File: test_624_global_bspline_interpolation.py

package info (click to toggle)
ezdxf 1.4.1-1
  • links: PTS, VCS
  • area: main
  • in suites: forky, sid, trixie
  • size: 104,528 kB
  • sloc: python: 182,341; makefile: 116; lisp: 20; ansic: 4
file content (312 lines) | stat: -rw-r--r-- 10,557 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
from typing import List
import pytest
import ezdxf
import math
from math import isclose
from ezdxf.math import Vec3, global_bspline_interpolation, close_vectors, cad_fit_point_interpolation
from ezdxf.math.parametrize import (
    uniform_t_vector,
    distance_t_vector,
    centripetal_t_vector,
    arc_t_vector,
    arc_distances,
    estimate_tangents,
)
from ezdxf.math.bspline import (
    knots_from_parametrization,
    required_knot_values,
    averaged_knots_unconstrained,
    natural_knots_constrained,
    averaged_knots_constrained,
    natural_knots_unconstrained,
    double_knots,
    create_t_vector,
)

POINTS1 = Vec3.list([(1, 1), (2, 4), (4, 1), (7, 6)])
POINTS2 = Vec3.list([(1, 1), (2, 4), (4, 1), (7, 6), (5, 8), (3, 3), (1, 7)])


@pytest.fixture(params=[POINTS1, POINTS2])
def fit_points(request):
    return request.param


def test_uniform_t_array(fit_points):
    t_vector = list(uniform_t_vector(len(fit_points)))
    assert len(t_vector) == len(fit_points)
    assert t_vector[0] == 0.0
    assert t_vector[-1] == 1.0
    for t1, t2 in zip(t_vector, t_vector[1:]):
        assert t1 <= t2


def test_chord_length_t_array(fit_points):
    t_vector = list(distance_t_vector(fit_points))
    assert len(t_vector) == len(fit_points)
    assert t_vector[0] == 0.0
    assert t_vector[-1] == pytest.approx(1.0)
    for t1, t2 in zip(t_vector, t_vector[1:]):
        assert t1 <= t2


def test_centripetal_length_t_array(fit_points):
    t_vector = list(centripetal_t_vector(fit_points))
    assert len(t_vector) == len(fit_points)
    assert t_vector[0] == 0.0
    assert t_vector[-1] == pytest.approx(1.0)
    for t1, t2 in zip(t_vector, t_vector[1:]):
        assert t1 <= t2


def test_arc_distances():
    p = Vec3.list([(0, 0), (2, 2), (4, 0), (6, -2), (8, 0)])
    # p[1]..p[3] are a straight line, radius calculation fails and
    # a straight line from p[1] to p[2] is used as replacement
    # for the second arc
    radius = 2.0
    arc_length = math.pi * 0.5 * radius
    diagonal = math.sqrt(2.0) * radius
    distances = list(arc_distances(p))
    assert len(distances) == 4
    assert isclose(distances[0], arc_length)
    assert isclose(distances[1], diagonal)  # replacement for arc
    assert isclose(distances[2], arc_length)
    assert isclose(distances[3], arc_length)


def test_arc_length_t_array(fit_points):
    t_vector = list(arc_t_vector(fit_points))
    assert len(t_vector) == len(fit_points)
    assert t_vector[0] == 0.0
    assert t_vector[-1] == pytest.approx(1.0)
    for t1, t2 in zip(t_vector, t_vector[1:]):
        assert t1 <= t2


def test_invalid_order_count_combination():
    count = 4
    order = 5
    with pytest.raises(ezdxf.DXFValueError):
        required_knot_values(count, order)
    with pytest.raises(ezdxf.DXFValueError):
        list(knots_from_parametrization(n=count - 1, p=order - 1, t=[]))


def check_knots(count: int, order: int, knots: List[float]):
    assert len(knots) == required_knot_values(count, order)
    assert len(set(knots[:order])) == 1, "first order elements have to be equal"
    assert len(set(knots[-order:])) == 1, "last order elements have to be equal"
    for k1, k2 in zip(knots, knots[1:]):
        assert k1 <= k2


