Пример #1
0
    def distances_per_degree(lat, a=SEMI_MAJOR_AXIS, inverse_flattening=INVERSE_FLATTENING):
        """ Returns a tuple containing arc distances in the units of the semi-major axis. 
        The first is the distance along an arc of one degree at a constant latitude (lat).
        The second is the distance along an arc of one degree at a constant lng centered on the given lat.

        Arguments:
            lat - the latitude at which the distances apply
            a - the semi-major axis of the ellipsoid for the coordinate reference system
            inverse_flattening - the inverse of the ellipsoid's flattening parameter 
        """

        f = 1.0 / inverse_flattening    
        e_squared = f * (2.0 - f) # e^2 = 2f - f^2

        # N - radius of curvature in the prime vertical, (tangent to ellipsoid at latitude)
        # N(lat) = a/(1-e^2*sin^2(lat))^0.5
        N = a / math.sqrt(1.0 - e_squared * (math.pow(math.sin(lat * math.pi / 180.0), 2.0))) 

        # M - radius of curvature in the prime meridian, (tangent to ellipsoid at latitude)
        # M(lat) = a(1-e^2)/(1-e^2*sin^2(lat))^1.5
        M = a * (1.0 - e_squared) / math.pow(1.0 - e_squared * math.pow(math.sin(lat * math.pi / 180.0), 2.0), 1.5)

        # longitude is irrelevant for the calculations to follow so simplify by using longitude = 0, so Y = 0
        # X = Ncos(lat)cos(long). long = 0, so cos(long) = 1.0
        X = N * math.cos(lat * math.pi / 180.0) * 1.0 
        lngdistanceperdegree = math.pi * X / 180.0 
        latdistanceperdegree = math.pi * M / 180.0
        return (lngdistanceperdegree, latdistanceperdegree)
Пример #2
0
def brachistochroneReal(x0, y0, x1, y1, n):
	dy = y0 - y1
	prec=10.0**-12
	
	t1=0.0
	t2=2*pi
	
	xm=x0
	while abs(xm-x1) > prec:
		tm = (t1+t2)/2
		
		if (1-cos(tm)==0):
			continue
		
		rm = dy / (1 - cos(tm))
		xm = x0 + rm * (tm - sin(tm))
		
		if (xm > x1):
			#pag 258
			t2 = tm
		else:
			t1 = tm
	
	L = []
	L2 = []
	r=rm
	for i in xrange(n+1):
		t=tm*i/n
		L.append ( [(x0+r*(t-sin(t))), (y0-r*(1-cos(t)))] )
		L2.extend ( [(x0+r*(t-sin(t))), (y0-r*(1-cos(t)))] )
	
	return L, L2
Пример #3
0
def GetSpindownStuff(tc, age, l0, b0, emax0, n0):

  t = np.logspace(0,math.log10(1000.*age),300)
  lumt = []
  emaxt = []
  bt = []
  nt = []
  n = 0
  for i in t:
    l = l0/math.pow(1.+i/tc,2.)
    btt = b0*math.sqrt(l/l0)*(1.+0.5*math.sin(0.1*n*3.14))
    lumtt = l*(1.+0.5*math.cos(0.1*n*3.14))
    emaxtt = emax0*math.pow(l/l0,0.25)*(1.+0.5*math.sin(0.05*n*3.14))
    ntt = n0*math.pow(l/l0,0.25)*(1.+0.5*math.cos(0.05*n*3.14))

    bt.append([])
    bt[n].append(i)
    bt[n].append(btt)
    lumt.append([])
    lumt[n].append(i)
    lumt[n].append(lumtt)
    emaxt.append([])
    emaxt[n].append(i)
    emaxt[n].append(emaxtt)
    nt.append([])
    nt[n].append(i)
    nt[n].append(ntt)

    n = n+1
  return lumt,bt,emaxt,nt
Пример #4
0
    def distance_on_unit_sphere(self,lat1, long1, lat2, long2):
        """
        from john d cook website http://www.johndcook.com/blog/python_longitude_latitude/
    
        :arg lat1: latitude value in degrees for clSite
        :arg lon1: longitude value in degrees for clSite
        :arg lat2: latitude value in degrees for zipcode
        :arg lon2: longitude value in degrees for zipcode
        :var all: see link for further explanation
        """
        degrees_to_radians = math.pi/180.0
             
        # phi = 90 - latitude
        phi1 = (90.0 - lat1)*degrees_to_radians
        phi2 = (90.0 - lat2)*degrees_to_radians
                 
        # theta = longitude
        theta1 = long1*degrees_to_radians
        theta2 = long2*degrees_to_radians
    
        cos = (math.sin(phi1)*math.sin(phi2)*math.cos(theta1 - theta2) + math.cos(phi1)*math.cos(phi2))
        arc = math.acos( cos )
 
        #To get the distance in miles, multiply by 3960. 
        #To get the distance in kilometers, multiply by 6373.
        arc = arc * 3960 #miles
        return arc 
def AngularDistance(RA1, DEC1, RA2, DEC2):

	try:
		RA1 = float(RA1)
		DEC1 = float(DEC1)
		RA2 = float(RA2)
		DEC2 = float(DEC2)

		# Converting everything to radians
		ra1rad = RA1 * math.pi/180.
		ra2rad = RA2 * math.pi/180.
		dec1rad = DEC1 * math.pi/180.
		dec2rad = DEC2 * math.pi/180.

