448
449 <objectType>
450 <vodml-id>TForward</vodml-id>
451 <name>TForward</name>
452 <description>Defines the forward transform operation of the mapping.</description>
453 <extends>
454 <vodml-ref>trans:TOperation</vodml-ref>
455 </extends>
456 </objectType>
457
458 <objectType>
459 <vodml-id>TInverse</vodml-id>
460 <name>TInverse</name>
461 <description>Defines the inverse transform operation of the mapping.</description>
462 <extends>
463 <vodml-ref>trans:TOperation</vodml-ref>
464 </extends>
465 </objectType>
466
467 <objectType abstract="true">
468 <vodml-id>TFunction</vodml-id>
469 <name>TFunction</name>
470 <description>Transform Function (TFunction) defines a mathematical operation to be performed on its inputs.
471 </description>
472 </objectType>
473
474 <objectType>
475 <vodml-id>Permute</vodml-id>
476 <name>Permute</name>
477 <description>Permute the order and possibly number of dimensions between operations. This operation facilitates the workflow through the operation sequence. It is comprised of an ordered axismap list defining the output axis sequence in terms of the source (input) axes. It supports the reorder, duplication, and dropping of dimensions.
478 Reorder Example: We have a 3-dimensional coordinate (x,y,z) and wish to perform a 2-dimensional transform on the (x,z) plane. Define a Permute operation to reorder the axes from (x,y,z) to (y,x,z) using an axismap list specifying the new axis order, [2,1,3]. The results feed into the next step ( 1D + 2D operations ).
479 Duplicate Example: We have 2-dimensional coordinate (x,y) feeding two Polynomial2D operations to form (x',y'). Define a Permute operation with axismap list specifying sourceAxis set [1,2,1,2]. The result feeds into the next step ( Polynomial2D + Polynomial2D operations).
480 Drop Example: We have a 5-dimensional input feeding into a 3x3 Matrix operation. Define a Permute operation selecting the relevant axis set [1,3,5], the remaining axes, [2,4], are dropped.
481 Add Example: We have a 2-dimensional operation feeding into axes [1,3] of a 3-dimensional operation. Define a Permute operation with numSourceAxes=2; and sourceAxis set [1,0,2] where output axis 2 also specifies the fixed seed value.
482 </description>
483 <extends>
484 <vodml-ref>trans:TFunction</vodml-ref>
485 </extends>
486 <attribute>
487 <vodml-id>Permute.numSourceAxes</vodml-id>
488 <name>numSourceAxes</name>
489 <description>The number of input axes. Used to verify dimensional coverage in forward and inverse directions. For example, numSourceAxes=4 with axismap=[1,3] indicates that axes [2,4] have been dropped.
490 </description>
491 <datatype>
492 <vodml-ref>ivoa:nonnegativeInteger</vodml-ref>
493 </datatype>
494 <multiplicity>
495 <minOccurs>1</minOccurs>
496 <maxOccurs>1</maxOccurs>
497 </multiplicity>
498 </attribute>
499 <composition>
500 <vodml-id>Permute.axismap</vodml-id>
501 <name>axismap</name>
502 <description>Ordered list defining the number and order of the resulting axis set. Each entry provides the source (input) dimension for that output dimension.</description>
503 <datatype>
504 <vodml-ref>trans:PermuteAxis</vodml-ref>
505 </datatype>
506 <multiplicity>
507 <minOccurs>0</minOccurs>
508 <maxOccurs>-1</maxOccurs>
509 </multiplicity>
510 <isOrdered>true</isOrdered>
511 </composition>
512 </objectType>
513
