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| # -*- coding: utf-8 -*- | |
| # Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. (MPG) is | |
| # holder of all proprietary rights on this computer program. | |
| # You can only use this computer program if you have closed | |
| # a license agreement with MPG or you get the right to use the computer | |
| # program from someone who is authorized to grant you that right. | |
| # Any use of the computer program without a valid license is prohibited and | |
| # liable to prosecution. | |
| # | |
| # Copyright©2019 Max-Planck-Gesellschaft zur Förderung | |
| # der Wissenschaften e.V. (MPG). acting on behalf of its Max Planck Institute | |
| # for Intelligent Systems. All rights reserved. | |
| # | |
| # Contact: [email protected] | |
| import os | |
| import trimesh | |
| import numpy as np | |
| import math | |
| from scipy.special import sph_harm | |
| import argparse | |
| from tqdm import tqdm | |
| from trimesh.util import bounds_tree | |
| def factratio(N, D): | |
| if N >= D: | |
| prod = 1.0 | |
| for i in range(D + 1, N + 1): | |
| prod *= i | |
| return prod | |
| else: | |
| prod = 1.0 | |
| for i in range(N + 1, D + 1): | |
| prod *= i | |
| return 1.0 / prod | |
| def KVal(M, L): | |
| return math.sqrt(((2 * L + 1) / (4 * math.pi)) * (factratio(L - M, L + M))) | |
| def AssociatedLegendre(M, L, x): | |
| if M < 0 or M > L or np.max(np.abs(x)) > 1.0: | |
| return np.zeros_like(x) | |
| pmm = np.ones_like(x) | |
| if M > 0: | |
| somx2 = np.sqrt((1.0 + x) * (1.0 - x)) | |
| fact = 1.0 | |
| for i in range(1, M + 1): | |
| pmm = -pmm * fact * somx2 | |
| fact = fact + 2 | |
| if L == M: | |
| return pmm | |
| else: | |
| pmmp1 = x * (2 * M + 1) * pmm | |
| if L == M + 1: | |
| return pmmp1 | |
| else: | |
| pll = np.zeros_like(x) | |
| for i in range(M + 2, L + 1): | |
| pll = (x * (2 * i - 1) * pmmp1 - (i + M - 1) * pmm) / (i - M) | |
| pmm = pmmp1 | |
| pmmp1 = pll | |
| return pll | |
| def SphericalHarmonic(M, L, theta, phi): | |
| if M > 0: | |
| return math.sqrt(2.0) * KVal(M, L) * np.cos( | |
| M * phi) * AssociatedLegendre(M, L, np.cos(theta)) | |
| elif M < 0: | |
| return math.sqrt(2.0) * KVal(-M, L) * np.sin( | |
| -M * phi) * AssociatedLegendre(-M, L, np.cos(theta)) | |
| else: | |
| return KVal(0, L) * AssociatedLegendre(0, L, np.cos(theta)) | |
| def save_obj(mesh_path, verts): | |
| file = open(mesh_path, 'w') | |
| for v in verts: | |
| file.write('v %.4f %.4f %.4f\n' % (v[0], v[1], v[2])) | |
| file.close() | |
| def sampleSphericalDirections(n): | |
| xv = np.random.rand(n, n) | |
| yv = np.random.rand(n, n) | |
| theta = np.arccos(1 - 2 * xv) | |
| phi = 2.0 * math.pi * yv | |
| phi = phi.reshape(-1) | |
| theta = theta.reshape(-1) | |
| vx = -np.sin(theta) * np.cos(phi) | |
| vy = -np.sin(theta) * np.sin(phi) | |
| vz = np.cos(theta) | |
| return np.stack([vx, vy, vz], 1), phi, theta | |
| def getSHCoeffs(order, phi, theta): | |
| shs = [] | |
| for n in range(0, order + 1): | |
| for m in range(-n, n + 1): | |
| s = SphericalHarmonic(m, n, theta, phi) | |
| shs.append(s) | |
| return np.stack(shs, 1) | |
| def computePRT(mesh_path, scale, n, order): | |
| prt_dir = os.path.join(os.path.dirname(mesh_path), "prt") | |
| bounce_path = os.path.join(prt_dir, "bounce.npy") | |
| face_path = os.path.join(prt_dir, "face.npy") | |
| os.makedirs(prt_dir, exist_ok=True) | |
| PRT = None | |
| F = None | |
| if os.path.exists(bounce_path) and os.path.exists(face_path): | |
| PRT = np.load(bounce_path) | |
| F = np.load(face_path) | |
| else: | |
| mesh = trimesh.load(mesh_path, | |
| skip_materials=True, | |
| process=False, | |
| maintain_order=True) | |
| mesh.vertices *= scale | |
| vectors_orig, phi, theta = sampleSphericalDirections(n) | |
| SH_orig = getSHCoeffs(order, phi, theta) | |
| w = 4.0 * math.pi / (n * n) | |
| origins = mesh.vertices | |
| normals = mesh.vertex_normals | |
| n_v = origins.shape[0] | |
| origins = np.repeat(origins[:, None], n, axis=1).reshape(-1, 3) | |
| normals = np.repeat(normals[:, None], n, axis=1).reshape(-1, 3) | |
| PRT_all = None | |
| for i in range(n): | |
| SH = np.repeat(SH_orig[None, (i * n):((i + 1) * n)], n_v, | |
| axis=0).reshape(-1, SH_orig.shape[1]) | |
| vectors = np.repeat(vectors_orig[None, (i * n):((i + 1) * n)], | |
| n_v, | |
| axis=0).reshape(-1, 3) | |
| dots = (vectors * normals).sum(1) | |
| front = (dots > 0.0) | |
| delta = 1e-3 * min(mesh.bounding_box.extents) | |
| hits = mesh.ray.intersects_any(origins + delta * normals, vectors) | |
| nohits = np.logical_and(front, np.logical_not(hits)) | |
| PRT = (nohits.astype(np.float) * dots)[:, None] * SH | |
| if PRT_all is not None: | |
| PRT_all += (PRT.reshape(-1, n, SH.shape[1]).sum(1)) | |
| else: | |
| PRT_all = (PRT.reshape(-1, n, SH.shape[1]).sum(1)) | |
| PRT = w * PRT_all | |
| F = mesh.faces | |
| np.save(bounce_path, PRT) | |
| np.save(face_path, F) | |
| # NOTE: trimesh sometimes break the original vertex order, but topology will not change. | |
| # when loading PRT in other program, use the triangle list from trimesh. | |
| return PRT, F | |
| def testPRT(obj_path, n=40): | |
| os.makedirs(os.path.join(os.path.dirname(obj_path), | |
| f'../bounce/{os.path.basename(obj_path)[:-4]}'), | |
| exist_ok=True) | |
| PRT, F = computePRT(obj_path, n, 2) | |
| np.savetxt( | |
| os.path.join(os.path.dirname(obj_path), | |
| f'../bounce/{os.path.basename(obj_path)[:-4]}', | |
| 'bounce.npy'), PRT) | |
| np.save( | |
| os.path.join(os.path.dirname(obj_path), | |
| f'../bounce/{os.path.basename(obj_path)[:-4]}', | |
| 'face.npy'), F) | |