		# Calculate scalar product for determination of angular separation      
		x=math.cos(ra1rad)*math.cos(dec1rad)*math.cos(ra2rad)*math.cos(dec2rad)
		y=math.sin(ra1rad)*math.cos(dec1rad)*math.sin(ra2rad)*math.cos(dec2rad)
		z=math.sin(dec1rad)*math.sin(dec2rad)
		rad=math.acos(x+y+z)

		# Use Pythargoras approximation if rad < 1 arcsec
		if rad<0.000004848:
			rad=math.sqrt((math.cos(dec1rad)*(ra1rad-ra2rad))**2+(dec1rad-dec2rad)**2)
			pass

		# Angular separation in degrees
		Angle = rad*180/math.pi

		return Angle

	except Exception, message:
		print message

		return float('nan')
Пример #6
0
def rotate_point(point, center, angle):
	""" Rotate a point around another point
	"""
	angle = math.radians(angle)
	x = center[0] + (point[0] - center[0]) * math.cos(angle) - (point[1] - center[1]) * math.sin(angle);
	y = center[1] - (point[0] - center[0]) * math.sin(angle) + (point[1] - center[1]) * math.cos(angle);
	return (x, y)
Пример #7
0
def show_visual(sec = False, radius = 39):
    c = Canvas(2*radius+1, 2*radius+1)
    x = 0
    while True:
        t = time.localtime()

        c.draw_circle(radius,radius,radius,1)
        c.draw_circle(radius,radius,radius-1,1)
        for i in xrange(12):
            dx = math.sin(2.0*math.pi*i/12)
            dy = math.cos(2.0*math.pi*i/12)
            if i%3 == 0:
                c.draw_line(radius+int(dx*radius), radius-int(dy*radius), radius+int(0.8*dx*radius), radius-int(0.8*dy*radius),1)
            else:
                c.draw_line(radius+int(dx*radius), radius-int(dy*radius), radius+int(0.9*dx*radius), radius-int(0.9*dy*radius),1)

        G = [((t[3]%12), 12, 0.4, 2), (t[4], 60, 0.6, 3), (t[5], 60, 0.8, 4)]
        for gnomon in G:
            dx = math.sin(2.0*math.pi*gnomon[0]/gnomon[1])
            dy = math.cos(2.0*math.pi*gnomon[0]/gnomon[1])

            c.draw_line(radius, radius, radius+int(dx*gnomon[2]*radius), radius-int(dy*gnomon[2]*radius), gnomon[3])
            c.draw_line(radius, radius, radius-int(dx*gnomon[2]*radius/4), radius+int(dy*gnomon[2]*radius/4), gnomon[3])

        c.render(width, height)
        time.sleep(1)

        for gnomon in G:
            dx = math.sin(2.0*math.pi*gnomon[0]/gnomon[1])
            dy = math.cos(2.0*math.pi*gnomon[0]/gnomon[1])

            c.draw_line(radius, radius, radius+int(dx*gnomon[2]*radius), radius-int(dy*gnomon[2]*radius), 0)
            c.draw_line(radius, radius, radius-int(dx*gnomon[2]*radius/4), radius+int(dy*gnomon[2]*radius/4), 0)
def findPointOnSphere(cx, cy, cz, radius, phi, theta):
    #phi - angle around the pole 0<= phi <= 360
    #theta - angle from plan 'up' -90 <= theta <= 90
    x = cx + radius * math.cos(math.radians(theta)) * math.cos(math.radians(phi))
    z = cz + radius * math.cos(math.radians(theta)) * math.sin(math.radians(phi))
    y = cy + radius * math.sin(math.radians(theta))
    return int(round(x,0)), int(round(y,0)), int(round(z,0))
Пример #9
0
def vorbiswindow(j, K):
    if j < 0:
        return 0
    elif j >= K:
        return 0
    z = sin(pi / K * (j + 0.5))
    return sin(pi * 0.5 * z * z)
Пример #10
0
def distance_on_unit_sphere(lat1, long1, lat2, long2):

    # Convert latitude and longitude to
    # spherical coordinates in radians.
    degrees_to_radians = math.pi/180.0

    # phi = 90 - latitude
    phi1 = (90.0 - lat1)*degrees_to_radians
    phi2 = (90.0 - lat2)*degrees_to_radians

    # theta = longitude
    theta1 = long1*degrees_to_radians
    theta2 = long2*degrees_to_radians

    # Compute spherical distance from spherical coordinates.

    # For two locations in spherical coordinates
    # (1, theta, phi) and (1, theta, phi)
    # cosine( arc length ) =
    #    sin phi sin phi' cos(theta-theta') + cos phi cos phi'
    # distance = rho * arc length

    cos = (math.sin(phi1)*math.sin(phi2)*math.cos(theta1 - theta2) +
           math.cos(phi1)*math.cos(phi2))
    arc = math.acos(cos)

    # Remember to multiply arc by the radius of the earth
    # in your favorite set of units to get length.
    return arc * EARTH_RADIUS_MILES
Пример #11
0
def gps_distance_between(point_a, point_b):
    """
    Calculate the orthodromic distance between two GPS readings.

    point_a and point_b can be either of the two:
    - tuples in the form (latitude, longitude).
    - instances of the class logwork.Signal
    The result is in metres.