514 <objectType>
515 <vodml-id>PermuteAxis</vodml-id>
516 <name>PermuteAxis</name>
517 <description>Entry for the Permute operation, this object defines the mapping of input dimension to output dimension. The output dimension is determined from its order in the axismap list.</description>
518 <attribute>
519 <vodml-id>PermuteAxis.sourceAxis</vodml-id>
520 <name>sourceAxis</name>
521 <description>Source (input) dimension number, 1 based.</description>
522 <datatype>
523 <vodml-ref>ivoa:nonnegativeInteger</vodml-ref>
524 </datatype>
525 <multiplicity>
526 <minOccurs>1</minOccurs>
527 <maxOccurs>1</maxOccurs>
528 </multiplicity>
529 </attribute>
530 <attribute>
531 <vodml-id>PermuteAxis.seedValue</vodml-id>
532 <name>seedValue</name>
533 <description>Value to assign for the new dimensional axis.</description>
534 <datatype>
535 <vodml-ref>ivoa:real</vodml-ref>
536 </datatype>
537 <multiplicity>
538 <minOccurs>0</minOccurs>
539 <maxOccurs>1</maxOccurs>
540 </multiplicity>
541 </attribute>
542 </objectType>
543
544 <objectType>
545 <vodml-id>Unit</vodml-id>
546 <name>Unit</name>
547 <description>A 1-Dimensional operation which makes no change to the inputs. ( X' = X )</description>
548 <extends>
549 <vodml-ref>trans:TFunction</vodml-ref>
550 </extends>
551 </objectType>
552
553 <objectType>
554 <vodml-id>Shift</vodml-id>
555 <name>Shift</name>
556 <description>A 1-Dimensional operation defining a simple offset. ( X' = X + offset )</description>
557 <extends>
558 <vodml-ref>trans:TFunction</vodml-ref>
559 </extends>
560 <attribute>
561 <vodml-id>Shift.offset</vodml-id>
562 <name>offset</name>
563 <description>The amount of offset to apply.</description>
564 <datatype>
565 <vodml-ref>ivoa:real</vodml-ref>
566 </datatype>
567 <multiplicity>
568 <minOccurs>1</minOccurs>
569 <maxOccurs>1</maxOccurs>
570 </multiplicity>
571 </attribute>
572 </objectType>
573
574 <objectType>
575 <vodml-id>Scale</vodml-id>
576 <name>Scale</name>
577 <description>A 1-Dimensional operator for simple scaling. ( X' = factor*X )</description>
578 <extends>
579 <vodml-ref>trans:TFunction</vodml-ref>
580 </extends>
581 <attribute>
582 <vodml-id>Scale.factor</vodml-id>
583 <name>factor</name>
584 <description>The scale factor.</description>
585 <datatype>
586 <vodml-ref>ivoa:real</vodml-ref>
587 </datatype>
588 <multiplicity>
589 <minOccurs>1</minOccurs>
590 <maxOccurs>1</maxOccurs>
591 </multiplicity>
592 </attribute>
593 </objectType>
594
595 <objectType>
596 <vodml-id>Rotate2D</vodml-id>
597 <name>Rotate2D</name>
598 <description>A 2-Dimensional rotation operation. </description>
599 <extends>
600 <vodml-ref>trans:TFunction</vodml-ref>
601 </extends>
602 <attribute>
603 <vodml-id>Rotate2D.angle</vodml-id>
604 <name>angle</name>
605 <description>Rotation angle, in degrees, from the positive direction of axis 1 toward the positive direction of axis 2.</description>
606 <datatype>
607 <vodml-ref>ivoa:real</vodml-ref>
608 </datatype>
609 <multiplicity>
610 <minOccurs>1</minOccurs>
611 <maxOccurs>1</maxOccurs>
612 </multiplicity>
613 </attribute>
614 </objectType>
615
616 <objectType>
617 <vodml-id>EulerRotation</vodml-id>
618 <name>EulerRotation</name>
619 <description>Defines a rotation operation in a 3-dimensional cartesian coordinate space, defined as a series of rotations about the native axes (x,y,z).
