File: test_sindex.py

package info (click to toggle)
python-geopandas 0.8.2-1
  • links: PTS, VCS
  • area: main
  • in suites: bullseye
  • size: 12,004 kB
  • sloc: python: 14,226; makefile: 150; sh: 14
file content (565 lines) | stat: -rw-r--r-- 22,394 bytes parent folder | download
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
import sys

from shapely.geometry import (
    Point,
    Polygon,
    MultiPolygon,
    box,
    GeometryCollection,
    LineString,
)
from numpy.testing import assert_array_equal

import geopandas
from geopandas import _compat as compat
from geopandas import GeoDataFrame, GeoSeries, read_file, sindex, datasets

import pytest
import numpy as np


class TestNoSindex:
    @pytest.mark.skipif(sindex.has_sindex(), reason="Spatial index present, skipping")
    def test_no_sindex_installed(self):
        """Checks that an error is raised when no spatial index is present."""
        with pytest.raises(ImportError):
            sindex.get_sindex_class()

    @pytest.mark.skipif(
        compat.HAS_RTREE or not compat.HAS_PYGEOS,
        reason="rtree cannot be disabled via flags",
    )
    def test_no_sindex_active(self):
        """Checks that an error is given when rtree is not installed
        and compat.USE_PYGEOS is False.
        """
        state = compat.USE_PYGEOS  # try to save state
        compat.set_use_pygeos(False)
        with pytest.raises(ImportError):
            sindex.get_sindex_class()
        compat.set_use_pygeos(state)  # try to restore state


@pytest.mark.skipif(sys.platform.startswith("win"), reason="fails on AppVeyor")
@pytest.mark.skipif(not sindex.has_sindex(), reason="Spatial index absent, skipping")
class TestSeriesSindex:
    def test_empty_geoseries(self):
        """Tests creating a spatial index from an empty GeoSeries."""
        with pytest.warns(FutureWarning, match="Generated spatial index is empty"):
            # TODO: add checking len(GeoSeries().sindex) == 0 once deprecated
            assert not GeoSeries(dtype=object).sindex

    def test_point(self):
        s = GeoSeries([Point(0, 0)])
        assert s.sindex.size == 1
        hits = s.sindex.intersection((-1, -1, 1, 1))
        assert len(list(hits)) == 1
        hits = s.sindex.intersection((-2, -2, -1, -1))
        assert len(list(hits)) == 0

    def test_empty_point(self):
        """Tests that a single empty Point results in an empty tree."""
        s = GeoSeries([Point()])

        with pytest.warns(FutureWarning, match="Generated spatial index is empty"):
            # TODO: add checking len(s) == 0 once deprecated
            assert not s.sindex

        assert s._sindex_generated is True

    def test_polygons(self):
        t1 = Polygon([(0, 0), (1, 0), (1, 1)])
        t2 = Polygon([(0, 0), (1, 1), (0, 1)])
        sq = Polygon([(0, 0), (1, 0), (1, 1), (0, 1)])
        s = GeoSeries([t1, t2, sq])
        assert s.sindex.size == 3

    def test_polygons_append(self):
        t1 = Polygon([(0, 0), (1, 0), (1, 1)])
        t2 = Polygon([(0, 0), (1, 1), (0, 1)])
        sq = Polygon([(0, 0), (1, 0), (1, 1), (0, 1)])
        s = GeoSeries([t1, t2, sq])
        t = GeoSeries([t1, t2, sq], [3, 4, 5])
        s = s.append(t)
        assert len(s) == 6
        assert s.sindex.size == 6

    def test_lazy_build(self):
        s = GeoSeries([Point(0, 0)])
        assert s._sindex is None
        assert s.sindex.size == 1
        assert s._sindex is not None


@pytest.mark.skipif(sys.platform.startswith("win"), reason="fails on AppVeyor")
@pytest.mark.skipif(not sindex.has_sindex(), reason="Spatial index absent, skipping")
class TestFrameSindex:
    def setup_method(self):
        data = {
            "A": range(5),
            "B": range(-5, 0),
            "location": [Point(x, y) for x, y in zip(range(5), range(5))],
        }
        self.df = GeoDataFrame(data, geometry="location")

    def test_sindex(self):
        self.df.crs = "epsg:4326"
        assert self.df.sindex.size == 5
        with pytest.warns(FutureWarning, match="`objects` is deprecated"):
            # TODO: remove warning check once deprecated
            hits = list(self.df.sindex.intersection((2.5, 2.5, 4, 4), objects=True))
        assert len(hits) == 2
        assert hits[0].object == 3

    def test_lazy_build(self):
        assert self.df._sindex is None
        assert self.df.sindex.size == 5
        assert self.df._sindex is not None

    def test_sindex_rebuild_on_set_geometry(self):
        # First build the sindex
        assert self.df.sindex is not None
        self.df.set_geometry(
            [Point(x, y) for x, y in zip(range(5, 10), range(5, 10))], inplace=True
        )
        assert self.df._sindex_generated is False


