Skip to content

Shapes class

mdna.utils.Shapes

Class for generating parametric shapes in 3D space.

Source code in mdna/utils.py 
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
class Shapes:
    """Class for generating parametric shapes in 3D space.
    """

    def __init__(self, parametric_function, t_values=None, num_points=100):
        self.num_points = num_points
        self.parametric_function = parametric_function
        self.points = self._generate_points(t_values)

    def _generate_points(self,t_values=None):
        x_values, y_values, z_values = self.parametric_function(t_values)
        return np.stack((x_values, y_values, z_values), axis=1)

    @classmethod
    def circle(cls, radius=1, t_values=None, num_points=100):
        """Create a circle in 3D space.

        Args:
            radius (int, optional): _description_. Defaults to 1.
            t_values (_type_, optional): _description_. Defaults to None.
            num_points (int, optional): _description_. Defaults to 100.

        Returns:
            points (np.ndarray): points on the circle of shape (num_points, 3)
        """
        if t_values is None:
            t_values = np.linspace(0, 2 * np.pi, num=num_points)
        parametric_function = lambda t_values: (
            radius * np.cos(t_values),
            radius * np.sin(t_values),
            np.zeros_like(t_values)
        )
        return cls(parametric_function, t_values, num_points=num_points).points

    @classmethod
    def line(cls, length=1, num_points=100):
        """Create a line in 3D space.

        Args:
            length (int, optional): _description_. Defaults to 1.
            num_points (int, optional): _description_. Defaults to 100.

        Returns:
            points (np.ndarray): points on the line of shape (num_points, 3)
        """
        t_values = np.linspace(0, 1, num=num_points)
        parametric_function = lambda t_values: (
            t_values * length,
            np.zeros_like(t_values),
            np.zeros_like(t_values)
        )
        return cls(parametric_function, t_values, num_points=num_points).points

    @classmethod
    def helix(cls, radius=1, pitch=1, height=1, num_turns=1, num_points=100):
        """Create a helix in 3D space.

        Args:
            radius (int, optional): _description_. Defaults to 1.
            pitch (int, optional): _description_. Defaults to 1.
            height (int, optional): _description_. Defaults to 1.
            num_turns (int, optional): _description_. Defaults to 1.
            num_points (int, optional): _description_. Defaults to 100.

        Returns:
            points (np.ndarray): points on the helix of shape (num_points, 3)
        """
        t_values = np.linspace(0, num_turns * 2 * np.pi, num=num_points)
        parametric_function = lambda t_values: (
            radius * np.cos(t_values),
            radius * np.sin(t_values),
            height * t_values / (2 * np.pi) - pitch * num_turns * t_values / (2 * np.pi)
        )
        return cls(parametric_function, t_values, num_points=num_points).points

    @classmethod
    def spiral(cls, radius=1, pitch=1, height=1, num_turns=1, num_points=100):
        """Create a spiral in 3D space.

        Args:
            radius (int, optional): _description_. Defaults to 1.
            pitch (int, optional): _description_. Defaults to 1.
            height (int, optional): _description_. Defaults to 1.
            num_turns (int, optional): _description_. Defaults to 1.
            num_points (int, optional): _description_. Defaults to 100.

        Returns:
            points (np.ndarray): points on the spiral of shape (num_points, 3)
        """
        t_values = np.linspace(0, num_turns * 2 * np.pi, num=num_points)
        parametric_function = lambda t_values: (
            radius * t_values * np.cos(t_values),
            radius * t_values * np.sin(t_values),
            height * t_values / (2 * np.pi) * pitch
        )
        return cls(parametric_function, t_values, num_points=num_points).points

    @classmethod
    def mobius_strip(cls, radius=1, width=0.5, num_twists=1, t_values=None, num_points=100):
        """Create a Mobius strip in 3D space.

        Args:
            radius (int, optional): _description_. Defaults to 1.
            width (float, optional): _description_. Defaults to 0.5.
            num_twists (int, optional): _description_. Defaults to 1.
            t_values (_type_, optional): _description_. Defaults to None.
            num_points (int, optional): _description_. Defaults to 100.

        Returns:
            points (np.ndarray): points on the Mobius strip of shape (num_points, 3)
        """
        if t_values is None:
            t_values = np.linspace(0, 2 * np.pi, num=num_points)
        u_values = np.linspace(0, width, num=num_points)
        u, t = np.meshgrid(u_values, t_values)
        x_values = (radius + u * np.cos(t / 2) * np.cos(num_twists * t)) * np.cos(t)
        y_values = (radius + u * np.cos(t / 2) * np.cos(num_twists * t)) * np.sin(t)
        z_values = u * np.sin(t / 2) * np.cos(num_twists * t)
        parametric_function = lambda t_values: (
            x_values.flatten(),
            y_values.flatten(),
            z_values.flatten()
        )
        return cls(parametric_function, t_values, num_points=num_points).points

    @classmethod
    def square(cls, side_length=1,t_values=None,num_points=100):
        """Create a square in 3D space.