620 </description>
621 <extends>
622 <vodml-ref>trans:TFunction</vodml-ref>
623 </extends>
624 <composition>
625 <vodml-id>EulerRotation.eulerAngle</vodml-id>
626 <name>eulerAngle</name>
627 <description>Rotation angle about specified axis.</description>
628 <datatype>
629 <vodml-ref>trans:EulerAngle</vodml-ref>
630 </datatype>
631 <multiplicity>
632 <minOccurs>1</minOccurs>
633 <maxOccurs>-1</maxOccurs>
634 </multiplicity>
635 </composition>
636 </objectType>
637
638 <objectType>
639 <vodml-id>EulerAngle</vodml-id>
640 <name>EulerAngle</name>
641 <description>Angular rotation about a particular axis of a 3-dimensional cartesian coordinate space.</description>
642 <attribute>
643 <vodml-id>EulerAngle.rotationAxis</vodml-id>
644 <name>rotationAxis</name>
645 <description>Identifies the axis of rotation. MUST be 'x', 'y', or 'z'.</description>
646 <datatype>
647 <vodml-ref>ivoa:string</vodml-ref>
648 </datatype>
649 <multiplicity>
650 <minOccurs>1</minOccurs>
651 <maxOccurs>1</maxOccurs>
652 </multiplicity>
653 </attribute>
654 <attribute>
655 <vodml-id>EulerAngle.angle</vodml-id>
656 <name>angle</name>
657 <description>Angle of rotation, in degrees. Angle sign follows the right-hand rule, where positive values indicate clockwise rotation (looking in +axis direction), negative values for counter-clockwise.</description>
658 <datatype>
659 <vodml-ref>ivoa:real</vodml-ref>
660 </datatype>
661 <multiplicity>
662 <minOccurs>1</minOccurs>
663 <maxOccurs>1</maxOccurs>
664 </multiplicity>
665 </attribute>
666 </objectType>
667
668 <objectType>
669 <vodml-id>Matrix</vodml-id>
670 <name>Matrix</name>
671 <description>An M x N matrix operation. Each cell of the matrix is provided by a MatrixElement object. Missing elements should be considered to equal 0.
672 </description>
673 <extends>
674 <vodml-ref>trans:TFunction</vodml-ref>
675 </extends>
676 <constraint>
677 <description>element maxlength = M*N</description>
678 </constraint>
679 <attribute>
680 <vodml-id>Matrix.M</vodml-id>
681 <name>M</name>
682 <description>Number of rows in the matrix.</description>
683 <datatype>
684 <vodml-ref>ivoa:nonnegativeInteger</vodml-ref>
685 </datatype>
686 <multiplicity>
687 <minOccurs>1</minOccurs>
688 <maxOccurs>1</maxOccurs>
689 </multiplicity>
690 </attribute>
691 <attribute>
692 <vodml-id>Matrix.N</vodml-id>
693 <name>N</name>
694 <description>Number of columns in the matrix.</description>
695 <datatype>
696 <vodml-ref>ivoa:nonnegativeInteger</vodml-ref>
697 </datatype>
698 <multiplicity>
699 <minOccurs>1</minOccurs>
700 <maxOccurs>1</maxOccurs>
701 </multiplicity>
702 </attribute>
703 <composition>
704 <vodml-id>Matrix.element</vodml-id>
705 <name>element</name>
706 <description>Collection of MatrixElements which define each cell of the matrix. The total number of elements MUST NOT exceed M*N, any missing elements result in a cell with value=0.0.</description>
707 <datatype>
708 <vodml-ref>trans:MatrixElement</vodml-ref>
709 </datatype>
710 <multiplicity>
711 <minOccurs>0</minOccurs>
712 <maxOccurs>-1</maxOccurs>
713 </multiplicity>
714 </composition>
715 </objectType>
716
717 <objectType>
718 <vodml-id>MatrixElement</vodml-id>
719 <name>MatrixElement</name>
720 <description>The value of cell m,n in an M x N matrix.</description>
721 <attribute>
722 <vodml-id>MatrixElement.m</vodml-id>
723 <name>m</name>
724 <description>Matrix cell row number.</description>
725 <datatype>
726 <vodml-ref>ivoa:nonnegativeInteger</vodml-ref>
727 </datatype>
728 <multiplicity>
729 <minOccurs>1</minOccurs>
730 <maxOccurs>1</maxOccurs>
731 </multiplicity>
732 </attribute>
733 <attribute>
734 <vodml-id>MatrixElement.n</vodml-id>
735 <name>n</name>
736 <description>Matrix cell column number.</description>
737 <datatype>
738 <vodml-ref>ivoa:nonnegativeInteger</vodml-ref>
739 </datatype>
740 <multiplicity>
741 <minOccurs>1</minOccurs>
742 <maxOccurs>1</maxOccurs>
743 </multiplicity>
744 </attribute>
745 <attribute>
746 <vodml-id>MatrixElement.value</vodml-id>
747 <name>value</name>
748 <description>Matrix cell value.</description>
749 <datatype>
750 <vodml-ref>ivoa:real</vodml-ref>
751 </datatype>
752 <multiplicity>
753 <minOccurs>1</minOccurs>
754 <maxOccurs>1</maxOccurs>
755 </multiplicity>
756 </attribute>
757 </objectType>
758
759 <objectType abstract="true">
760 <vodml-id>Projection</vodml-id>
761 <name>Projection</name>
762 <description>Abstract head of World Coordinate System (WCS) projection operations. We do not attempt to define the operations here, but instead, provide extensions which support the transforms described in the FITS WCS papers II and III.