    ATTENTION: since latitude is given before longitude, if we are using the
    X and Y representation, then we must pass in (Y, X) and *not* (X, Y)

    Computed with the Haversine formula
    (http://en.wikipedia.org/wiki/Haversine_formula)
    """
    if hasattr(point_a, "latitude"):
        a_lat, a_lon = math.radians(point_a.latitude), math.radians(point_a.longitude)
    else:
        a_lat, a_lon = math.radians(point_a[0]), math.radians(point_a[1])
    if hasattr(point_b, "latitude"):
        b_lat, b_lon = math.radians(point_b.latitude), math.radians(point_b.longitude)
    else:
        b_lat, b_lon = math.radians(point_b[0]), math.radians(point_b[1])
    d_lat = b_lat - a_lat
    d_lon = b_lon - a_lon
    a = math.sin(d_lat / 2.0) ** 2 + math.cos(a_lat) * math.cos(b_lat) * math.sin(d_lon / 2.0) ** 2
    c = 2 * math.asin(math.sqrt(a))
    return EARTH_RADIUS * c * 1000
Пример #12
0
	def cart2tether_actual(sz,xyz):
		#convert a cartesian goal to tether length goals. assumes the tethers go to points on the outside edge of the end effector.
		#returns a more precise estimate of tether length, but one that is inadmissible to the get_xyz_pos function
		#goal : 1x3 array [x,y,z]
			# L = 1x4 array [L0,L1,L2,L3] spiral zipper and each tether length
		#finds the axis-angle rotation matrix from the column's vertical pose.
		theta = sz.angle_between([0,0,sz.L[0]], xyz)
		k = np.cross([0,0,sz.L[0]],xyz)

		if np.linalg.norm(k) != 0: #ensures k is a unit vector where its norm == 1
			k = k/np.linalg.norm(k)

		Xk = k[0]
		Yk = k[1]
		Zk = k[2]
		v = 1 - m.cos(theta)

		R = np.array( [[m.cos(theta) + (Xk**2*v)   , (Xk*Yk*v) - (Zk*m.sin(theta)), (Xk*Zk*v) + Yk*m.sin(theta)],\
					   [((Yk*Xk*v) + Zk*m.sin(theta)), m.cos(theta) + (Yk**2*v)     , (Yk*Zk*v) - Xk*m.sin(theta)],\
					   [(Zk*Xk*v) - Yk*m.sin(theta), (Zk*Yk*v) + Xk*m.sin(theta)  , m.cos(theta) + (Zk**2*v)   ]])


		#calculates position vector of the column tether attachment points in the world frame
		OB1 = xyz + np.dot(R,sz.ef[0])  
		OB2 = xyz + np.dot(R,sz.ef[1])		
		OB3 = xyz + np.dot(R,sz.ef[2])

		L0 = m.sqrt((xyz[0]**2+xyz[1]**2+xyz[2]**2)) # should just be sz.L[0] if not there is a math mistake
		L1 = np.linalg.norm(OB1 - sz.p[0])
		L2 = np.linalg.norm(OB2 - sz.p[1])
		L3 = np.linalg.norm(OB3 - sz.p[2])
		L = [L0,L1,L2,L3]
		return L
Пример #13
0
    def execute(self, context):

        A = 6.283185307179586476925286766559 / 3

        verts = [(sin(A * 1), 0.0, cos(A * 1)),
                 (sin(A * 2), 0.0, cos(A * 2)),
                 (sin(A * 3), 0.0, cos(A * 3)),
                 ]

        faces = [(0, 1, 2)]

        mesh = bpy.data.meshes.new("Cube")

        bm = bmesh.new()

        for v_co in verts:
            bm.verts.new(v_co)

        for f_idx in faces:
            bm.faces.new([bm.verts[i] for i in f_idx])

        bm.to_mesh(mesh)
        mesh.update()

        object_utils.object_data_add(context, mesh)

        return{'FINISHED'}
Пример #14
0
 def __init__(self,pos,direction,d_range):
     self.surface = pygame.surface.Surface((50,50))
     self.surface.fill((0,250,200))
     self.rect = pygame.rect.Rect(pos[0],pos[1],50,50)
     self.dir = direction
     self.dist = 0
     self.range = d_range
     speed = 2
     dx = 0
     dy = 0
     if self.dir>0:
         if self.dir>90:
             dy = speed*math.sin(180-self.dir)
             dx = speed*math.cos(180-self.dir)
         else:
             dy = speed*math.sin(self.dir)
             dx = speed*math.cos(self.dir)
     else:
         if self.dir<-90:
             dy = speed*math.sin(180+self.dir)
             dx = speed*math.cos(180+self.dir)
         else:
             dy = speed*math.sin(self.dir)
             dx = speed*math.cos(self.dir)
     self.dx = dx
     self.dy = dy
 def __init__(self, lb, lb_length, up_angle, dn_angle, hb, hb_length):
     # define the name
     # (there is only one launchbar element) --> isn't it ?
     name = 'YASim_Launchbar'
     
