예제 #1
0
def compute_critical_values(P, Q, p, q, mdist, P_dist, Q_dist):
    """
    Usage
    -----
    Compute all the critical values between trajectories P and Q

    Parameters
    ----------
    param P : px2 numpy_array, Trajectory P
    param Q : qx2 numpy_array, Trajectory Q
    param p : int, number of points in Trajectory P
    param q : int, number of points in Trajectory Q
    mdist : p x q numpy array, pairwise distance between points of trajectories t1 and t2
    param P_dist:  p x 1 numpy_array,  distances between consecutive points in P
    param Q_dist:  q x 1 numpy_array,  distances between consecutive points in Q

    Returns
    -------
    cc : list, all critical values between trajectories P and Q
    """
    origin = eucl_dist(P[0], Q[0])
    end = eucl_dist(P[-1], Q[-1])
    end_point = max(origin, end)
    cc = set([end_point])
    for i in range(p - 1):
        for j in range(q - 1):
            Lij = point_to_seg(Q[j], P[i], P[i + 1], mdist[i, j],
                               mdist[i + 1, j], P_dist[i])
            if Lij > end_point:
                cc.add(Lij)
            Bij = point_to_seg(P[i], Q[j], Q[j + 1], mdist[i, j],
                               mdist[i, j + 1], Q_dist[j])
            if Bij > end_point:
                cc.add(Bij)
    return sorted(list(cc))
예제 #2
0
def compute_critical_values(P, Q, p, q):
    """
    Usage
    -----
    Compute all the critical values between trajectories P and Q

    Parameters
    ----------
    param P : px2 numpy_array, Trajectory P
    param Q : qx2 numpy_array, Trajectory Q
    param p : float, number of points in Trajectory P
    param q : float, number of points in Trajectory Q

    Returns
    -------
    cc : list, all critical values between trajectories P and Q
    """
    origin = eucl_dist(P[0], Q[0])
    end = eucl_dist(P[-1], Q[-1])
    end_point = max(origin, end)
    cc = set([end_point])
    for i in range(p - 1):
        for j in range(q - 1):
            Lij = point_to_seg(Q[j], P[i], P[i + 1])
            if Lij > end_point:
                cc.add(Lij)
            Bij = point_to_seg(P[i], Q[j], Q[j + 1])
            if Bij > end_point:
                cc.add(Bij)
    return sorted(list(cc))
예제 #3
0
def compute_critical_values(P, Q, p, q):
    """
    Usage
    -----
    Compute all the critical values between trajectories P and Q

    Parameters
    ----------
    param P : px2 numpy_array, Trajectory P
    param Q : qx2 numpy_array, Trajectory Q
    param p : float, number of points in Trajectory P
    param q : float, number of points in Trajectory Q

    Returns
    -------
    cc : list, all critical values between trajectories P and Q
    """
    origin = eucl_dist(P[0], Q[0])
    end = eucl_dist(P[-1], Q[-1])
    end_point = max(origin, end)
    cc = set([end_point])
    for i in range(p - 1):
        for j in range(q - 1):
            Lij = point_to_seg(Q[j], P[i], P[i + 1])
            if Lij > end_point:
                cc.add(Lij)
            Bij = point_to_seg(P[i], Q[j], Q[j + 1])
            if Bij > end_point:
                cc.add(Bij)
    return sorted(list(cc))
예제 #4
0
def free_line(p, eps, s, dps1, dps2, ds):
    """
    Usage
    -----
    Return the free space in the segment s, from point p.
    This free space is the set of all point in s whose distance from p is at most eps.
    Since s is a segment, the free space is also a segment.
    We return a 1x2 array whit the fraction of the segment s which are in the free space.
    If no part of s are in the free space, return [-1,-1]

    Parameters
    ----------
    param p : 1x2 numpy_array, centre of the circle
    param eps : float, radius of the circle
    param s : 2x2 numpy_array, line