# Skip to accommodate Shapely geometries being unhashable
@pytest.mark.skip
class TestJoinSindex:
    def setup_method(self):
        nybb_filename = geopandas.datasets.get_path("nybb")
        self.boros = read_file(nybb_filename)

    def test_merge_geo(self):
        # First check that we gets hits from the boros frame.
        tree = self.boros.sindex
        with pytest.warns(FutureWarning, match="`objects` is deprecated"):
            # TODO: remove warning check once deprecated
            hits = tree.intersection((1012821.80, 229228.26), objects=True)
        res = [self.boros.loc[hit.object]["BoroName"] for hit in hits]
        assert res == ["Bronx", "Queens"]

        # Check that we only get the Bronx from this view.
        first = self.boros[self.boros["BoroCode"] < 3]
        tree = first.sindex
        with pytest.warns(FutureWarning, match="`objects` is deprecated"):
            # TODO: remove warning check once deprecated
            hits = tree.intersection((1012821.80, 229228.26), objects=True)
        res = [first.loc[hit.object]["BoroName"] for hit in hits]
        assert res == ["Bronx"]

        # Check that we only get Queens from this view.
        second = self.boros[self.boros["BoroCode"] >= 3]
        tree = second.sindex
        with pytest.warns(FutureWarning, match="`objects` is deprecated"):
            # TODO: remove warning check once deprecated
            hits = tree.intersection((1012821.80, 229228.26), objects=True)
        res = ([second.loc[hit.object]["BoroName"] for hit in hits],)
        assert res == ["Queens"]

        # Get both the Bronx and Queens again.
        merged = first.merge(second, how="outer")
        assert len(merged) == 5
        assert merged.sindex.size == 5
        tree = merged.sindex
        with pytest.warns(FutureWarning, match="`objects` is deprecated"):
            # TODO: remove warning check once deprecated
            hits = tree.intersection((1012821.80, 229228.26), objects=True)
        res = [merged.loc[hit.object]["BoroName"] for hit in hits]
        assert res == ["Bronx", "Queens"]


@pytest.mark.skipif(not sindex.has_sindex(), reason="Spatial index absent, skipping")
class TestPygeosInterface:
    def setup_method(self):
        data = {
            "location": [Point(x, y) for x, y in zip(range(5), range(5))]
            + [box(10, 10, 20, 20)]  # include a box geometry
        }
        self.df = GeoDataFrame(data, geometry="location")
        self.expected_size = len(data["location"])

    # --------------------------- `intersection` tests -------------------------- #
    @pytest.mark.parametrize(
        "test_geom, expected",
        (
            ((-1, -1, -0.5, -0.5), []),
            ((-0.5, -0.5, 0.5, 0.5), [0]),
            ((0, 0, 1, 1), [0, 1]),
            ((0, 0), [0]),
        ),
    )
    def test_intersection_bounds_tuple(self, test_geom, expected):
        """Tests the `intersection` method with valid inputs."""
        res = list(self.df.sindex.intersection(test_geom))
        assert_array_equal(res, expected)

    @pytest.mark.parametrize("test_geom", ((-1, -1, -0.5), -0.5, None, Point(0, 0)))
    def test_intersection_invalid_bounds_tuple(self, test_geom):
        """Tests the `intersection` method with invalid inputs."""
        if compat.USE_PYGEOS:
            with pytest.raises(TypeError):
                # we raise a useful TypeError
                self.df.sindex.intersection(test_geom)
        else:
            with pytest.raises((TypeError, Exception)):
                # catch a general exception
                # rtree raises an RTreeError which we need to catch
                self.df.sindex.intersection(test_geom)