     # Calculate points for the mesh
     
     # here in the original script hb = hb - lb
     # --> seems to be tuple - vector, that is not working
     # assuming: (this step is necessary to get from global to local coordinates !!)
     hb = hb - Vector(lb)
     
     lb_tip = ORIGIN + lb_length * math.cos(dn_angle * DEG2RAD) * X - lb_length * math.sin(dn_angle * DEG2RAD) * Z
     hb_tip = hb - hb_length * math.cos(dn_angle * DEG2RAD) * X - hb_length * math.sin(dn_angle * DEG2RAD) * Z
     
     # create the mesh: launchbar and holdback extended position
     lb_obj = mesh_create(name, lb, [ORIGIN, lb_tip, hb, hb_tip, lb_tip+0.05*Y, lb_tip-0.05*Y, hb_tip+0.05*Y, hb_tip-0.05*Y],
                                 [(0,1),(0,2),(2,3),(4,5),(6,7)], [])
     
     # set the created object active !!!!!!!
     bpy.context.scene.objects.active = lb_obj
     
     # draw dashed lines for the retracted position
     # get the active mesh
     mesh = bpy.context.object.data
     
     lb_up = lb_length * math.cos(up_angle * DEG2RAD) * X - lb_length * math.sin(up_angle * DEG2RAD) * Z
     hb_up = hb - hb_length * math.cos(up_angle * DEG2RAD) * X - hb_length * math.sin(up_angle * DEG2RAD) * Z
     
     draw_dashed_line(mesh, ORIGIN, lb_up)
     draw_dashed_line(mesh, hb, hb_up)
     
     # set material
     Item.set_material('grey2', (0.3,0.3,0.3), 1)
Пример #16
0
    def get_geo_distance_from(self, lat2, long2):
        lat1 = self.geo_latitude
        long1 = self.geo_longitude
        if not lat1 or not long1 or not lat2 or not long2:
            return -1
        # Convert latitude and longitude to
        # spherical coordinates in radians.
        degrees_to_radians = math.pi / 180.0

        # phi = 90 - latitude
        phi1 = (90.0 - lat1) * degrees_to_radians
        phi2 = (90.0 - lat2) * degrees_to_radians

        # theta = longitude
        theta1 = long1 * degrees_to_radians
        theta2 = long2 * degrees_to_radians

        # Compute spherical distance from spherical coordinates.

        # For two locations in spherical coordinates
        # (1, theta, phi) and (1, theta, phi)
        # cosine( arc length ) =
        # sin phi sin phi' cos(theta-theta') + cos phi cos phi'
        # distance = rho * arc length

        cos = (math.sin(phi1) * math.sin(phi2) * math.cos(theta1 - theta2) +
               math.cos(phi1) * math.cos(phi2))
        arc = math.acos(cos)

        # Remember to multiply arc by the radius of the earth
        # in your favorite set of units to get length.
        return float(round(arc * 6371 * 1000))
Пример #17
0
	def calc_point_distance( self, p1, p2 ) :
		x1    = float( p1['x'] )
		y1    = float( p1['y'] )
		lat1  = x1 * math.pi / 180.0
		long1 = y1 * math.pi / 180.0
		sinl1 = math.sin( lat1 )
		cosl1 = math.cos( lat1 )
		
		x2    = float( p2['x'] )
		y2    = float( p2['y'] )
		lat2  = x2 * math.pi / 180.0
		long2 = y2 * math.pi / 180.0
		sinl2 = math.sin( lat2 )
		cosl2 = math.cos( lat2 )
		
		dl    = long2 - long1
		sindl = math.sin( dl )
		cosdl = math.cos( dl )
		
		a = cosl2 * sindl
		b = cosl1 * sinl2 - sinl1 * cosl2 * cosdl
		y = math.sqrt( a*a + b*b )
		x = sinl1 * sinl2 + cosl1 * cosl2 * cosdl
		d = math.atan2( y, x ) * 6372795 # радиус Земли
		
		#print( "d=%d" % ( d ) )
		return d
Пример #18
0
def day_length(doy, yr_days, latitude):
    """ Daylength in hours

    Eqns come from Leuning A4, A5 and A6, pg. 1196
    
    Reference:
    ----------
    Leuning et al (1995) Plant, Cell and Environment, 18, 1183-1200.
    
    Parameters:
    -----------
    doy : int
        day of year, 1=jan 1
    yr_days : int
        number of days in a year, 365 or 366
    latitude : float
        latitude [degrees]

    Returns:
    --------
    dayl : float
        daylength [hrs]

    """
    deg2rad = pi / 180.0
    latr = latitude * deg2rad
    sindec = -sin(23.5 * deg2rad) * cos(2.0 * pi * (doy + 10.0) / yr_days)
    a = sin(latr) * sindec
    b = cos(latr) * cos(asin(sindec))
    dayl = 12.0 * (1.0 + (2.0 / pi) * asin(a / b))
    
    return dayl
Пример #19
0
    def mat_unitary(self):
        s = [
            math.sin(2 * self.at0),
            math.sin(2 * self.at1),
            math.sin(2 * self.aq0),
            math.sin(2 * self.aq1),
            math.sin(2 * self.aq2),
        ]
        c = [
            math.cos(2 * self.at0),
            math.cos(2 * self.at1),
            math.cos(2 * self.aq0),
            math.cos(2 * self.aq1),
            math.cos(2 * self.aq2),
        ]
        phi = [
            numpy.exp(complex(0, 4 * self.pt1)),
            numpy.exp(complex(0, 2 * self.pt2)),
            numpy.exp(complex(0, -2 * self.pt2)),
        ]