        Args:
            side_length (int, optional): _description_. Defaults to 1.
            t_values (_type_, optional): _description_. Defaults to None.
            num_points (int, optional): _description_. Defaults to 100.

        Returns:
            points (np.ndarray): points on the square of shape (num_points, 3)
        """
        if t_values is None:
            t_values = np.linspace(0, 1, num=num_points)
        parametric_function = lambda t_values: (
            side_length * (2 * (t_values < 0.25) - 1),
            side_length * (2 * (t_values >= 0.25) & (t_values < 0.5)) - side_length,
            np.zeros_like(t_values)
        )
        return cls(parametric_function, t_values).points

    @classmethod
    def trefoil(cls, radius=1, num_turns=1,t_values=None,num_points=100):
        """Create a trefoil knot in 3D space.

        Args:
            radius (int, optional): _description_. Defaults to 1.
            num_turns (int, optional): _description_. Defaults to 1.
            t_values (_type_, optional): _description_. Defaults to None.
            num_points (int, optional): _description_. Defaults to 100.

        Returns:
            points (np.ndarray): points on the trefoil knot of shape (num_points, 3)
        """
        if t_values is None:
            t_values = np.linspace(0, num_turns * 2 * np.pi, num=num_points)
        x_values = np.sin(t_values) + 2 * np.sin(2 * t_values)
        y_values = np.cos(t_values) - 2 * np.cos(2 * t_values)
        z_values = -np.sin(3 * t_values)
        parametric_function = lambda t_values: (
            radius * x_values,
            radius * y_values,
            radius * z_values
        )
        return cls(parametric_function, t_values).points

    @classmethod
    def square(cls, side=1, t_values=None,num_points=100):
        """Create a square in 3D space.

        Args:
            side (int, optional): _description_. Defaults to 1.
            t_values (_type_, optional): _description_. Defaults to None.
            num_points (int, optional): _description_. Defaults to 100.

        Returns:
            points (np.ndarray): points on the square of shape (num_points, 3)
        """
        if t_values is None:
            t_values = np.linspace(0, 4, num=num_points)
        # Calculate x and y coordinates based on t_values
        x_values = np.zeros_like(t_values)
        y_values = np.zeros_like(t_values)
        for i, t in enumerate(t_values):
            if 0 <= t < 1:
                x_values[i] = t * side
                y_values[i] = 0
            elif 1 <= t < 2:
                x_values[i] = side
                y_values[i] = (t - 1) * side
            elif 2 <= t < 3:
                x_values[i] = (3 - t) * side
                y_values[i] = side
            elif 3 <= t <= 4:
                x_values[i] = 0
                y_values[i] = (4 - t) * side
        z_values = np.zeros_like(t_values)
        parametric_function = lambda t_values: (
            x_values,
            y_values,
            z_values
        )
        return cls(parametric_function, t_values).points

    @classmethod
    def heart(cls, a=1, b=1, c=1,t_values=None,num_points=100):
        """Create a heart shape in 3D space.

        Args:
            a (int, optional): _description_. Defaults to 1.
            b (int, optional): _description_. Defaults to 1.
            c (int, optional): _description_. Defaults to 1.
            t_values (_type_, optional): _description_. Defaults to None.
            num_points (int, optional): _description_. Defaults to 100.

        Returns:
            points (np.ndarray): points on the heart shape of shape (num_points, 3)
        """
        if t_values is None:
            t_values = np.linspace(-np.pi, np.pi, num=num_points)
        x_values = a * np.sin(t_values) ** 3
        y_values = b * np.cos(t_values) - c * np.cos(2 * t_values)
        z_values = np.zeros_like(t_values)
        parametric_function = lambda t_values: (x_values, y_values, z_values)
        return cls(parametric_function, t_values).points

    @classmethod
    def ellipse(cls, a=1, b=1, t_values=None,num_points=100):
        """Create an ellipse in 3D space.

        Args:
            a (int, optional): _description_. Defaults to 1.
            b (int, optional): _description_. Defaults to 1.
            t_values (_type_, optional): _description_. Defaults to None.
            num_points (int, optional): _description_. Defaults to 100.

        Returns:
            points (np.ndarray): points on the ellipse of shape (num_points, 3) 
        """
        if t_values is None:
            t_values = np.linspace(0, 2 * np.pi, num=num_points)
        x_values = a * np.cos(t_values)
        y_values = b * np.sin(t_values)
        z_values = np.zeros_like(t_values)
        parametric_function = lambda t_values: (x_values, y_values, z_values)
        return cls(parametric_function, t_values).points

    @classmethod
    def lemniscate_of_bernoulli(cls, a=1, b=1, t_values=None,num_points=100):
        """Create a lemniscate of Bernoulli in 3D space.

