def volume_curvature_normal_smooth(triangles, vertices, nb_iter=1, diffusion_step=1.0, area_weighted=False, backward_step=False, flow_file=None): if isinstance(diffusion_step, (int, float)): diffusion_step = diffusion_step * np.ones(len(vertices)) if flow_file is not None: mem_map = np.memmap(flow_file, dtype=G_DTYPE, mode='w+', shape=(nb_iter, vertices.shape[0], vertices.shape[1])) for i in range(nb_iter): stdout.write("\r step %d on %d done" % (i, nb_iter)) stdout.flush() if flow_file is not None: mem_map[i] = vertices # get curvature_normal_matrix # todo not optimal, because operation done twice etc curvature_normal_mtx = mean_curvature_normal_matrix( triangles, vertices, area_weighted=area_weighted) # do the first step next_vertices = euler_step(curvature_normal_mtx, csc_matrix( vertices), diffusion_step, backward_step).toarray() # test if direction is positive direction = next_vertices - vertices normal_dir = vertices_cotan_normal(triangles, vertices, normalize=True) dotv = dot(normalize_vectors(direction), normal_dir, keepdims=True) vertices += direction * np.maximum(0.0, -dotv) stdout.write("\r step %d on %d done \n" % (nb_iter, nb_iter)) return vertices
def vertices_normal(triangles, vertices, normalize=True, area_weighted=True): tri_normal = triangles_normal(triangles, vertices, normalize=area_weighted) tv_matrix = triangle_vertex_map(triangles, vertices) vts_normal = tv_matrix.T.dot(tri_normal) if normalize: return normalize_vectors(vts_normal) return vts_normal
def triangles_normal(triangles, vertices, normalize=True): if scipy.sparse.__name__ in type(vertices).__module__: vertices = vertices.toarray() e1 = vertices[triangles[:, 1]] - vertices[triangles[:, 0]] e2 = vertices[triangles[:, 2]] - vertices[triangles[:, 0]] normal = np.cross(e1, e2) if normalize: return normalize_vectors(normal) return normal
def vertices_cotan_direction(triangles, vertices, normalize=True, area_weighted=True): from trimeshpy.math.matrix import mean_curvature_normal_matrix curvature_normal_mtx = mean_curvature_normal_matrix( triangles, vertices, area_weighted=area_weighted) cotan_normal = curvature_normal_mtx.dot(vertices) if normalize: return normalize_vectors(cotan_normal) return cotan_normal
def volume_mass_stiffness_smooth(triangles, vertices, nb_iter=1, diffusion_step=1.0, flow_file=None): vertices_csc = csc_matrix(vertices) curvature_normal_mtx = mean_curvature_normal_matrix(triangles, vertices, area_weighted=False) if isinstance(diffusion_step, (int, long, float)): diffusion_step = diffusion_step * np.ones(len(vertices)) if flow_file is not None: mem_map = np.memmap(flow_file, dtype=G_DTYPE, mode='w+', shape=(nb_iter, vertices.shape[0], vertices.shape[1])) for i in range(nb_iter): stdout.write("\r step %d on %d done" % (i, nb_iter)) stdout.flush() if flow_file is not None: mem_map[i] = vertices_csc.toarray() # get curvature_normal_matrix mass_mtx = mass_matrix(triangles, vertices) raise NotImplementedError() # (D - d*L)*y = D*x = b A_matrix = mass_mtx - \ diags(diffusion_step, 0).dot(curvature_normal_mtx) b_matrix = mass_mtx.dot(csc_matrix(vertices_csc)) next_vertices = spsolve(A_matrix, b_matrix) # test if direction is positive direction = next_vertices.toarray() - vertices_csc normal_dir = vertices_cotan_normal(triangles, next_vertices, normalize=True) dotv = normalize_vectors(direction).multiply(normal_dir) vertices_csc += direction * np.maximum(0.0, -dotv) # vertices_csc += direction * sigmoid(-np.arctan(dotv)*np.pi - np.pi) # vertices_csc += direction * softplus(-dotv) stdout.write("\r step %d on %d done \n" % (nb_iter, nb_iter)) return vertices_csc.toarray()
def vertices_cotan_normal(triangles, vertices, normalize=True, area_weighted=True): from trimeshpy.math.curvature import vertices_cotan_direction if scipy.sparse.__name__ in type(vertices).__module__: vertices = vertices.toarray() cotan_normal = vertices_cotan_direction(triangles, vertices, normalize=False, area_weighted=area_weighted) vts_normal = vertices_normal(triangles, vertices, normalize=False, area_weighted=area_weighted) # inverse inverted cotan_normal direction cotan_normal = np.sign(dot(cotan_normal, vts_normal, keepdims=True)) * cotan_normal if normalize: return normalize_vectors(cotan_normal) return cotan_normal