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Kochanek–Bartels-like Rotation Splines§

[1]:

import numpy as np

helper.py

[2]:

from helper import angles2quat, animate_rotations, display_animation

splines.quaternion.KochanekBartels

[3]:

from splines.quaternion import KochanekBartels

[4]:

rotations = [
    angles2quat(0, 0, 0),
    angles2quat(90, 0, 0),
    angles2quat(90, 90, 0),
    angles2quat(90, 90, 90),
]

Uniform Catmull–Rom§

[5]:

s = KochanekBartels(rotations)

[6]:

times = np.linspace(s.grid[0], s.grid[-1], 100)

[7]:

ani = animate_rotations(s.evaluate(times), figsize=(4, 3))

[8]:

display_animation(ani, default_mode='reflect')

Non-Uniform Catmull–Rom§

[9]:

grid = 0, 0.2, 0.9, 1.2

[10]:

s = KochanekBartels(rotations, grid)

[11]:

times = np.linspace(s.grid[0], s.grid[-1], 100)

[12]:

ani = animate_rotations(s.evaluate(times), figsize=(4, 3))

[13]:

display_animation(ani, default_mode='reflect')

TCB§

[14]:

s = KochanekBartels(rotations, tcb=[0, 1, 1])

[15]:

times = np.linspace(s.grid[0], s.grid[-1], 100)

[16]:

ani = animate_rotations(s.evaluate(times), figsize=(4, 3))

[17]:

display_animation(ani, default_mode='reflect')

Edge Cases§

  • 0 or 1 quaternions: not allowed

  • 2 quaternions: Slerp

  • 180° rotations (dot product = 0)?

  • …

2 quaternions:

[18]:

rotations = [
    angles2quat(0, 0, 0),
    angles2quat(90, 90, 90),
]

[19]:

s = KochanekBartels(rotations)

[20]:

times = np.linspace(s.grid[0], s.grid[-1], 100)

[21]:

ani = animate_rotations(s.evaluate(times), figsize=(4, 3))

[22]:

display_animation(ani, default_mode='reflect')