    # ------------------------------ `query` tests ------------------------------ #
    @pytest.mark.parametrize(
        "predicate, test_geom, expected",
        (
            (None, box(-1, -1, -0.5, -0.5), []),  # bbox does not intersect
            (None, box(-0.5, -0.5, 0.5, 0.5), [0]),  # bbox intersects
            (None, box(0, 0, 1, 1), [0, 1]),  # bbox intersects multiple
            (
                None,
                LineString([(0, 1), (1, 0)]),
                [0, 1],
            ),  # bbox intersects but not geometry
            ("intersects", box(-1, -1, -0.5, -0.5), []),  # bbox does not intersect
            (
                "intersects",
                box(-0.5, -0.5, 0.5, 0.5),
                [0],
            ),  # bbox and geometry intersect
            (
                "intersects",
                box(0, 0, 1, 1),
                [0, 1],
            ),  # bbox and geometry intersect multiple
            (
                "intersects",
                LineString([(0, 1), (1, 0)]),
                [],
            ),  # bbox intersects but not geometry
            ("within", box(0.25, 0.28, 0.75, 0.75), []),  # does not intersect
            ("within", box(0, 0, 10, 10), []),  # intersects but is not within
            ("within", box(11, 11, 12, 12), [5]),  # intersects and is within
            ("within", LineString([(0, 1), (1, 0)]), []),  # intersects but not within
            ("contains", box(0, 0, 1, 1), []),  # intersects but does not contain
            ("contains", box(0, 0, 1.001, 1.001), [1]),  # intersects and contains
            ("contains", box(0.5, 0.5, 1.5, 1.5), [1]),  # intersects and contains
            ("contains", box(-1, -1, 2, 2), [0, 1]),  # intersects and contains multiple
            (
                "contains",
                LineString([(0, 1), (1, 0)]),
                [],
            ),  # intersects but not contains
            ("touches", box(-1, -1, 0, 0), [0]),  # bbox intersects and touches
            (
                "touches",
                box(-0.5, -0.5, 1.5, 1.5),
                [],
            ),  # bbox intersects but geom does not touch
        ),
    )
    def test_query(self, predicate, test_geom, expected):
        """Tests the `query` method with valid inputs and valid predicates."""
        res = self.df.sindex.query(test_geom, predicate=predicate)
        assert_array_equal(res, expected)

    def test_query_invalid_geometry(self):
        """Tests the `query` method with invalid geometry.
        """
        with pytest.raises(TypeError):
            self.df.sindex.query("notavalidgeom")

    @pytest.mark.parametrize(
        "test_geom, expected_value",
        [
            (None, []),
            (GeometryCollection(), []),
            (Point(), []),
            (MultiPolygon(), []),
            (Polygon(), []),
        ],
    )
    def test_query_empty_geometry(self, test_geom, expected_value):
        """Tests the `query` method with empty geometry.
        """
        res = self.df.sindex.query(test_geom)
        assert_array_equal(res, expected_value)

    def test_query_invalid_predicate(self):
        """Tests the `query` method with invalid predicates.
        """
        test_geom = box(-1, -1, -0.5, -0.5)
        with pytest.raises(ValueError):
            self.df.sindex.query(test_geom, predicate="test")

    @pytest.mark.parametrize(
        "sort, expected",
        (
            (True, [[0, 0, 0], [0, 1, 2]]),
            # False could be anything, at least we'll know if it changes
            (False, [[0, 0, 0], [0, 1, 2]]),
        ),
    )
    def test_query_sorting(self, sort, expected):
        """Check that results from `query` don't depend on the
        order of geometries.
        """
        # these geometries come from a reported issue:
        # https://github.com/geopandas/geopandas/issues/1337
        # there is no theoretical reason they were chosen
        test_polys = GeoSeries([Polygon([(1, 1), (3, 1), (3, 3), (1, 3)])])
        tree_polys = GeoSeries(
            [
                Polygon([(1, 1), (3, 1), (3, 3), (1, 3)]),
                Polygon([(-1, 1), (1, 1), (1, 3), (-1, 3)]),
                Polygon([(3, 3), (5, 3), (5, 5), (3, 5)]),
            ]
        )
        expected = [0, 1, 2]

        # pass through GeoSeries to have GeoPandas
        # determine if it should use shapely or pygeos geometry objects
        tree_df = geopandas.GeoDataFrame(geometry=tree_polys)
        test_df = geopandas.GeoDataFrame(geometry=test_polys)

        test_geo = test_df.geometry.values.data[0]
        res = tree_df.sindex.query(test_geo, sort=sort)
        try:
            assert_array_equal(res, expected)
        except AssertionError as e:
            if not compat.USE_PYGEOS and sort is False:
                pytest.xfail(
                    "rtree results are known to be unordered, see "
                    "https://github.com/geopandas/geopandas/issues/1337\n"
                    "Expected:\n {}\n".format(expected)
                    + "Got:\n {}\n".format(res.tolist())
                )
            raise e