@pytest.mark.parametrize("p", (2, 3, 4))
@pytest.mark.parametrize("method", ("average", "natural"))
def test_knot_generation(p, method):
    fit_points = Vec3.list(
        [
            (0, 0),
            (0, 10),
            (10, 10),
            (20, 10),
            (20, 0),
            (30, 0),
            (30, 10),
            (40, 10),
            (40, 0),
        ]
    )
    count = len(fit_points)
    n = count - 1
    order = p + 1
    t_vector = distance_t_vector(fit_points)
    knots = list(knots_from_parametrization(n, p, t_vector, method))
    check_knots(n + 1, p + 1, knots)


@pytest.fixture
def fit_points_2():
    return Vec3.list(
        [
            (0, 0),
            (0, 10),
            (10, 10),
            (20, 10),
            (20, 0),
            (30, 0),
            (30, 10),
            (40, 10),
            (40, 0),
        ]
    )


@pytest.mark.parametrize("p", (2, 3, 4, 5))
def test_unconstrained_averaged_knots(p, fit_points_2):
    t_vector = list(distance_t_vector(fit_points_2))
    n = len(fit_points_2) - 1

    knots = averaged_knots_unconstrained(n, p, t_vector)
    check_knots(n + 1, p + 1, knots)


@pytest.mark.parametrize("p", (2, 3, 4, 5))
def test_constrained_averaged_knots(p, fit_points_2):
    t_vector = list(distance_t_vector(fit_points_2))
    n = len(fit_points_2) - 1

    # add 2 knots for tangents
    knots = averaged_knots_constrained(n + 2, p, t_vector)
    check_knots(n + 3, p + 1, knots)


@pytest.mark.parametrize("p", (2, 3, 4, 5))
def test_unconstrained_natural_knots(p, fit_points_2):
    t_vector = list(distance_t_vector(fit_points_2))
    n = len(fit_points_2) - 1

    # add 2 knots for tangents
    knots = natural_knots_unconstrained(n, p, t_vector)
    check_knots(n + 1, p + 1, knots)


@pytest.mark.parametrize("p", (2, 3, 4, 5))
def test_constrained_natural_knots(p, fit_points_2):
    t_vector = list(distance_t_vector(fit_points_2))
    n = len(fit_points_2) - 1

    # add 2 knots for tangents
    knots = natural_knots_constrained(n + 2, p, t_vector)
    check_knots(n + 3, p + 1, knots)


@pytest.mark.parametrize("p", (2, 3, 4, 5))
def test_double_knots(p, fit_points_2):
    t_vector = list(distance_t_vector(fit_points_2))
    n = len(fit_points_2) - 1

    # create knots for each control point and 1st derivative
    knots = double_knots(n, p, t_vector)
    check_knots((n + 1) * 2, p + 1, knots)


def test_bspline_interpolation(fit_points):
    spline = global_bspline_interpolation(fit_points, degree=3, method="chord")
    assert len(spline.control_points) == len(fit_points)

    t_array = list(create_t_vector(fit_points, "chord"))
    assert t_array[0] == 0.0
    assert t_array[-1] == pytest.approx(1.0)
    assert len(t_array) == len(fit_points)

    t_points = [spline.point(t) for t in t_array]
    assert close_vectors(t_points, fit_points)


@pytest.mark.parametrize("method", ["distance", "centripetal", "arc"])
def test_create_t_vectors_for_identical_points(method):
    assert len(list(create_t_vector(Vec3.list([(0, 0), (0, 0)]), method))) == 0


def test_bspline_interpolation_first_derivatives(fit_points):
    tangents = estimate_tangents(fit_points)
    spline = global_bspline_interpolation(
        fit_points, degree=3, tangents=tangents
    )
    assert len(spline.control_points) == 2 * len(fit_points)