        U = numpy.array(
            [
                [c[2] * c[3], -phi[0] * s[0] * s[2] * c[3] - phi[1] * c[0] * s[1] * s[3]],
                [c[2] * s[3], -phi[0] * s[0] * s[2] * s[3] + phi[1] * c[0] * s[1] * c[3]],
                [s[2] * c[4], phi[0] * s[0] * c[2] * c[4] + phi[2] * c[0] * c[1] * s[4]],
                [s[2] * s[4], phi[0] * s[0] * c[2] * s[4] - phi[2] * c[0] * c[1] * c[4]],
            ]
        )

        theta = cmath.phase(U[0, 1])
        for i in range(4):
            U[i, 1] = U[i, 1] * numpy.exp(complex(0, -theta))

        return U
def flange(typeofFlange):

    #variables
    points = [] #collection
    nP = 100
    nSin = 10


    #conditional assignment

    if (typeofFlange == "floppy"):
        t = 3
        r = 15
        amp = 10
        
    if (typeofFlange == "extrafloppy"):
        t = 3
        r = 30
        amp = 20

#iteration to calculate points
    for i in rs.frange(0, nP, 1):
        x = r * math.sin(i*360/(nP-1))
        y = r * math.cos(i*360/(nP-1))
        z = amp*math.sin(i*nSin*360/(nP-1))
#Feature
        point = rs.AddPoint([x,y,z])
        points.append(point)
Пример #21
0
    def paint(self, painter, option, widget):
        if not self.source or not self.dest:
            return

        # Draw the line itself.
        line = QtCore.QLineF(self.sourcePoint, self.destPoint)

        if line.length() == 0.0:
            return

        painter.setPen(QtGui.QPen(QtCore.Qt.black, 1, QtCore.Qt.SolidLine, QtCore.Qt.RoundCap, QtCore.Qt.RoundJoin))
        painter.drawLine(line)

        # Draw the arrows if there's enough room.
        angle = math.acos(line.dx() / line.length())
        if line.dy() >= 0:
            angle = Edge.TwoPi - angle

        sourceArrowP1 = self.sourcePoint + QtCore.QPointF(math.sin(angle + Edge.Pi / 3) * self.arrowSize,
                                                          math.cos(angle + Edge.Pi / 3) * self.arrowSize)
        sourceArrowP2 = self.sourcePoint + QtCore.QPointF(math.sin(angle + Edge.Pi - Edge.Pi / 3) * self.arrowSize,
                                                          math.cos(angle + Edge.Pi - Edge.Pi / 3) * self.arrowSize);
        destArrowP1 = self.destPoint + QtCore.QPointF(math.sin(angle - Edge.Pi / 3) * self.arrowSize,
                                                      math.cos(angle - Edge.Pi / 3) * self.arrowSize)
        destArrowP2 = self.destPoint + QtCore.QPointF(math.sin(angle - Edge.Pi + Edge.Pi / 3) * self.arrowSize,
                                                      math.cos(angle - Edge.Pi + Edge.Pi / 3) * self.arrowSize)

        painter.setBrush(QtCore.Qt.black)
        painter.drawPolygon(QtGui.QPolygonF([line.p1(), sourceArrowP1, sourceArrowP2]))
        painter.drawPolygon(QtGui.QPolygonF([line.p2(), destArrowP1, destArrowP2]))
Пример #22
0
    def update(self):
        if self.turning_right:
            self.rot -= 5
        if self.turning_left:
            self.rot += 5

        a = [0.0,0.0]
        if self.boost_endtime > rabbyt.get_time():
            f = 3*(self.boost_endtime - rabbyt.get_time())/self.boost_length
            a[0] += cos(radians(self.boost_rot))*f
            a[1] += sin(radians(self.boost_rot))*f
            self.create_boost_particle()

        if self.accelerating:
            a[0] += cos(radians(self.rot))*.9
            a[1] += sin(radians(self.rot))*.9
            self.create_dust_particle(self.dust_r)
            self.create_dust_particle(self.dust_l)

        ff = .9 # Friction Factor

        self.velocity[0] *= ff
        self.velocity[1] *= ff

        self.velocity[0] += a[0]
        self.velocity[1] += a[1]

        self.x += self.velocity[0]
        self.y += self.velocity[1]
Пример #23
0
    def __init__(self, scale=1.0):
        self.translation = Vector3()
        self.rotation = Vector3()
        self.initialHeight = Vector3(0, 0, scale*StewartPlatformMath.SCALE_INITIAL_HEIGHT)
        self.baseJoint = []
        self.platformJoint = []
        self.q = []
        self.l = []
        self.alpha = []
        self.baseRadius = scale*StewartPlatformMath.SCALE_BASE_RADIUS
        self.platformRadius = scale*StewartPlatformMath.SCALE_PLATFORM_RADIUS
        self.hornLength = scale*StewartPlatformMath.SCALE_HORN_LENGTH
        self.legLength = scale*StewartPlatformMath.SCALE_LEG_LENGTH;