    # ------------------------- `query_bulk` tests -------------------------- #
    @pytest.mark.parametrize(
        "predicate, test_geom, expected",
        (
            (None, [(-1, -1, -0.5, -0.5)], [[], []]),
            (None, [(-0.5, -0.5, 0.5, 0.5)], [[0], [0]]),
            (None, [(0, 0, 1, 1)], [[0, 0], [0, 1]]),
            ("intersects", [(-1, -1, -0.5, -0.5)], [[], []]),
            ("intersects", [(-0.5, -0.5, 0.5, 0.5)], [[0], [0]]),
            ("intersects", [(0, 0, 1, 1)], [[0, 0], [0, 1]]),
            # only second geom intersects
            ("intersects", [(-1, -1, -0.5, -0.5), (-0.5, -0.5, 0.5, 0.5)], [[1], [0]]),
            # both geoms intersect
            (
                "intersects",
                [(-1, -1, 1, 1), (-0.5, -0.5, 0.5, 0.5)],
                [[0, 0, 1], [0, 1, 0]],
            ),
            ("within", [(0.25, 0.28, 0.75, 0.75)], [[], []]),  # does not intersect
            ("within", [(0, 0, 10, 10)], [[], []]),  # intersects but is not within
            ("within", [(11, 11, 12, 12)], [[0], [5]]),  # intersects and is within
            ("contains", [(0, 0, 1, 1)], [[], []]),  # intersects but does not contain
            (
                "contains",
                [(0, 0, 1.001, 1.001)],
                [[0], [1]],
            ),  # intersects 2 and contains 1
            (
                "contains",
                [(0.5, 0.5, 1.001, 1.001)],
                [[0], [1]],
            ),  # intersects 1 and contains 1
            ("contains", [(0.5, 0.5, 1.5, 1.5)], [[0], [1]]),  # intersects and contains
            (
                "contains",
                [(-1, -1, 2, 2)],
                [[0, 0], [0, 1]],
            ),  # intersects and contains multiple
        ),
    )
    def test_query_bulk(self, predicate, test_geom, expected):
        """Tests the `query_bulk` method with valid
        inputs and valid predicates.
        """
        # pass through GeoSeries to have GeoPandas
        # determine if it should use shapely or pygeos geometry objects
        test_geom = geopandas.GeoSeries(
            [box(*geom) for geom in test_geom], index=range(len(test_geom))
        )
        res = self.df.sindex.query_bulk(test_geom, predicate=predicate)
        assert_array_equal(res, expected)

    @pytest.mark.parametrize(
        "test_geoms, expected_value",
        [
            # single empty geometry
            ([GeometryCollection()], [[], []]),
            # None should be skipped
            ([GeometryCollection(), None], [[], []]),
            ([None], [[], []]),
            ([None, box(-0.5, -0.5, 0.5, 0.5), None], [[1], [0]]),
        ],
    )
    def test_query_bulk_empty_geometry(self, test_geoms, expected_value):
        """Tests the `query_bulk` method with an empty geometry.
        """
        # pass through GeoSeries to have GeoPandas
        # determine if it should use shapely or pygeos geometry objects
        # note: for this test, test_geoms (note plural) is a list already
        test_geoms = geopandas.GeoSeries(test_geoms, index=range(len(test_geoms)))
        res = self.df.sindex.query_bulk(test_geoms)
        assert_array_equal(res, expected_value)

    def test_query_bulk_empty_input_array(self):
        """Tests the `query_bulk` method with an empty input array.
        """
        test_array = np.array([], dtype=object)
        expected_value = [[], []]
        res = self.df.sindex.query_bulk(test_array)
        assert_array_equal(res, expected_value)

    def test_query_bulk_invalid_input_geometry(self):
        """Tests the `query_bulk` method with invalid input for the `geometry` parameter.
        """
        test_array = "notanarray"
        with pytest.raises(TypeError):
            self.df.sindex.query_bulk(test_array)

    def test_query_bulk_invalid_predicate(self):
        """Tests the `query_bulk` method with invalid predicates.
        """
        test_geom_bounds = (-1, -1, -0.5, -0.5)
        test_predicate = "test"

        # pass through GeoSeries to have GeoPandas
        # determine if it should use shapely or pygeos geometry objects
        test_geom = geopandas.GeoSeries([box(*test_geom_bounds)], index=["0"])

        with pytest.raises(ValueError):
            self.df.sindex.query_bulk(test_geom.geometry, predicate=test_predicate)