    Returns
    -------
    lf : 1x2 numpy_array
         fraction of segment which is in the free space (i.e [0.3,0.7], [0.45,1], ...)
         If no part of s are in the free space, return [-1,-1]
    """
    px = p[0]
    py = p[1]
    s1x = s[0, 0]
    s1y = s[0, 1]
    s2x = s[1, 0]
    s2y = s[1, 1]
    if s1x == s2x and s1y == s2y:
        if eucl_dist(p, s[0]) > eps:
            lf = [-1, -1]
        else:
            lf = [0, 1]
    else:
        if point_to_seg(p, s[0], s[1], dps1, dps2, ds) > eps:
            # print("No Intersection")
            lf = [-1, -1]
        else:
            segl = eucl_dist(s[0], s[1])
            segl2 = segl * segl
            intersect = circle_line_intersection(px, py, s1x, s1y, s2x, s2y,
                                                 eps)
            if intersect[0][0] != intersect[1][0] or intersect[0][
                    1] != intersect[1][1]:
                i1x = intersect[0, 0]
                i1y = intersect[0, 1]
                u1 = (((i1x - s1x) * (s2x - s1x)) + ((i1y - s1y) *
                                                     (s2y - s1y))) / segl2

                i2x = intersect[1, 0]
                i2y = intersect[1, 1]
                u2 = (((i2x - s1x) * (s2x - s1x)) + ((i2y - s1y) *
                                                     (s2y - s1y))) / segl2
                ordered_point = sorted((0, 1, u1, u2))
                lf = ordered_point[1:3]
            else:
                if px == s1x and py == s1y:
                    lf = [0, 0]
                elif px == s2x and py == s2y:
                    lf = [1, 1]
                else:
                    i1x = intersect[0][0]
                    i1y = intersect[0][1]
                    u1 = (((i1x - s1x) * (s2x - s1x)) + ((i1y - s1y) *
                                                         (s2y - s1y))) / segl2
                    if 0 <= u1 <= 1:
                        lf = [u1, u1]
                    else:
                        lf = [-1, -1]
    return lf
예제 #5
0
def free_line(p, eps, s):
    """
    Usage
    -----
    Return the free space in the segment s, from point p.
    This free space is the set of all point in s whose distance from p is at most eps.
    Since s is a segment, the free space is also a segment.
    We return a 1x2 array whit the fraction of the segment s which are in the free space.
    If no part of s are in the free space, return [-1,-1]

    Parameters
    ----------
    param p : 1x2 numpy_array, centre of the circle
    param eps : float, radius of the circle
    param s : 2x2 numpy_array, line

    Returns
    -------
    lf : 1x2 numpy_array
         fraction of segment which is in the free space (i.e [0.3,0.7], [0.45,1], ...)
         If no part of s are in the free space, return [-1,-1]
    """
    px = p[0]
    py = p[1]
    s1x = s[0, 0]
    s1y = s[0, 1]
    s2x = s[1, 0]
    s2y = s[1, 1]
    if s1x == s2x and s1y==s2y:
        if eucl_dist(p, s[0]) > eps:
            lf = [-1, -1]
        else:
            lf = [0, 1]
    else:
        if point_to_seg(p, s[0], s[1]) > eps:
            #print("No Intersection")
            lf = [-1, -1]
        else:
            segl = eucl_dist(s[0], s[1])
            segl2 = segl * segl
            intersect = circle_line_intersection(px, py, s1x, s1y, s2x, s2y, eps)
            if intersect[0][0] != intersect[1][0] or intersect[0][1] != intersect[1][1]:
                i1x = intersect[0, 0]
                i1y = intersect[0, 1]
                u1 = (((i1x - s1x) * (s2x - s1x)) + ((i1y - s1y) * (s2y - s1y))) / segl2

                i2x = intersect[1, 0]
                i2y = intersect[1, 1]
                u2 = (((i2x - s1x) * (s2x - s1x)) + ((i2y - s1y) * (s2y - s1y))) / segl2
                ordered_point = sorted((0, 1, u1, u2))
                lf = ordered_point[1:3]
            else:
                if px == s1x and py==s1y:
                    lf = [0, 0]
                elif px == s2x and py==s2y:
                     lf = [1, 1]
                else:
                    i1x = intersect[0][0]
                    i1y = intersect[0][1]
                    u1 = (((i1x - s1x) * (s2x - s1x)) + ((i1y - s1y) * (s2y - s1y))) / segl2
                    if 0 <= u1 <= 1:
                        lf = [u1, u1]
                    else:
                        lf = [-1, -1]
    return lf