        Args:
            a (int, optional): _description_. Defaults to 1.
            b (int, optional): _description_. Defaults to 1.
            t_values (_type_, optional): _description_. Defaults to None.
            num_points (int, optional): _description_. Defaults to 100.

        Returns:
            points (np.ndarray): points on the leminscate of Bernouli of shape (num_points, 3)
        """
        if t_values is None:
            t_values = np.linspace(0, 2 * np.pi, num=num_points)
        x_values = a * np.sqrt(2) * np.cos(t_values) / (np.sin(t_values) ** 2 + 1)
        y_values = b * np.sqrt(2) * np.cos(t_values) * np.sin(t_values) / (np.sin(t_values) ** 2 + 1)
        z_values = np.zeros_like(t_values)
        parametric_function = lambda t_values: (x_values, y_values, z_values)
        return cls(parametric_function, t_values).points

    @classmethod
    def torus_helix(cls, R=1, r=2, num_windings=3, t_values=None, num_points=100):
        """Create a torus helix in 3D space.

        Args:
            R (int, optional): _description_. Defaults to 1.
            r (int, optional): _description_. Defaults to 2.
            num_windings (int, optional): _description_. Defaults to 3.
            t_values (_type_, optional): _description_. Defaults to None.
            num_points (int, optional): _description_. Defaults to 100.

        Returns:
            points (np.ndarray): points on the torus helix of shape (num_points, 3)
        """
        if t_values is None:
            t_values = np.linspace(0, 2 * np.pi, num=num_points)

        parametric_function = lambda t_values: (
            (R + r * np.cos(num_windings*t_values)) * np.cos( t_values),
            (R + r * np.cos(num_windings*t_values)) * np.sin( t_values),
            r * np.sin(t_values)
        )
        return cls(parametric_function, t_values, num_points=num_points).points

    @classmethod
    def bonus(cls, t_values=None,num_points=100):
        """Create a bonus shape in 3D space.

        Credit: https://www.geogebra.org/m/pH8wD3rW, Author:Simona Riva"

        Args:
            t_values (_type_, optional): _description_. Defaults to None.
            num_points (int, optional): _description_. Defaults to 100.