    @pytest.mark.parametrize(
        "predicate, test_geom, expected",
        (
            (None, (-1, -1, -0.5, -0.5), [[], []]),
            ("intersects", (-1, -1, -0.5, -0.5), [[], []]),
            ("contains", (-1, -1, 1, 1), [[0], [0]]),
        ),
    )
    def test_query_bulk_input_type(self, predicate, test_geom, expected):
        """Tests that query_bulk can accept a GeoSeries, GeometryArray or
        numpy array.
        """
        # pass through GeoSeries to have GeoPandas
        # determine if it should use shapely or pygeos geometry objects
        test_geom = geopandas.GeoSeries([box(*test_geom)], index=["0"])

        # test GeoSeries
        res = self.df.sindex.query_bulk(test_geom, predicate=predicate)
        assert_array_equal(res, expected)

        # test GeometryArray
        res = self.df.sindex.query_bulk(test_geom.geometry, predicate=predicate)
        assert_array_equal(res, expected)
        res = self.df.sindex.query_bulk(test_geom.geometry.values, predicate=predicate)
        assert_array_equal(res, expected)

        # test numpy array
        res = self.df.sindex.query_bulk(
            test_geom.geometry.values.data, predicate=predicate
        )
        assert_array_equal(res, expected)
        res = self.df.sindex.query_bulk(
            test_geom.geometry.values.data, predicate=predicate
        )
        assert_array_equal(res, expected)

    @pytest.mark.parametrize(
        "sort, expected",
        (
            (True, [[0, 0, 0], [0, 1, 2]]),
            # False could be anything, at least we'll know if it changes
            (False, [[0, 0, 0], [0, 1, 2]]),
        ),
    )
    def test_query_bulk_sorting(self, sort, expected):
        """Check that results from `query_bulk` don't depend
        on the order of geometries.
        """
        # these geometries come from a reported issue:
        # https://github.com/geopandas/geopandas/issues/1337
        # there is no theoretical reason they were chosen
        test_polys = GeoSeries([Polygon([(1, 1), (3, 1), (3, 3), (1, 3)])])
        tree_polys = GeoSeries(
            [
                Polygon([(1, 1), (3, 1), (3, 3), (1, 3)]),
                Polygon([(-1, 1), (1, 1), (1, 3), (-1, 3)]),
                Polygon([(3, 3), (5, 3), (5, 5), (3, 5)]),
            ]
        )

        # pass through GeoSeries to have GeoPandas
        # determine if it should use shapely or pygeos geometry objects
        tree_df = geopandas.GeoDataFrame(geometry=tree_polys)
        test_df = geopandas.GeoDataFrame(geometry=test_polys)

        res = tree_df.sindex.query_bulk(test_df.geometry, sort=sort)
        try:
            assert_array_equal(res, expected)
        except AssertionError as e:
            if not compat.USE_PYGEOS and sort is False:
                pytest.xfail(
                    "rtree results are known to be unordered, see "
                    "https://github.com/geopandas/geopandas/issues/1337\n"
                    "Expected:\n {}\n".format(expected)
                    + "Got:\n {}\n".format(res.tolist())
                )
            raise e

    # --------------------------- misc tests ---------------------------- #

    def test_empty_tree_geometries(self):
        """Tests building sindex with interleaved empty geometries.
        """
        geoms = [Point(0, 0), None, Point(), Point(1, 1), Point()]
        df = geopandas.GeoDataFrame(geometry=geoms)
        assert df.sindex.query(Point(1, 1))[0] == 3

    def test_size(self):
        """Tests the `size` property."""
        assert self.df.sindex.size == self.expected_size

    def test_len(self):
        """Tests the `__len__` method of spatial indexes."""
        assert len(self.df.sindex) == self.expected_size

    def test_is_empty(self):
        """Tests the `is_empty` property."""
        # create empty tree
        cls_ = sindex.get_sindex_class()
        empty = geopandas.GeoSeries(dtype=object)
        tree = cls_(empty)
        assert tree.is_empty
        # create a non-empty tree
        non_empty = geopandas.GeoSeries([Point(0, 0)])
        tree = cls_(non_empty)
        assert not tree.is_empty

    @pytest.mark.parametrize(
        "predicate, expected_shape",
        [
            (None, (2, 396)),
            ("intersects", (2, 172)),
            ("within", (2, 172)),
            ("contains", (2, 0)),
            ("overlaps", (2, 0)),
            ("crosses", (2, 0)),
            ("touches", (2, 0)),
        ],
    )
    def test_integration_natural_earth(self, predicate, expected_shape):
        """Tests output sizes for the naturalearth datasets."""
        world = read_file(datasets.get_path("naturalearth_lowres"))
        capitals = read_file(datasets.get_path("naturalearth_cities"))

        res = world.sindex.query_bulk(capitals.geometry, predicate)
        assert res.shape == expected_shape