        for angle in self.baseAngles:
            mx = self.baseRadius*cos(radians(angle))
            my = self.baseRadius*sin(radians(angle))
            self.baseJoint.append(Vector3(mx, my))

        for angle in self.platformAngles:
            mx = self.platformRadius*cos(radians(angle))
            my = self.platformRadius*sin(radians(angle))
            self.platformJoint.append(Vector3(mx, my))

        self.q = [Vector3()]*len(self.platformAngles)
        self.l = [Vector3()]*len(self.platformAngles)
        self.alpha = [0]*len(self.beta)
Пример #24
0
def distance(origin, destination):
    """ 
    Calculates both distance and bearing
    """
    lat1, lon1 = origin
    lat2, lon2 = destination
    if lat1>1000:
        (lat1,lon1)=dm2dd(lat1,lon1)
        (lat2,lon2)=dm2dd(lat2,lon2)
        print('converted to from ddmm to dd.ddd')
    radius = 6371 # km
    

    dlat = math.radians(lat2-lat1)
    dlon = math.radians(lon2-lon1)
    a = math.sin(dlat/2) * math.sin(dlat/2) + math.cos(math.radians(lat1)) \
        * math.cos(math.radians(lat2)) * math.sin(dlon/2) * math.sin(dlon/2)
    c = 2 * math.atan2(math.sqrt(a), math.sqrt(1-a))
    d = radius * c
    
    def calcBearing(lat1, lon1, lat2, lon2):
       dLon = lon2 - lon1
       y = math.sin(dLon) * math.cos(lat2)
       x = math.cos(lat1) * math.sin(lat2) \
           - math.sin(lat1) * math.cos(lat2) * math.cos(dLon)
       return math.atan2(y, x)
       
    bear= math.degrees(calcBearing(lat1, lon1, lat2, lon2))  
    return d,bear
Пример #25
0
    def sumVectors(self, vectors):
        """ sum all vectors (including targetvector)"""
        endObstacleVector = (0,0)

        ##generate endvector of obstacles
        #sum obstaclevectors
        for vector in vectors:
            vectorX = math.sin(math.radians(vector[1])) * vector[0] # x-position
            vectorY = math.cos(math.radians(vector[1])) * vector[0] # y-position
            endObstacleVector = (endObstacleVector[0]+vectorX,endObstacleVector[1]+vectorY)
        #mean obstaclevectors
        if len(vectors) > 0:
            endObstacleVector = (endObstacleVector[0]/len(vectors), endObstacleVector[1]/len(vectors))

        #add targetvector
        targetVector = self.target
        if targetVector != 0 and targetVector != None:
            vectorX = math.sin(math.radians(targetVector[1])) * targetVector[0] # x-position
            vectorY = math.cos(math.radians(targetVector[1])) * targetVector[0] # y-position
            endVector = (endObstacleVector[0]+vectorX,endObstacleVector[1]+vectorY)
            #endVector = (endVector[0]/2, endVector[1]/2)
        else:
            endVector = endObstacleVector


        return endVector
Пример #26
0
def distance(xlat, xlon, ylat, ylon):
    dlon = ylon - xlon
    dlat = ylat - xlat
    a = sin(dlat / 2) ** 2 + cos(xlat) * cos(ylat) * sin(dlon / 2) ** 2
    c = 2 * atan2(sqrt(a), sqrt(1 - a))
    distance = R * c
    return distance
Пример #27
0
    def update_location(self, delta_encoder_count_1, delta_encoder_count_2):
        """
        Update the robot's location

        @rtype : DifferentialDriveRobotLocation
        @return: Updated location
        @param delta_encoder_count_1: Count of wheel 1's encoder since last update
        @param delta_encoder_count_2: Count of wheel 2's encoder since last update
        @type delta_encoder_count_1: int
        @type delta_encoder_count_2: int
        """
        dfr = delta_encoder_count_2 * 2 * math.pi / self.robot_parameters.steps_per_revolution
        dfl = delta_encoder_count_1 * 2 * math.pi / self.robot_parameters.steps_per_revolution

        ds = (dfr + dfl) * self.robot_parameters.wheel_radius / 2
        dz = (dfr - dfl) * self.robot_parameters.wheel_radius / self.robot_parameters.wheel_distance

        self.location.x_position += ds * math.cos(self.location.z_position + dz / 2)
        self.location.y_position += ds * math.sin(self.location.z_position + dz / 2)
        self.location.z_position += dz

        self.globalLocation.x_position += ds * math.cos(self.globalLocation.z_position + dz / 2)
        self.globalLocation.y_position += ds * math.sin(self.globalLocation.z_position + dz / 2)
        self.globalLocation.z_position += dz

        return self.location, self.globalLocation
Пример #28
0
    def refresh(self, matrix):
        matrix.fade(0.995)

        y0 = matrix.height/2
        x0 = matrix.width/2

        if self.angle >= pi:
            x0 -= 1

        if self.angle > (0.5*pi) and self.angle < (1.5*pi):
            y0 -= 1

        x1 = int(self.x0 + self.radius * sin(self.angle-self.astep))
        y1 = int(self.y0 + self.radius * cos(self.angle+self.astep))

        x2 = int(self.x0 + self.radius * sin(self.angle))
        y2 = int(self.y0 + self.radius * cos(self.angle))

        matrix.drawPoly(
            [(self.x0, self.y0), (x1, y1), (x2, y2)],
            hsvToRgb(self.hue)
        )

        self.hue = fmod(self.hue+self.hstep, 1.0)
        self.angle += self.astep
    def calculate_initial_compass_bearing(self, pointA, pointB):
        """
        Calculates direction between two points.
        Code based on compassbearing.py module
        https://gist.github.com/jeromer/2005586

        pointA: latitude/longitude for first point (decimal degrees)
        pointB: latitude/longitude for second point (decimal degrees)
    