        Returns:
            points (np.ndarray): points on the bonus function of shape (num_points, 3)
        """
        if t_values is None:
            t_values = np.linspace(0, 2 * np.pi, num=num_points)
        t = t_values
        parametric_function = lambda t: (
                                        -(721*np.sin(t))/4 + 196/3*np.sin(2*t) - 86/3*np.sin(3*t) - 131/2*np.sin(4*t) + 477/14*np.sin(5*t) 
                                        + 27*np.sin(6*t) - 29/2*np.sin(7*t) + 68/5*np.sin(8*t) + 1/10*np.sin(9*t) + 23/4*np.sin(10*t) 
                                        - 19/2*np.sin(12*t) - 85/21*np.sin(13*t) + 2/3*np.sin(14*t) + 27/5*np.sin(15*t) + 7/4*np.sin(16*t) 
                                        + 17/9*np.sin(17*t) - 4*np.sin(18*t) - 1/2*np.sin(19*t) + 1/6*np.sin(20*t) + 6/7*np.sin(21*t) 
                                        - 1/8*np.sin(22*t) + 1/3*np.sin(23*t) + 3/2*np.sin(24*t) + 13/5*np.sin(25*t) + np.sin(26*t) 
                                        - 2*np.sin(27*t) + 3/5*np.sin(28*t) - 1/5*np.sin(29*t) + 1/5*np.sin(30*t) + (2337*np.cos(t))/8 
                                        - 43/5*np.cos(2*t) + 322/5*np.cos(3*t) - 117/5*np.cos(4*t) - 26/5*np.cos(5*t) - 23/3*np.cos(6*t) 
                                        + 143/4*np.cos(7*t) - 11/4*np.cos(8*t) - 31/3*np.cos(9*t) - 13/4*np.cos(10*t) - 9/2*np.cos(11*t) 
                                        + 41/20*np.cos(12*t) + 8*np.cos(13*t) + 2/3*np.cos(14*t) + 6*np.cos(15*t) + 17/4*np.cos(16*t) 
                                        - 3/2*np.cos(17*t) - 29/10*np.cos(18*t) + 11/6*np.cos(19*t) + 12/5*np.cos(20*t) + 3/2*np.cos(21*t) 
                                        + 11/12*np.cos(22*t) - 4/5*np.cos(23*t) + np.cos(24*t) + 17/8*np.cos(25*t) - 7/2*np.cos(26*t) 
                                        - 5/6*np.cos(27*t) - 11/10*np.cos(28*t) + 1/2*np.cos(29*t) - 1/5*np.cos(30*t),
                                        -(637/2)*np.sin(t) - (188/5)*np.sin(2*t) - (11/7)*np.sin(3*t) - (12/5)*np.sin(4*t) + (11/3)*np.sin(5*t)
                                        - (37/4)*np.sin(6*t) + (8/3)*np.sin(7*t) + (65/6)*np.sin(8*t) - (32/5)*np.sin(9*t) - (41/4)*np.sin(10*t)
                                        - (38/3)*np.sin(11*t) - (47/8)*np.sin(12*t) + (5/4)*np.sin(13*t) - (41/7)*np.sin(14*t) - (7/3)*np.sin(15*t)
                                        - (13/7)*np.sin(16*t) + (17/4)*np.sin(17*t) - (9/4)*np.sin(18*t) + (8/9)*np.sin(19*t) + (3/5)*np.sin(20*t)
                                        - (2/5)*np.sin(21*t) + (4/3)*np.sin(22*t) + (1/3)*np.sin(23*t) + (3/5)*np.sin(24*t) - (3/5)*np.sin(25*t)
                                        + (6/5)*np.sin(26*t) - (1/5)*np.sin(27*t) + (10/9)*np.sin(28*t) + (1/3)*np.sin(29*t) - (3/4)*np.sin(30*t)
                                        - (125/2)*np.cos(t) - (521/9)*np.cos(2*t) - (359/3)*np.cos(3*t) + (47/3)*np.cos(4*t) - (33/2)*np.cos(5*t)
                                        - (5/4)*np.cos(6*t) + (31/8)*np.cos(7*t) + (9/10)*np.cos(8*t) - (119/4)*np.cos(9*t) - (17/2)*np.cos(10*t)
                                        + (22/3)*np.cos(11*t) + (15/4)*np.cos(12*t) - (5/2)*np.cos(13*t) + (19/6)*np.cos(14*t) + (7/4)*np.cos(15*t)
                                        + (31/4)*np.cos(16*t) - np.cos(17*t) + (11/10)*np.cos(18*t) - (2/3)*np.cos(19*t) + (13/3)*np.cos(20*t)
                                        - (5/4)*np.cos(21*t) + (2/3)*np.cos(22*t) + (1/4)*np.cos(23*t) + (5/6)*np.cos(24*t) + (3/4)*np.cos(26*t)
                                        - (1/2)*np.cos(27*t) - (1/10)*np.cos(28*t) - (1/3)*np.cos(29*t) - (1/19)*np.cos(30*t),
                                        np.zeros_like(t))
        return cls(parametric_function, t_values).points*0.1

bonus(t_values=None, num_points=100) classmethod

Create a bonus shape in 3D space.

Credit: https://www.geogebra.org/m/pH8wD3rW, Author:Simona Riva"

Parameters:

Name Type Description Default
t_values _type_

description. Defaults to None.

 None
num_points int

description. Defaults to 100.

 100

Returns:

Name Type Description
points ndarray

points on the bonus function of shape (num_points, 3)
Source code in mdna/utils.py 
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
@classmethod
def bonus(cls, t_values=None,num_points=100):
    """Create a bonus shape in 3D space.

    Credit: https://www.geogebra.org/m/pH8wD3rW, Author:Simona Riva"

    Args:
        t_values (_type_, optional): _description_. Defaults to None.
        num_points (int, optional): _description_. Defaults to 100.

