import numpy as np import torch from typing import Union, List def lerp( t: float, v0: Union[np.ndarray, torch.Tensor], v1: Union[np.ndarray, torch.Tensor] ) -> Union[np.ndarray, torch.Tensor]: return (1 - t) * v0 + t * v1 def maybe_torch(v: np.ndarray, is_torch: bool): if is_torch: return torch.from_numpy(v) return v def normalize(v: np.ndarray, eps: float): norm_v = np.linalg.norm(v) if norm_v > eps: v = v / norm_v return v class slerp: def __init__(self): pass def execute( self, t: Union[float, List[float]], v0: Union[List[torch.Tensor], torch.Tensor], v1: Union[List[torch.Tensor], torch.Tensor], DOT_THRESHOLD: float = 0.9995, eps: float = 1e-8, densities = None, ): if type(v0) is list: v0 = v0[0] if type(v1) is list: v1 = v1[0] if type(t) is list: t = t[0] """ Spherical linear interpolation From: https://gist.github.com/dvschultz/3af50c40df002da3b751efab1daddf2c Args: t (float/np.ndarray): Float value between 0.0 and 1.0 v0 (np.ndarray): Starting vector v1 (np.ndarray): Final vector DOT_THRESHOLD (float): Threshold for considering the two vectors as colinear. Not recommended to alter this. Returns: v2 (np.ndarray): Interpolation vector between v0 and v1 """ is_torch = False if not isinstance(v0, np.ndarray): is_torch = True v0 = v0.detach().cpu().float().numpy() if not isinstance(v1, np.ndarray): is_torch = True v1 = v1.detach().cpu().float().numpy() # Copy the vectors to reuse them later v0_copy = np.copy(v0) v1_copy = np.copy(v1) # Normalize the vectors to get the directions and angles v0 = normalize(v0, eps) v1 = normalize(v1, eps) # Dot product with the normalized vectors (can't use np.dot in W) dot = np.sum(v0 * v1) # If absolute value of dot product is almost 1, vectors are ~colinear, so use lerp if np.abs(dot) > DOT_THRESHOLD: res = lerp(t, v0_copy, v1_copy) return maybe_torch(res, is_torch) # Calculate initial angle between v0 and v1 theta_0 = np.arccos(dot) sin_theta_0 = np.sin(theta_0) # Angle at timestep t theta_t = theta_0 * t sin_theta_t = np.sin(theta_t) # Finish the slerp algorithm s0 = np.sin(theta_0 - theta_t) / sin_theta_0 s1 = sin_theta_t / sin_theta_0 res = s0 * v0_copy + s1 * v1_copy return maybe_torch(res, is_torch)