expected = [
    (0.0, 0.0),
    (0.010310831479728222, 0.32375901937484741),
    (0.030277278274297714, 0.6140977144241333),
    (0.059526983648538589, 0.87245100736618042),
    (0.097687594592571259, 1.1002539396286011),
    (0.14438676834106445, 1.2989413738250732),
    (0.19925214350223541, 1.469948410987854),
    (0.26191136240959167, 1.6147100925445557),
    (0.33199205994606018, 1.7346612215042114),
    (0.40912193059921265, 1.8312369585037231),
    (0.49292856454849243, 1.9058722257614136),
    (0.58303964138031006, 1.9600019454956055),
    (0.67908281087875366, 1.9950611591339111),
    (0.78068572282791138, 2.0124847888946533),
    (0.88747602701187134, 2.0137078762054443),
    (0.9990813136100769, 2.0001654624938965),
    (1.1151292324066162, 1.973292350769043),
    (1.2352476119995117, 1.9345237016677856),
    (1.3590638637542725, 1.8852944374084473),
    (1.4862056970596313, 1.8270395994186401),
    (1.6163008213043213, 1.761194109916687),
    (1.7489768266677856, 1.6891928911209106),
    (1.8838614225387573, 1.6124709844589233),
    (2.0205821990966797, 1.532463550567627),
    (2.1587669849395752, 1.4506052732467651),
    (2.2980430126190186, 1.3683313131332397),
    (2.4380383491516113, 1.2870765924453735),
    (2.5783803462982178, 1.2082761526107788),
    (2.7186968326568604, 1.1333650350570679),
    (2.8586153984069824, 1.0637780427932739),
    (2.9977638721466064, 1.0009502172470093),
    (3.1357693672180176, 0.94631654024124146),
    (3.2722601890563965, 0.90131211280822754),
    (3.4068636894226074, 0.86737185716629028),
    (3.5392072200775146, 0.84593069553375244),
    (3.6689188480377197, 0.83842372894287109),
    (3.795626163482666, 0.84628582000732422),
    (3.9189567565917969, 0.87095201015472412),
    (4.0385379791259766, 0.91385728120803833),
    (4.1539978981018066, 0.97643661499023438),
    (4.2649641036987305, 1.0601249933242798),
    (4.3710641860961914, 1.1663573980331421),
    (4.4719257354736328, 1.2965688705444336),
    (4.567176342010498, 1.4521942138671875),
    (4.6564435958862305, 1.6346687078475952),
    (4.7393555641174316, 1.8454270362854004),
    (4.8155393600463867, 2.0859043598175049),
    (4.8846230506896973, 2.3575356006622314),
    (4.9462337493896484, 2.6617558002471924),
    (5.0, 3.0),
]


def test_check_values():
    test_points = [(0.0, 0.0), (1.0, 2.0), (3.0, 1.0), (5.0, 3.0)]
    spline = global_bspline_interpolation(
        test_points, degree=3, method="distance"
    )
    result = list(spline.approximate(49))
    assert len(result) == 50
    for p1, p2 in zip(result, expected):
        assert isclose(p1[0], p2[0], abs_tol=1e-6)
        assert isclose(p1[1], p2[1], abs_tol=1e-6)


def test_cad_fit_point_interpolation_for_2_points():
    points = Vec3.list([(0, 0), (0, 10)])
    control_points, knots = cad_fit_point_interpolation(points)
    assert control_points[0].isclose(points[0])
    assert control_points[-1].isclose(points[-1])
    assert len(control_points) == 4
    assert len(knots) == required_knot_values(4, 4) == 8


def test_cad_fit_point_interpolation_for_5_points():
    points = Vec3.list([(0, 0), (0, 10), (10, 10), (20, 10), (20, 0)])
    control_points, knots = cad_fit_point_interpolation(points)
    assert len(control_points) == 7
    assert len(knots) == required_knot_values(7, 4) == 11

    # Checked visually by BricsCAD 2022 and TrueView 2022:
    # See function check_visually_fit_points_to_cad_cv() in script
    # exploration/spline_end_tangent_estimation.py
    assert control_points[0].isclose(points[0])
    assert control_points[1].isclose(Vec3(-0.8333333333333334, 4.285714285714286, -0.0))
    assert control_points[2].isclose(Vec3(-2.5, 12.857142857142858, 0.0))
    assert control_points[3].isclose(Vec3(10.0, 8.571428571428573, 0.0))
    assert control_points[4].isclose(Vec3(22.5, 12.857142857142858, 0.0))
    assert control_points[5].isclose(Vec3(20.833333333333332, 4.2857142857142865, -0.0))
    assert control_points[6].isclose(points[-1])