763 </description>
764 <extends>
765 <vodml-ref>trans:TFunction</vodml-ref>
766 </extends>
767 <composition>
768 <vodml-id>Projection.param</vodml-id>
769 <name>param</name>
770 <description>Set of 0 or more parameters providing supplemental metadata required to execute a particular projection algorithm. The number and meaning of the parameters depends on the algorithm. They are typically in the from of keyword/value pairs, so we provide a simple ProjectionParam element to accommodate these. The detailed content specification is left to the WCS paper.</description>
771 <datatype>
772 <vodml-ref>trans:ProjectionParam</vodml-ref>
773 </datatype>
774 <multiplicity>
775 <minOccurs>0</minOccurs>
776 <maxOccurs>-1</maxOccurs>
777 </multiplicity>
778 </composition>
779 </objectType>
780
781 <objectType>
782 <vodml-id>ProjectionParam</vodml-id>
783 <name>ProjectionParam</name>
784 <description>Simple parameter specification for WCS Projections. The parameter is modeled as a simple name/value pair. The details of expectations for the various projection algorithms is left to the WCS paper describing the algorithm.</description>
785 <attribute>
786 <vodml-id>ProjectionParam.name</vodml-id>
787 <name>name</name>
788 <description>The parameter name as described in the WCS papers for each operation type.</description>
789 <datatype>
790 <vodml-ref>ivoa:string</vodml-ref>
791 </datatype>
792 <multiplicity>
793 <minOccurs>1</minOccurs>
794 <maxOccurs>1</maxOccurs>
795 </multiplicity>
796 </attribute>
797 <attribute>
798 <vodml-id>ProjectionParam.value</vodml-id>
799 <name>value</name>
800 <description>The value for the parameter. </description>
801 <datatype>
802 <vodml-ref>ivoa:real</vodml-ref>
803 </datatype>
804 <multiplicity>
805 <minOccurs>1</minOccurs>
806 <maxOccurs>1</maxOccurs>
807 </multiplicity>
808 </attribute>
809 </objectType>
810
811 <objectType>
812 <vodml-id>SkyProjection</vodml-id>
813 <name>SkyProjection</name>
814 <description>This class corresponds to the Spherical Projection component of the FITS WCS paper II. As in the paper, this operation describes the mapping between the intermediate "Projection Plane" and the "Native Spherical" coordinate systems. This model supports all defined projection types, where the appropriate code is specified in the algorithm attribute. All projection parameters are to be provided through the ProjectionParam list according to the descriptions given in the FITS WCS paper.