        Return: direction heading in degrees (0-360 degrees, with 90 = North)
        """

        if (type(pointA) != tuple) or (type(pointB) != tuple):
            raise TypeError("Only tuples are supported as arguments")
    
        lat1 = math.radians(pointA[0])
        lat2 = math.radians(pointB[0])
    
        diffLong = math.radians(pointB[1] - pointA[1])
    
        # Direction angle (-180 to +180 degrees):
        # θ = atan2(sin(Δlong).cos(lat2),cos(lat1).sin(lat2) − sin(lat1).cos(lat2).cos(Δlong))

        x = math.sin(diffLong) * math.cos(lat2)
        y = math.cos(lat1) * math.sin(lat2) - (math.sin(lat1) * math.cos(lat2) * math.cos(diffLong))
    
        initial_bearing = math.atan2(x, y)
    
        # Direction calculation requires to normalize direction angle (0 - 360)
        initial_bearing = math.degrees(initial_bearing)
        compass_bearing = (initial_bearing + 360) % 360
    
        return compass_bearing
Пример #30
0
    def __init__(self, matrix=None, scale=None, rotation=None,
                 translation=None):
        params = any(param is not None
                     for param in (scale, rotation, translation))

        if params and matrix is not None:
            raise ValueError("You cannot specify the transformation matrix and"
                             " the implicit parameters at the same time.")
        elif matrix is not None:
            if matrix.shape != (3, 3):
                raise ValueError("Invalid shape of transformation matrix.")
            self._matrix = matrix
        elif params:
            if scale is None:
                scale = 1
            if rotation is None:
                rotation = 0
            if translation is None:
                translation = (0, 0)

            self._matrix = np.array([
                [math.cos(rotation), - math.sin(rotation), 0],
                [math.sin(rotation),   math.cos(rotation), 0],
                [                 0,                    0, 1]
            ])
            self._matrix[0:2, 0:2] *= scale
            self._matrix[0:2, 2] = translation
        else:
            # default to an identity transform
            self._matrix = np.eye(3)
Пример #31
0
def PointsFromAngle(angle):
    ### Returns The Unit Direction Vector With Given Angle ###
    return math.cos(angle), math.sin(angle)
Пример #32
0
 def SunShape(x, y, r, e, l, b):
     p, a, h=[], 2*pi/e, r*l
     c, d=[0, -a/2][b], [a/2, 0][b]
     for i in range(e):
         p+=[(x+r*cos(i*a+c), y+r*sin(i*a+c)), (x+h*cos(i*a+d), y+h*sin(i*a+d))]
     canvas.create_polygon(p, fill="white")
Пример #33
0
def calculate_distance(lng1, lat1, lng2, lat2):  # 经度和纬度 longitude and latitude,计算球上两点的距离
    RADIUS = 6378.137  # 半径,单位km
    PI = math.pi
    return 2 * RADIUS * math.asin(math.sqrt(pow(math.sin(PI * (lat1 - lat2) / 360), 2) + math.cos(PI * lat1 / 180) * \
                                            math.cos(PI * lat2 / 180) * pow(math.sin(PI * (lng1 - lng2) / 360), 2)))
Пример #34
0
def f(x):
    return math.sin(x) - 3 * math.cos(x**2) + 2 * (math.sin(x))**2
Пример #35
0
	def dzjolt(self, dz):
		dzj = self.Ajolt * math.sin(self.tjolt * 20)
		f = min(math.exp(-self.tjolt), 0.05 * self.tjolt)
		return math.mix(dz, dzj, f)
Пример #36
0
	def sway(self):
		return self.Asway * math.sin(math.tau * (self.t / self.Tsway + self.swayphase))
print("Find the correct paralltic angle")
# https://en.wikipedia.org/wiki/HR_8799
Declination = 21 + 8 * (1 / 60) + 0.302 * (1 / 3600)
print("Declination of HR8799; 21° 08' 03.302''")
print("Declination=", Declination, "°")
Declination = math.radians(Declination)
# https://www.ifa.hawaii.edu/mko/coordinates.shtml
Geographical_latitude = 19 + 49 * (1 / 60) + 35.61788 * (1 / 3600)
print("Geographical latitude of Keck 2: 19° 49' 35.61788''")
print("Geographical latitude=", Geographical_latitude, "°")
Geographical_latitude = math.radians(Geographical_latitude)

para_angle_thm = np.zeros(len(fn_list))
for i in range(len(fn_list)):

    x = (math.sin(
        HA[i])) / (math.tan(Geographical_latitude) * math.cos(Declination) -
                   math.sin(Declination) * math.cos(HA[i]))
    para_angle_thm[i] = math.atan(x)