    Returns:
        points (np.ndarray): points on the bonus function of shape (num_points, 3)
    """
    if t_values is None:
        t_values = np.linspace(0, 2 * np.pi, num=num_points)
    t = t_values
    parametric_function = lambda t: (
                                    -(721*np.sin(t))/4 + 196/3*np.sin(2*t) - 86/3*np.sin(3*t) - 131/2*np.sin(4*t) + 477/14*np.sin(5*t) 
                                    + 27*np.sin(6*t) - 29/2*np.sin(7*t) + 68/5*np.sin(8*t) + 1/10*np.sin(9*t) + 23/4*np.sin(10*t) 
                                    - 19/2*np.sin(12*t) - 85/21*np.sin(13*t) + 2/3*np.sin(14*t) + 27/5*np.sin(15*t) + 7/4*np.sin(16*t) 
                                    + 17/9*np.sin(17*t) - 4*np.sin(18*t) - 1/2*np.sin(19*t) + 1/6*np.sin(20*t) + 6/7*np.sin(21*t) 
                                    - 1/8*np.sin(22*t) + 1/3*np.sin(23*t) + 3/2*np.sin(24*t) + 13/5*np.sin(25*t) + np.sin(26*t) 
                                    - 2*np.sin(27*t) + 3/5*np.sin(28*t) - 1/5*np.sin(29*t) + 1/5*np.sin(30*t) + (2337*np.cos(t))/8 
                                    - 43/5*np.cos(2*t) + 322/5*np.cos(3*t) - 117/5*np.cos(4*t) - 26/5*np.cos(5*t) - 23/3*np.cos(6*t) 
                                    + 143/4*np.cos(7*t) - 11/4*np.cos(8*t) - 31/3*np.cos(9*t) - 13/4*np.cos(10*t) - 9/2*np.cos(11*t) 
                                    + 41/20*np.cos(12*t) + 8*np.cos(13*t) + 2/3*np.cos(14*t) + 6*np.cos(15*t) + 17/4*np.cos(16*t) 
                                    - 3/2*np.cos(17*t) - 29/10*np.cos(18*t) + 11/6*np.cos(19*t) + 12/5*np.cos(20*t) + 3/2*np.cos(21*t) 
                                    + 11/12*np.cos(22*t) - 4/5*np.cos(23*t) + np.cos(24*t) + 17/8*np.cos(25*t) - 7/2*np.cos(26*t) 
                                    - 5/6*np.cos(27*t) - 11/10*np.cos(28*t) + 1/2*np.cos(29*t) - 1/5*np.cos(30*t),
                                    -(637/2)*np.sin(t) - (188/5)*np.sin(2*t) - (11/7)*np.sin(3*t) - (12/5)*np.sin(4*t) + (11/3)*np.sin(5*t)
                                    - (37/4)*np.sin(6*t) + (8/3)*np.sin(7*t) + (65/6)*np.sin(8*t) - (32/5)*np.sin(9*t) - (41/4)*np.sin(10*t)
                                    - (38/3)*np.sin(11*t) - (47/8)*np.sin(12*t) + (5/4)*np.sin(13*t) - (41/7)*np.sin(14*t) - (7/3)*np.sin(15*t)
                                    - (13/7)*np.sin(16*t) + (17/4)*np.sin(17*t) - (9/4)*np.sin(18*t) + (8/9)*np.sin(19*t) + (3/5)*np.sin(20*t)
                                    - (2/5)*np.sin(21*t) + (4/3)*np.sin(22*t) + (1/3)*np.sin(23*t) + (3/5)*np.sin(24*t) - (3/5)*np.sin(25*t)
                                    + (6/5)*np.sin(26*t) - (1/5)*np.sin(27*t) + (10/9)*np.sin(28*t) + (1/3)*np.sin(29*t) - (3/4)*np.sin(30*t)
                                    - (125/2)*np.cos(t) - (521/9)*np.cos(2*t) - (359/3)*np.cos(3*t) + (47/3)*np.cos(4*t) - (33/2)*np.cos(5*t)
                                    - (5/4)*np.cos(6*t) + (31/8)*np.cos(7*t) + (9/10)*np.cos(8*t) - (119/4)*np.cos(9*t) - (17/2)*np.cos(10*t)
                                    + (22/3)*np.cos(11*t) + (15/4)*np.cos(12*t) - (5/2)*np.cos(13*t) + (19/6)*np.cos(14*t) + (7/4)*np.cos(15*t)
                                    + (31/4)*np.cos(16*t) - np.cos(17*t) + (11/10)*np.cos(18*t) - (2/3)*np.cos(19*t) + (13/3)*np.cos(20*t)
                                    - (5/4)*np.cos(21*t) + (2/3)*np.cos(22*t) + (1/4)*np.cos(23*t) + (5/6)*np.cos(24*t) + (3/4)*np.cos(26*t)
                                    - (1/2)*np.cos(27*t) - (1/10)*np.cos(28*t) - (1/3)*np.cos(29*t) - (1/19)*np.cos(30*t),
                                    np.zeros_like(t))
    return cls(parametric_function, t_values).points*0.1

circle(radius=1, t_values=None, num_points=100) classmethod

Create a circle in 3D space.

Parameters:

Name Type Description Default
radius int

description. Defaults to 1.

 1
t_values _type_

description. Defaults to None.

 None
num_points int

description. Defaults to 100.

 100

Returns:

Name Type Description
points ndarray

points on the circle of shape (num_points, 3)
Source code in mdna/utils.py 
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
@classmethod
def circle(cls, radius=1, t_values=None, num_points=100):
    """Create a circle in 3D space.

    Args:
        radius (int, optional): _description_. Defaults to 1.
        t_values (_type_, optional): _description_. Defaults to None.
        num_points (int, optional): _description_. Defaults to 100.

    Returns:
        points (np.ndarray): points on the circle of shape (num_points, 3)
    """
    if t_values is None:
        t_values = np.linspace(0, 2 * np.pi, num=num_points)
    parametric_function = lambda t_values: (
        radius * np.cos(t_values),
        radius * np.sin(t_values),
        np.zeros_like(t_values)
    )
    return cls(parametric_function, t_values, num_points=num_points).points

ellipse(a=1, b=1, t_values=None, num_points=100) classmethod

Create an ellipse in 3D space.

