Return length, i.e. Euclidean norm, of ndarray along axis. >>> v = numpy.random.random(3) >>> n = vector_norm(v) >>> numpy.allclose(n, nu

Return ndarray normalized by length, i.e. Euclidean norm, along axis. >>> v0 = numpy.random.random(3) >>> v1 = unit_vector(v0) >>> numpy.

Saves the model.

Return homogeneous rotation matrix from quaternion. >>> M = quaternion_matrix([0.99810947, 0.06146124, 0, 0]) >>> numpy.allclose(M, rotation_

Return sphere point perpendicular to axis.

Takes num_indept+num_sym verts and makes it num_indept + num_sym + num_sym Is identity if model is not symmetric

verts is |V| x 3 cuda torch Variable cams is 7, cuda torch Variable Returns N x N x 3 numpy

Return unit sphere coordinates from window coordinates.

Compute gradient of vertices given mask gradients. Args: grad_masks: B X 256 X 256 numpy array Returns: grad_

Renders masks. Args: vertices: B X N X 3 numpy array faces: B X F X 3 numpy array Returns: masks:

Should be implemented by the child class.

Multiply qa by qb. Args: qa: B X N X 4 quaternions qb: B X N X 4 quaternions Returns: q_mult: B X N X 4

batch has B x C x H x W numpy

Rotate points by quaternions. Args: X: B X N X 3 points q: B X 4 quaternions Returns: X_rot: B X N X 3 (rotated poin

Return affine transform matrix to register two point sets. v0 and v1 are shape (ndims, \*) arrays of at least ndims non-homogeneous coordinat

Return axis, which arc is nearest to point.

Compute gradient of vertices given image gradients. Args: grad_images: B X 3? X 256 X 256 numpy array Returns:

Simple 3D encoder with nlayers. Args: nlayers: number of decoder layers nz_shape: number of bottleneck nc_input: num

Should be implemented by the child class.

Should be implemented by the child class.

Should be implemented by the child class.

kp is 15 x 2 or 3 numpy. img can be either RGB or Gray Draws bird points.

Return Euler angles from rotation matrix for specified axis sequence. axes : One of 24 axis sequences as string or encoded tuple Note that m

Return homogeneous rotation matrix from Euler angles and axis sequence. ai, aj, ak : Euler's roll, pitch and yaw angles axes : One of 24 axis

Compute IOU and keypoint error

Should compute self.total_loss. To be implemented by the child class.

Renders masks. Args: vertices: B X N X 3 numpy array faces: B X F X 3 numpy array textures: B X F X T X T

Should be implemented by the child class.

Should be implemented by the child class.

ious: N x 1

kp_errs: N x 15 kp_vis: N x 15

Should be implemented by the child class.

Should be implemented by the child class.

Input is numpy array or torch.cuda.Tensor img can be H x W, H x W x C, or C x H x W kp is |KP| x 2

This reorders the faces, such that it has this order: F_indept - independent face ids F_right (x>0) F_left 1. For each fac

Geodesic rotation loss. Args: q1: N X 4 q2: N X 4 Returns: loss : N x 1

Return quaternion from rotation matrix. If isprecise is True, the input matrix is assumed to be a precise rotation matrix and a faster algori

Return multiplication of two quaternions. >>> q = quaternion_multiply([4, 1, -2, 3], [8, -5, 6, 7]) >>> numpy.allclose(q, [28, -44, -14, 48])

Return spherical linear interpolation between two quaternions. >>> q0 = random_quaternion() >>> q1 = random_quaternion() >>> q = quaterni

Return uniform random unit quaternion. rand: array like or None Three independent random variables that are uniformly distributed

Should be implemented by the child class.