815 </description>
816 <extends>
817 <vodml-ref>trans:Projection</vodml-ref>
818 </extends>
819 <attribute>
820 <vodml-id>SkyProjection.algorithm</vodml-id>
821 <name>algorithm</name>
822 <description>The projection algorithm to apply. The value MUST be taken from the enumeration of standard sky projection algorithms. Extracted from 'ctype' in the FITS WCS representations.</description>
823 <datatype>
824 <vodml-ref>trans:SkyProjectionType</vodml-ref>
825 </datatype>
826 <multiplicity>
827 <minOccurs>1</minOccurs>
828 <maxOccurs>1</maxOccurs>
829 </multiplicity>
830 </attribute>
831 </objectType>
832
833 <objectType>
834 <vodml-id>SkyProjRotate</vodml-id>
835 <name>SkyProjRotate</name>
836 <description>This class extends SkyProjection to include the Spherical Rotation component of the FITS WCS paper II. This operation describes the mapping between the "Native Spherical" and "Celestial" coordinate systems. The reference values are provided at the appropriate attribute, while all other parameters (e.g. LONPOLE, LATPOLE) are to be provided through the ProjectionParam list according to the descriptions given in the FITS WCS paper.
837 </description>
838 <extends>
839 <vodml-ref>trans:SkyProjection</vodml-ref>
840 </extends>
841 <attribute>
842 <vodml-id>SkyProjRotate.referenceValue</vodml-id>
843 <name>referenceValue</name>
844 <description>The target reference values in each dimension. Equivalent to 'crval' in FITS WCS representations.</description>
845 <datatype>
846 <vodml-ref>ivoa:real</vodml-ref>
847 </datatype>
848 <multiplicity>
849 <minOccurs>2</minOccurs>
850 <maxOccurs>2</maxOccurs>
851 </multiplicity>
852 </attribute>
853 </objectType>
854
855 <objectType>
856 <vodml-id>SpectralProjection</vodml-id>
857 <name>SpectralProjection</name>
858 <description>This class represents a nonlinear one-dimensional spectral transform as detailed in the FITS WCS paper III.</description>
859 <extends>
860 <vodml-ref>trans:Projection</vodml-ref>
861 </extends>
862 <attribute>
863 <vodml-id>SpectralProjection.referenceValue</vodml-id>
864 <name>referenceValue</name>
865 <description>The target reference value for the axis. Equivalent to 'crval' in FITS WCS representations.</description>
866 <datatype>
867 <vodml-ref>ivoa:real</vodml-ref>
868 </datatype>
869 <multiplicity>
870 <minOccurs>1</minOccurs>
871 <maxOccurs>1</maxOccurs>
872 </multiplicity>
873 </attribute>
874 <attribute>
875 <vodml-id>SpectralProjection.algorithm</vodml-id>
876 <name>algorithm</name>
877 <description>The projection algorithm to apply. The value MUST be taken from the enumeration of non-linear spectral projection algorithms. Extracted from 'ctype' in FITS WCS representations.</description>
878 <datatype>
879 <vodml-ref>trans:SpectralProjectionType</vodml-ref>
880 </datatype>
881 <multiplicity>
882 <minOccurs>1</minOccurs>
883 <maxOccurs>1</maxOccurs>
884 </multiplicity>
885 </attribute>
886 <attribute>
887 <vodml-id>SpectralProjection.coordType</vodml-id>
888 <name>coordType</name>
889 <description>The resulting spectral coordinate type code. Values MUST be taken from the enumerated list of spectral coordinate types. Extracted from 'ctype' in FITS WCS representations.</description>
890 <datatype>
891 <vodml-ref>trans:SpectralCoordType</vodml-ref>
892 </datatype>
893 <multiplicity>
894 <minOccurs>1</minOccurs>
895 <maxOccurs>1</maxOccurs>
896 </multiplicity>
897 </attribute>
