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import numpy as np
def create_grid(resX, resY, resZ, b_min=np.array([0, 0, 0]), b_max=np.array([1, 1, 1]), transform=None):
'''
Create a dense grid of given resolution and bounding box
:param resX: resolution along X axis
:param resY: resolution along Y axis
:param resZ: resolution along Z axis
:param b_min: vec3 (x_min, y_min, z_min) bounding box corner
:param b_max: vec3 (x_max, y_max, z_max) bounding box corner
:return: [3, resX, resY, resZ] coordinates of the grid, and transform matrix from mesh index
'''
coords = np.mgrid[:resX, :resY, :resZ]
coords = coords.reshape(3, -1)
coords_matrix = np.eye(4)
length = b_max - b_min
coords_matrix[0, 0] = length[0] / resX
coords_matrix[1, 1] = length[1] / resY
coords_matrix[2, 2] = length[2] / resZ
coords_matrix[0:3, 3] = b_min
coords = np.matmul(coords_matrix[:3, :3], coords) + coords_matrix[:3, 3:4]
if transform is not None:
coords = np.matmul(transform[:3, :3], coords) + transform[:3, 3:4]
coords_matrix = np.matmul(transform, coords_matrix)
coords = coords.reshape(3, resX, resY, resZ)
return coords, coords_matrix
def batch_eval(points, eval_func, num_samples=512 * 512 * 512):
num_pts = points.shape[1]
sdf = np.zeros(num_pts)
num_batches = num_pts // num_samples
for i in range(num_batches):
sdf[i * num_samples:i * num_samples + num_samples] = eval_func(
points[:, i * num_samples:i * num_samples + num_samples])
if num_pts % num_samples:
sdf[num_batches * num_samples:] = eval_func(points[:, num_batches * num_samples:])
return sdf
def eval_grid(coords, eval_func, num_samples=512 * 512 * 512):
resolution = coords.shape[1:4]
coords = coords.reshape([3, -1])
sdf = batch_eval(coords, eval_func, num_samples=num_samples)
return sdf.reshape(resolution)
def eval_grid_octree(coords, eval_func,
init_resolution=64, threshold=0.01,
num_samples=512 * 512 * 512):
resolution = coords.shape[1:4]
sdf = np.zeros(resolution)
dirty = np.ones(resolution, dtype=np.bool)
grid_mask = np.zeros(resolution, dtype=np.bool)
reso = resolution[0] // init_resolution
while reso > 0:
# subdivide the grid
grid_mask[0:resolution[0]:reso, 0:resolution[1]:reso, 0:resolution[2]:reso] = True
# test samples in this iteration
test_mask = np.logical_and(grid_mask, dirty)
#print('step size:', reso, 'test sample size:', test_mask.sum())
points = coords[:, test_mask]
sdf[test_mask] = batch_eval(points, eval_func, num_samples=num_samples)
dirty[test_mask] = False
# do interpolation
if reso <= 1:
break
for x in range(0, resolution[0] - reso, reso):
for y in range(0, resolution[1] - reso, reso):
for z in range(0, resolution[2] - reso, reso):
# if center marked, return
if not dirty[x + reso // 2, y + reso // 2, z + reso // 2]:
continue
v0 = sdf[x, y, z]
v1 = sdf[x, y, z + reso]
v2 = sdf[x, y + reso, z]
v3 = sdf[x, y + reso, z + reso]
v4 = sdf[x + reso, y, z]
v5 = sdf[x + reso, y, z + reso]
v6 = sdf[x + reso, y + reso, z]
v7 = sdf[x + reso, y + reso, z + reso]
v = np.array([v0, v1, v2, v3, v4, v5, v6, v7])
v_min = v.min()
v_max = v.max()
# this cell is all the same
if (v_max - v_min) < threshold:
sdf[x:x + reso, y:y + reso, z:z + reso] = (v_max + v_min) / 2
dirty[x:x + reso, y:y + reso, z:z + reso] = False
reso //= 2
return sdf.reshape(resolution)