Parameters:

Name Type Description Default
a int

description. Defaults to 1.

 1
b int

description. Defaults to 1.

 1
t_values _type_

description. Defaults to None.

 None
num_points int

description. Defaults to 100.

 100

Returns:

Name Type Description
points ndarray

points on the ellipse of shape (num_points, 3)
Source code in mdna/utils.py 
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
@classmethod
def ellipse(cls, a=1, b=1, t_values=None,num_points=100):
    """Create an ellipse in 3D space.

    Args:
        a (int, optional): _description_. Defaults to 1.
        b (int, optional): _description_. Defaults to 1.
        t_values (_type_, optional): _description_. Defaults to None.
        num_points (int, optional): _description_. Defaults to 100.

    Returns:
        points (np.ndarray): points on the ellipse of shape (num_points, 3) 
    """
    if t_values is None:
        t_values = np.linspace(0, 2 * np.pi, num=num_points)
    x_values = a * np.cos(t_values)
    y_values = b * np.sin(t_values)
    z_values = np.zeros_like(t_values)
    parametric_function = lambda t_values: (x_values, y_values, z_values)
    return cls(parametric_function, t_values).points

heart(a=1, b=1, c=1, t_values=None, num_points=100) classmethod

Create a heart shape in 3D space.

Parameters:

Name Type Description Default
a int

description. Defaults to 1.

 1
b int

description. Defaults to 1.

 1
c int

description. Defaults to 1.

 1
t_values _type_

description. Defaults to None.

 None
num_points int

description. Defaults to 100.

 100

Returns:

Name Type Description
points ndarray

points on the heart shape of shape (num_points, 3)
Source code in mdna/utils.py 
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
@classmethod
def heart(cls, a=1, b=1, c=1,t_values=None,num_points=100):
    """Create a heart shape in 3D space.

    Args:
        a (int, optional): _description_. Defaults to 1.
        b (int, optional): _description_. Defaults to 1.
        c (int, optional): _description_. Defaults to 1.
        t_values (_type_, optional): _description_. Defaults to None.
        num_points (int, optional): _description_. Defaults to 100.

    Returns:
        points (np.ndarray): points on the heart shape of shape (num_points, 3)
    """
    if t_values is None:
        t_values = np.linspace(-np.pi, np.pi, num=num_points)
    x_values = a * np.sin(t_values) ** 3
    y_values = b * np.cos(t_values) - c * np.cos(2 * t_values)
    z_values = np.zeros_like(t_values)
    parametric_function = lambda t_values: (x_values, y_values, z_values)
    return cls(parametric_function, t_values).points

helix(radius=1, pitch=1, height=1, num_turns=1, num_points=100) classmethod

Create a helix in 3D space.

Parameters:

Name Type Description Default
radius int

description. Defaults to 1.

 1
pitch int

description. Defaults to 1.

 1
height int

description. Defaults to 1.

 1
num_turns int

description. Defaults to 1.

 1
num_points int

description. Defaults to 100.

 100

Returns:

Name Type Description
points ndarray

points on the helix of shape (num_points, 3)
Source code in mdna/utils.py 
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
@classmethod
def helix(cls, radius=1, pitch=1, height=1, num_turns=1, num_points=100):
    """Create a helix in 3D space.

    Args:
        radius (int, optional): _description_. Defaults to 1.
        pitch (int, optional): _description_. Defaults to 1.
        height (int, optional): _description_. Defaults to 1.
        num_turns (int, optional): _description_. Defaults to 1.
        num_points (int, optional): _description_. Defaults to 100.

    Returns:
        points (np.ndarray): points on the helix of shape (num_points, 3)
    """
    t_values = np.linspace(0, num_turns * 2 * np.pi, num=num_points)
    parametric_function = lambda t_values: (
        radius * np.cos(t_values),
        radius * np.sin(t_values),
        height * t_values / (2 * np.pi) - pitch * num_turns * t_values / (2 * np.pi)
    )
    return cls(parametric_function, t_values, num_points=num_points).points

lemniscate_of_bernoulli(a=1, b=1, t_values=None, num_points=100) classmethod

Create a lemniscate of Bernoulli in 3D space.

Parameters:

Name Type Description Default
a int

description. Defaults to 1.

 1
b int

description. Defaults to 1.

 1
t_values _type_

description. Defaults to None.

 None
num_points int

description. Defaults to 100.

 100

Returns:

Name Type Description
points ndarray

points on the leminscate of Bernouli of shape (num_points, 3)
Source code in mdna/utils.py 
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
@classmethod
def lemniscate_of_bernoulli(cls, a=1, b=1, t_values=None,num_points=100):
    """Create a lemniscate of Bernoulli in 3D space.