898 </objectType>
899
900 <objectType abstract="true">
901 <vodml-id>Polynomial</vodml-id>
902 <name>Polynomial</name>
903 <description>Abstract head of a family of Polynomial distortion operations.</description>
904 <extends>
905 <vodml-ref>trans:TFunction</vodml-ref>
906 </extends>
907 <attribute>
908 <vodml-id>Polynomial.order</vodml-id>
909 <name>order</name>
910 <description>The order, or degree, of the polynomial expression.</description>
911 <datatype>
912 <vodml-ref>ivoa:nonnegativeInteger</vodml-ref>
913 </datatype>
914 <multiplicity>
915 <minOccurs>1</minOccurs>
916 <maxOccurs>1</maxOccurs>
917 </multiplicity>
918 </attribute>
919 </objectType>
920
921 <objectType>
922 <vodml-id>Polynomial1D</vodml-id>
923 <name>Polynomial1D</name>
924 <description>A 1-Dimensional Polynomial transform represented by the expression: X' = SUM( Ci*X**i), i=0..order. Each term is provided by a PolyCoeff1D object. Missing terms are considered to have a coefficient of 0.0.</description>
925 <extends>
926 <vodml-ref>trans:Polynomial</vodml-ref>
927 </extends>
928 <composition>
929 <vodml-id>Polynomial1D.term</vodml-id>
930 <name>term</name>
931 <description>A term in the polynomial expression.</description>
932 <datatype>
933 <vodml-ref>trans:PolyCoeff1D</vodml-ref>
934 </datatype>
935 <multiplicity>
936 <minOccurs>1</minOccurs>
937 <maxOccurs>-1</maxOccurs>
938 </multiplicity>
939 </composition>
940 </objectType>
941
942 <objectType>
943 <vodml-id>PolyCoeff1D</vodml-id>
944 <name>PolyCoeff1D</name>
945 <description>A term of the polynomial expression. This object provides the coefficient (c) and power (p) of the term, forming the expression c*X**p.
946 </description>
947 <attribute>
948 <vodml-id>PolyCoeff1D.coeff</vodml-id>
949 <name>coeff</name>
950 <description>Multiplicitive coefficient of the term.</description>
951 <datatype>
952 <vodml-ref>ivoa:real</vodml-ref>
953 </datatype>
954 <multiplicity>
955 <minOccurs>1</minOccurs>
956 <maxOccurs>1</maxOccurs>
957 </multiplicity>
958 </attribute>
959 <attribute>
960 <vodml-id>PolyCoeff1D.power</vodml-id>
961 <name>power</name>
962 <description>The power to raise the value for this term.</description>
963 <datatype>
964 <vodml-ref>ivoa:nonnegativeInteger</vodml-ref>
965 </datatype>
966 <multiplicity>
967 <minOccurs>1</minOccurs>
968 <maxOccurs>1</maxOccurs>
969 </multiplicity>
970 </attribute>
971 </objectType>
972
973 <objectType>
974 <vodml-id>Polynomial2D</vodml-id>
975 <name>Polynomial2D</name>
976 <description>A 2-Dimensional Polynomial transform represented by the expression: X' = SUMi,j( Cij*X**i*Y**j), i+j&lt;=order. Each term is provided by a PolyCoeff2D object. Missing terms are considered to have a coefficient of 0.0.</description>
977 <extends>
978 <vodml-ref>trans:Polynomial</vodml-ref>
979 </extends>
980 <composition>
981 <vodml-id>Polynomial2D.term</vodml-id>
982 <name>term</name>
983 <description>A term in the polynomial expression.</description>
984 <datatype>
985 <vodml-ref>trans:PolyCoeff2D</vodml-ref>
986 </datatype>
987 <multiplicity>
988 <minOccurs>1</minOccurs>
989 <maxOccurs>-1</maxOccurs>
990 </multiplicity>
991 </composition>
992 </objectType>
993
994 <objectType>
995 <vodml-id>PolyCoeff2D</vodml-id>
996 <name>PolyCoeff2D</name>
997 <description>A term of the polynomial expression. This object provides the coefficient (c) and power (p) of the term, forming the expression c*X**p[0]*Y**p[1].
