如何测试四元数slerp

Question

我已经用这个wikipedia article实现了一个四元数slerp。在

我了解slerp是如何工作的，我的问题是我需要值来测试我的功能。有谁能提供四元数slerp的例子吗？在

完整的源代码是here

def slerp(quat1, quat2, t):
    """Spherically interpolates between quat1 and quat2 by t.
    The parameter t is clamped to the range [0, 1]
    """

    # https://en.wikipedia.org/wiki/Slerp

    v0 = normalise(quat1)
    v1 = normalise(quat2)

    dot = vector4.dot(v0, v1)

    # TODO: fixlater
    # If the inputs are too close for comfort,
    # linearly interpolate and normalize the result.
    # if abs(dot) > 0.9995:
    #     pass

    # If the dot product is negative, the quaternions
    # have opposite handed-ness and slerp won't take
    # the shorter path. Fix by reversing one quaternion.
    if dot < 0.0:
        v1 = -v1
        dot = -dot

    # clamp
    dot = np.clamp(dot, -1.0, 1.0)
    theta = np.acos(dot) * t

    v2 = v1 - v0 * dot
    res = v0 * np.cos(theta) + v2 * np.sin(theta)
    return res

Answer 1

使用numpy-quaternion，可以将结果与quaternion.slerp_evaluate的输出进行比较。例如：

>>> import numpy as np
>>> import quaternion
>>> q1 = np.quaternion(1, 0, 0, 0)
>>> q2 = np.quaternion(0, 1, 0, 0)
>>> quaternion.slerp_evaluate(q1, q2, .0)
quaternion(1, 0, 0, 0)
>>> quaternion.slerp_evaluate(q1, q2, .2)
quaternion(0.951056516295154, 0.309016994374947, 0, 0)
>>> quaternion.slerp_evaluate(q1, q2, .4)
quaternion(0.809016994374947, 0.587785252292473, 0, 0)
>>> quaternion.slerp_evaluate(q1, q2, .6)
quaternion(0.587785252292473, 0.809016994374947, 0, 0)
>>> quaternion.slerp_evaluate(q1, q2, .8)
quaternion(0.309016994374947, 0.951056516295154, 0, 0)
>>> quaternion.slerp_evaluate(q1, q2, 1.)
quaternion(6.12323399573677e-17, 1, 0, 0)