    Args:
        a (int, optional): _description_. Defaults to 1.
        b (int, optional): _description_. Defaults to 1.
        t_values (_type_, optional): _description_. Defaults to None.
        num_points (int, optional): _description_. Defaults to 100.

    Returns:
        points (np.ndarray): points on the leminscate of Bernouli of shape (num_points, 3)
    """
    if t_values is None:
        t_values = np.linspace(0, 2 * np.pi, num=num_points)
    x_values = a * np.sqrt(2) * np.cos(t_values) / (np.sin(t_values) ** 2 + 1)
    y_values = b * np.sqrt(2) * np.cos(t_values) * np.sin(t_values) / (np.sin(t_values) ** 2 + 1)
    z_values = np.zeros_like(t_values)
    parametric_function = lambda t_values: (x_values, y_values, z_values)
    return cls(parametric_function, t_values).points

line(length=1, num_points=100) classmethod

Create a line in 3D space.

Parameters:

Name Type Description Default
length int

description. Defaults to 1.

 1
num_points int

description. Defaults to 100.

 100

Returns:

Name Type Description
points ndarray

points on the line of shape (num_points, 3)
Source code in mdna/utils.py 
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
@classmethod
def line(cls, length=1, num_points=100):
    """Create a line in 3D space.

    Args:
        length (int, optional): _description_. Defaults to 1.
        num_points (int, optional): _description_. Defaults to 100.

    Returns:
        points (np.ndarray): points on the line of shape (num_points, 3)
    """
    t_values = np.linspace(0, 1, num=num_points)
    parametric_function = lambda t_values: (
        t_values * length,
        np.zeros_like(t_values),
        np.zeros_like(t_values)
    )
    return cls(parametric_function, t_values, num_points=num_points).points

mobius_strip(radius=1, width=0.5, num_twists=1, t_values=None, num_points=100) classmethod

Create a Mobius strip in 3D space.

Parameters:

Name Type Description Default
radius int

description. Defaults to 1.

 1
width float

description. Defaults to 0.5.

 0.5
num_twists int

description. Defaults to 1.

 1
t_values _type_

description. Defaults to None.

 None
num_points int

description. Defaults to 100.

 100

Returns:

Name Type Description
points ndarray

points on the Mobius strip of shape (num_points, 3)
Source code in mdna/utils.py 
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
@classmethod
def mobius_strip(cls, radius=1, width=0.5, num_twists=1, t_values=None, num_points=100):
    """Create a Mobius strip in 3D space.

    Args:
        radius (int, optional): _description_. Defaults to 1.
        width (float, optional): _description_. Defaults to 0.5.
        num_twists (int, optional): _description_. Defaults to 1.
        t_values (_type_, optional): _description_. Defaults to None.
        num_points (int, optional): _description_. Defaults to 100.

    Returns:
        points (np.ndarray): points on the Mobius strip of shape (num_points, 3)
    """
    if t_values is None:
        t_values = np.linspace(0, 2 * np.pi, num=num_points)
    u_values = np.linspace(0, width, num=num_points)
    u, t = np.meshgrid(u_values, t_values)
    x_values = (radius + u * np.cos(t / 2) * np.cos(num_twists * t)) * np.cos(t)
    y_values = (radius + u * np.cos(t / 2) * np.cos(num_twists * t)) * np.sin(t)
    z_values = u * np.sin(t / 2) * np.cos(num_twists * t)
    parametric_function = lambda t_values: (
        x_values.flatten(),
        y_values.flatten(),
        z_values.flatten()
    )
    return cls(parametric_function, t_values, num_points=num_points).points

spiral(radius=1, pitch=1, height=1, num_turns=1, num_points=100) classmethod

Create a spiral in 3D space.

Parameters:

Name Type Description Default
radius int

description. Defaults to 1.

 1
pitch int

description. Defaults to 1.

 1
height int

description. Defaults to 1.

 1
num_turns int

description. Defaults to 1.

 1
num_points int

description. Defaults to 100.

 100

Returns:

Name Type Description
points ndarray

points on the spiral of shape (num_points, 3)
Source code in mdna/utils.py 
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
@classmethod
def spiral(cls, radius=1, pitch=1, height=1, num_turns=1, num_points=100):
    """Create a spiral in 3D space.

    Args:
        radius (int, optional): _description_. Defaults to 1.
        pitch (int, optional): _description_. Defaults to 1.
        height (int, optional): _description_. Defaults to 1.
        num_turns (int, optional): _description_. Defaults to 1.
        num_points (int, optional): _description_. Defaults to 100.