998 </description>
999 <attribute>
1000 <vodml-id>PolyCoeff2D.coeff</vodml-id>
1001 <name>coeff</name>
1002 <description>Multiplicitive coefficient of the term.</description>
1003 <datatype>
1004 <vodml-ref>ivoa:real</vodml-ref>
1005 </datatype>
1006 <multiplicity>
1007 <minOccurs>1</minOccurs>
1008 <maxOccurs>1</maxOccurs>
1009 </multiplicity>
1010 </attribute>
1011 <attribute>
1012 <vodml-id>PolyCoeff2D.power</vodml-id>
1013 <name>power</name>
1014 <description>The power to raise the values for this term in each dimension.</description>
1015 <datatype>
1016 <vodml-ref>ivoa:nonnegativeInteger</vodml-ref>
1017 </datatype>
1018 <multiplicity>
1019 <minOccurs>2</minOccurs>
1020 <maxOccurs>2</maxOccurs>
1021 </multiplicity>
1022 </attribute>
1023 </objectType>
1024
1025 <objectType>
1026 <vodml-id>Lookup</vodml-id>
1027 <name>Lookup</name>
1028 <description>Defines a lookup table operation. The Lookup is comprised of a series of value pairs (LookupEntry). All members of the series MUST be of the same type.
1029 Handling Enumerated data:
1030 A common usage of a Lookup operation is to map image pixel index to an enumeration, such as a Polarization state. This can be handled by two means:
1031 1) Define a numeric equivalent for each enumeration literal, and use NumericEntry types. Casting to the corresponding literal occurs outside of the operation.
1032 2) Your local model can define a LookupEntry extension which maps the native value directly the target EnumerationLiteral.
1033
1034 The details of either approach for particular enumerations is considered outside the scope of this document.
1035 </description>
1036 <extends>
1037 <vodml-ref>trans:TFunction</vodml-ref>
1038 </extends>
1039 <attribute>
1040 <vodml-id>Lookup.interpolation</vodml-id>
1041 <name>interpolation</name>
1042 <description>Specifies the form of interpolation, if any, prescribed to be performed.</description>
1043 <datatype>
1044 <vodml-ref>trans:InterpolationMethod</vodml-ref>
1045 </datatype>
1046 <multiplicity>
1047 <minOccurs>0</minOccurs>
1048 <maxOccurs>1</maxOccurs>
1049 </multiplicity>
1050 </attribute>
1051 <attribute>
1052 <vodml-id>Lookup.bounds_error</vodml-id>
1053 <name>bounds_error</name>
1054 <description>Flag to specify behaviour outside the lookup table data bounds. True indicates an error condition, False indicates that the associated "fill" entry should be returned. If no "fill" entry is provided, the value should be extrapolated.</description>
1055 <datatype>
1056 <vodml-ref>ivoa:boolean</vodml-ref>
1057 </datatype>
1058 <multiplicity>
1059 <minOccurs>0</minOccurs>
1060 <maxOccurs>1</maxOccurs>
1061 </multiplicity>
1062 </attribute>
1063 <composition>
1064 <vodml-id>Lookup.entry</vodml-id>
1065 <name>entry</name>
1066 <description>Set of lookup table entries forming a discrete mapping from the native space to the target space.</description>
1067 <datatype>
1068 <vodml-ref>trans:LookupEntry</vodml-ref>
1069 </datatype>
1070 <multiplicity>
1071 <minOccurs>1</minOccurs>
1072 <maxOccurs>-1</maxOccurs>
1073 </multiplicity>
1074 <isOrdered>true</isOrdered>
1075 </composition>
1076 </objectType>
1077
1078 <objectType abstract="true">
1079 <vodml-id>LookupEntry</vodml-id>
1080 <name>LookupEntry</name>
1081 <description>This is an abstract head of lookup table entry objects. Each entry provides a discrete translation of a 'native' value to the corresponding 'target' value. </description>
1082 <attribute>
1083 <vodml-id>LookupEntry.fill</vodml-id>
1084 <name>fill</name>
1085 <description>When TRUE, the entry provides values to be used outside the Lookup table data domain. MUST only appear first or last in the sequence. If missing, it is considered to be FALSE.</description>
