property_topomesh_optimization.py 文件源码

def property_topomesh_taubin_smoothing_force(topomesh,gaussian_sigma=10.0,positive_factor=0.33,negative_factor=-0.34,cellwise_smoothing=True):

    if not topomesh.has_wisp_property('vertices',degree=1,is_computed=True):
        compute_topomesh_property(topomesh,'vertices',degree=1)

    if cellwise_smoothing:
        edge_vertices = topomesh.wisp_property('vertices',degree=1).values(np.concatenate([np.array(list(topomesh.borders(3,c,2)),int) for c in topomesh.wisps(3)]))
    else:
        edge_vertices = topomesh.wisp_property('vertices',degree=1).values()

    reversed_edge_vertices = np.transpose([edge_vertices[:,1],edge_vertices[:,0]])
    edge_vertices = np.append(edge_vertices,reversed_edge_vertices,axis=0)

    edge_vectors = topomesh.wisp_property('barycenter',degree=0).values(edge_vertices[:,1]) - topomesh.wisp_property('barycenter',degree=0).values(edge_vertices[:,0])
    edge_lengths = np.linalg.norm(edge_vectors,axis=1)
    gaussian_edge_lengths = np.exp(-np.power(edge_lengths,2.0)/np.power(gaussian_sigma,2.0))
    gaussian_edge_vectors = gaussian_edge_lengths[:,np.newaxis]*edge_vectors

    taubin_force = np.transpose([nd.sum(gaussian_edge_vectors[:,0],edge_vertices[:,0],index=list(topomesh.wisps(0))),
                                 nd.sum(gaussian_edge_vectors[:,1],edge_vertices[:,0],index=list(topomesh.wisps(0))),
                                 nd.sum(gaussian_edge_vectors[:,2],edge_vertices[:,0],index=list(topomesh.wisps(0)))])
    #vertices_weights = 1.+nd.sum(gaussian_edge_lengths,edge_vertices[:,0],index=list(topomesh.wisps(0)))
    vertices_weights = nd.sum(gaussian_edge_lengths,edge_vertices[:,0],index=list(topomesh.wisps(0)))
    taubin_positive_force = positive_factor*taubin_force/vertices_weights[:,np.newaxis]

    taubin_positions = array_dict(topomesh.wisp_property('barycenter',degree=0).values(list(topomesh.wisps(0)))+taubin_positive_force, list(topomesh.wisps(0)))

    edge_vectors = taubin_positions.values(edge_vertices[:,1]) - taubin_positions.values(edge_vertices[:,0])
    edge_lengths = np.linalg.norm(edge_vectors,axis=1)
    gaussian_edge_lengths = np.exp(-np.power(edge_lengths,2.0)/np.power(gaussian_sigma,2.0))
    gaussian_edge_vectors = gaussian_edge_lengths[:,np.newaxis]*edge_vectors

    taubin_force = np.transpose([nd.sum(gaussian_edge_vectors[:,0],edge_vertices[:,0],index=list(topomesh.wisps(0))),
                                 nd.sum(gaussian_edge_vectors[:,1],edge_vertices[:,0],index=list(topomesh.wisps(0))),
                                 nd.sum(gaussian_edge_vectors[:,2],edge_vertices[:,0],index=list(topomesh.wisps(0)))])
    #vertices_weights = 1.+nd.sum(gaussian_edge_lengths,edge_vertices[:,0],index=list(topomesh.wisps(0)))
    vertices_weights = nd.sum(gaussian_edge_lengths,edge_vertices[:,0],index=list(topomesh.wisps(0)))
    taubin_negative_force = negative_factor*taubin_force/vertices_weights[:,np.newaxis]

    taubin_force = taubin_positive_force + taubin_negative_force

    return taubin_force