    Returns:
        points (np.ndarray): points on the spiral of shape (num_points, 3)
    """
    t_values = np.linspace(0, num_turns * 2 * np.pi, num=num_points)
    parametric_function = lambda t_values: (
        radius * t_values * np.cos(t_values),
        radius * t_values * np.sin(t_values),
        height * t_values / (2 * np.pi) * pitch
    )
    return cls(parametric_function, t_values, num_points=num_points).points

square(side=1, t_values=None, num_points=100) classmethod

Create a square in 3D space.

Parameters:

Name Type Description Default
side int

description. Defaults to 1.

 1
t_values _type_

description. Defaults to None.

 None
num_points int

description. Defaults to 100.

 100

Returns:

Name Type Description
points ndarray

points on the square of shape (num_points, 3)
Source code in mdna/utils.py 
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
@classmethod
def square(cls, side=1, t_values=None,num_points=100):
    """Create a square in 3D space.

    Args:
        side (int, optional): _description_. Defaults to 1.
        t_values (_type_, optional): _description_. Defaults to None.
        num_points (int, optional): _description_. Defaults to 100.

    Returns:
        points (np.ndarray): points on the square of shape (num_points, 3)
    """
    if t_values is None:
        t_values = np.linspace(0, 4, num=num_points)
    # Calculate x and y coordinates based on t_values
    x_values = np.zeros_like(t_values)
    y_values = np.zeros_like(t_values)
    for i, t in enumerate(t_values):
        if 0 <= t < 1:
            x_values[i] = t * side
            y_values[i] = 0
        elif 1 <= t < 2:
            x_values[i] = side
            y_values[i] = (t - 1) * side
        elif 2 <= t < 3:
            x_values[i] = (3 - t) * side
            y_values[i] = side
        elif 3 <= t <= 4:
            x_values[i] = 0
            y_values[i] = (4 - t) * side
    z_values = np.zeros_like(t_values)
    parametric_function = lambda t_values: (
        x_values,
        y_values,
        z_values
    )
    return cls(parametric_function, t_values).points

torus_helix(R=1, r=2, num_windings=3, t_values=None, num_points=100) classmethod

Create a torus helix in 3D space.

Parameters:

Name Type Description Default
R int

description. Defaults to 1.

 1
r int

description. Defaults to 2.

 2
num_windings int

description. Defaults to 3.

 3
t_values _type_

description. Defaults to None.

 None
num_points int

description. Defaults to 100.

 100

Returns:

Name Type Description
points ndarray

points on the torus helix of shape (num_points, 3)
Source code in mdna/utils.py 
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
@classmethod
def torus_helix(cls, R=1, r=2, num_windings=3, t_values=None, num_points=100):
    """Create a torus helix in 3D space.

    Args:
        R (int, optional): _description_. Defaults to 1.
        r (int, optional): _description_. Defaults to 2.
        num_windings (int, optional): _description_. Defaults to 3.
        t_values (_type_, optional): _description_. Defaults to None.
        num_points (int, optional): _description_. Defaults to 100.

    Returns:
        points (np.ndarray): points on the torus helix of shape (num_points, 3)
    """
    if t_values is None:
        t_values = np.linspace(0, 2 * np.pi, num=num_points)

    parametric_function = lambda t_values: (
        (R + r * np.cos(num_windings*t_values)) * np.cos( t_values),
        (R + r * np.cos(num_windings*t_values)) * np.sin( t_values),
        r * np.sin(t_values)
    )
    return cls(parametric_function, t_values, num_points=num_points).points

trefoil(radius=1, num_turns=1, t_values=None, num_points=100) classmethod

Create a trefoil knot in 3D space.

Parameters:

Name Type Description Default
radius int

description. Defaults to 1.

 1
num_turns int

description. Defaults to 1.

 1
t_values _type_

description. Defaults to None.

 None
num_points int

description. Defaults to 100.

 100

Returns:

Name Type Description
points ndarray

points on the trefoil knot of shape (num_points, 3)
Source code in mdna/utils.py 
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
@classmethod
def trefoil(cls, radius=1, num_turns=1,t_values=None,num_points=100):
    """Create a trefoil knot in 3D space.

    Args:
        radius (int, optional): _description_. Defaults to 1.
        num_turns (int, optional): _description_. Defaults to 1.
        t_values (_type_, optional): _description_. Defaults to None.
        num_points (int, optional): _description_. Defaults to 100.

    Returns:
        points (np.ndarray): points on the trefoil knot of shape (num_points, 3)
    """
    if t_values is None:
        t_values = np.linspace(0, num_turns * 2 * np.pi, num=num_points)
    x_values = np.sin(t_values) + 2 * np.sin(2 * t_values)
    y_values = np.cos(t_values) - 2 * np.cos(2 * t_values)
    z_values = -np.sin(3 * t_values)
    parametric_function = lambda t_values: (
        radius * x_values,
        radius * y_values,
        radius * z_values
    )
    return cls(parametric_function, t_values).points