1086 <datatype>
1087 <vodml-ref>ivoa:boolean</vodml-ref>
1088 </datatype>
1089 <multiplicity>
1090 <minOccurs>0</minOccurs>
1091 <maxOccurs>1</maxOccurs>
1092 </multiplicity>
1093 </attribute>
1094 </objectType>
1095
1096 <objectType>
1097 <vodml-id>NumericEntry</vodml-id>
1098 <name>NumericEntry</name>
1099 <description>A 1-Dimensional discrete mapping of numeric values. </description>
1100 <extends>
1101 <vodml-ref>trans:LookupEntry</vodml-ref>
1102 </extends>
1103 <attribute>
1104 <vodml-id>NumericEntry.nativeValue</vodml-id>
1105 <name>nativeValue</name>
1106 <description>The native, or reference, value of the lookup entry.</description>
1107 <datatype>
1108 <vodml-ref>ivoa:real</vodml-ref>
1109 </datatype>
1110 <multiplicity>
1111 <minOccurs>1</minOccurs>
1112 <maxOccurs>1</maxOccurs>
1113 </multiplicity>
1114 </attribute>
1115 <attribute>
1116 <vodml-id>NumericEntry.targetValue</vodml-id>
1117 <name>targetValue</name>
1118 <description>The target, or resulting, value of the lookup entry.</description>
1119 <datatype>
1120 <vodml-ref>ivoa:real</vodml-ref>
1121 </datatype>
1122 <multiplicity>
1123 <minOccurs>1</minOccurs>
1124 <maxOccurs>1</maxOccurs>
1125 </multiplicity>
1126 </attribute>
1127 </objectType>
1128
1129 <objectType>
1130 <vodml-id>NumericEntry2D</vodml-id>
1131 <name>NumericEntry2D</name>
1132 <description>A 2-Dimensional discrete mapping of numeric values. </description>
1133 <extends>
1134 <vodml-ref>trans:LookupEntry</vodml-ref>
1135 </extends>
1136 <attribute>
1137 <vodml-id>NumericEntry2D.nativeValue</vodml-id>
1138 <name>nativeValue</name>
1139 <description>The native, or reference, value of the lookup entry.</description>
1140 <datatype>
1141 <vodml-ref>ivoa:real</vodml-ref>
1142 </datatype>
1143 <multiplicity>
1144 <minOccurs>2</minOccurs>
1145 <maxOccurs>2</maxOccurs>
1146 </multiplicity>
1147 </attribute>
1148 <attribute>
1149 <vodml-id>NumericEntry2D.targetValue</vodml-id>
1150 <name>targetValue</name>
1151 <description>The target, or resulting, value of the lookup entry.</description>
1152 <datatype>
1153 <vodml-ref>ivoa:real</vodml-ref>
1154 </datatype>
1155 <multiplicity>
1156 <minOccurs>2</minOccurs>
1157 <maxOccurs>2</maxOccurs>
1158 </multiplicity>
1159 </attribute>
1160 </objectType>
1161
1162 <objectType>
1163 <vodml-id>StringEntry</vodml-id>
1164 <name>StringEntry</name>
1165 <description>A 1-Dimensional discrete mapping of an integer counter to a corresponding string form. Since the result is non-numeric, a Lookup operation with StringEntry-s can only be used at the end of a Transform sequence.</description>
1166 <extends>
1167 <vodml-ref>trans:LookupEntry</vodml-ref>
1168 </extends>
1169 <attribute>
1170 <vodml-id>StringEntry.nativeValue</vodml-id>
1171 <name>nativeValue</name>
1172 <description>The native, or reference, value of the lookup entry.</description>
1173 <datatype>
1174 <vodml-ref>ivoa:integer</vodml-ref>
1175 </datatype>
1176 <multiplicity>
1177 <minOccurs>1</minOccurs>
1178 <maxOccurs>1</maxOccurs>
1179 </multiplicity>
1180 </attribute>
1181 <attribute>
1182 <vodml-id>StringEntry.targetValue</vodml-id>
1183 <name>targetValue</name>
1184 <description>The target, or resulting, value of the lookup entry.</description>
1185 <datatype>
1186 <vodml-ref>ivoa:string</vodml-ref>
1187 </datatype>
1188 <multiplicity>
1189 <minOccurs>1</minOccurs>
1190 <maxOccurs>1</maxOccurs>
1191 </multiplicity>
1192 </attribute>
1193 </objectType>
1194
1195 </vo-dml:model>

msdemlei@ari.uni-heidelberg.de
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