start = time.time()
for img, angle in zip(imgcube, para_angle_thm):
    img_cADI += ndimage.rotate(
        img - PSF_cADI,  # subtract the PSF before rotationg
        -angle,  # in degree. rotate the image counter-clockwisely if the value is positive
        reshape=False)  # retain the same shape as the input image

plt.ion()
plt.figure(figsize=(6, 6))
plt.imshow(img_cADI, cmap="gray")
plt.xlim(344, 680)
plt.ylim(344, 680)
Пример #38
0
import random
import math
import pygame

background_colour = (255,255,255)
(width, height) = (1024, 720)
gravity = (math.pi/2, 0.08)
drag = 0.999
elasticity = 0.95

def addVectors((angle1,length1), (angle2,length2)):
  x = math.cos(angle1)*length1 + math.cos(angle2)*length2
  y = math.sin(angle1)*length1+math.sin(angle2)*length2
  length = math.sqrt(x*x+y*y)
  angle = math.atan2(y,x)
  return (angle, length)

def findParticle(particles, x, y):
  for p in particles:
    if math.sqrt((p.x-x)**2+(p.y-y)**2) <= p.size:
      return p
  return None

def collide(p1,p2):
	dx = p1.x - p2.x
	dy = p1.y - p2.y
	lengd = math.sqrt(dx**2+dy**2)
	if lengd < (p1.size + p2.size):
		tangAngle = math.atan2(dy,dx)
		(p1.angle,p2.angle) = (p1.angle + math.pi/2.0 - tangAngle, p2.angle + math.pi/2.0 - tangAngle)
		(p1.speed,p2.speed) = (p2.speed, p1.speed)
Пример #39
0
    #########################################################
    # FINDING THETAS #
    #########################################################

    theta0 = 2 * math.pi * np.random.randn(
    )  # initial theta; consider adding 2 pi times randn
    theta_list = np.empty(colnum)  # list of all thetas

    euler_theta(theta0, t, theta_list, func_theta)  # stored in theta_list

    #########################################################
    # FINDING POSITION #
    #########################################################

    r_x0 = math.cos(theta0)  # initial x-coordinate of position
    r_y0 = math.sin(theta0)  # initial y-coordinate of position

    euler_r(r_x0, t, all_r[i, :, 0], theta_list, funcx_r)  # x-coordinates
    euler_r(r_y0, t, all_r[i, :, 1], theta_list, funcy_r)  # y-coordinates

    #########################################################
    # PLOT RESULTS #
    #########################################################

    # Plots Theta values

    plt.plot(t, theta_list, 'g')
    plt.xlabel('Time (Seconds)')
    plt.ylabel('Angle (Radians)')
    plt.title('Angle v. Time: Trial ' + str((i + 1)))
Пример #40
0
 def move(self):
     self.x += math.cos(self.angle) * self.speed
     self.y += math.sin(self.angle) * self.speed
     (self.angle, self.speed) = addVectors((self.angle,self.speed),gravity)
     self.speed*=drag
Пример #41
0
    # readFile = open('dataDynamic/'+filename+'.txt', 'r')
    # filename = str(i)
    # readFile = open('dataraw/'+filename+'.txt', 'r')
    readFile = open('out.txt', 'r')
    txt = readFile.readlines()
    readFile.close()
    x = []
    y = []
    xy = []
    fig = plt.figure()
    for i in range(len(txt)):
        if i % 2 == 0:
            tmp = txt[i]
            r = int(tmp.split(' ')[0])
            angle = int(tmp.split(' ')[1])
            x.append(r * math.sin(math.radians(angle)))
            y.append(r * math.cos(math.radians(angle)))
            xy.append((int(r * math.sin(math.radians(angle))),
                       int(r * math.cos(math.radians(angle)))))

    def select_x(tmp):
        return tmp[0]

    xy.sort(key=select_x)

    # print(xy)


    def plot():
        ax = fig.add_subplot(1, 1, 1)
        ax.grid(True)
Пример #42
0
def funcy_r(theta,
            posit_y):  # differential equation for y-component of position
    return (v0 * math.sin(theta) + k * math.cos(posit_y))
Пример #43
0
# Draw a solid blue circle in the center

#pygame.draw.circle(screen, (255, 0, 0), (startx, starty), 1)

anglectr = angleStart

for r in list:

    coordinates = []

    radian = anglectr * (math.pi / 180)
    #print(str(r) +" at angle of "+str(radian))
    anglectr = anglectr + 0.25

    x = float(scaling) * float(r) * math.cos(radian)
    y = float(scaling) * float(r) * math.sin(radian)

    coordinates.append(x)
    coordinates.append(y)
    #print(angleStart)
    #pygame.draw.circle(screen, (0, 255, 0), (x+startx, y+starty), 1)

    pointlist.append(coordinates)
    #time.sleep(0.1)
    #pygame.display.flip()

#print(pointlist)
#time.sleep(50)
# Flip the display

import matplotlib.pyplot as plt
Пример #44
0
wbeamX=0.35
wbeamY=0.5
wcolumnZ=0.40
deckTh=0.20
wallTh=0.5
footTh=0.7

 #Actions
qdeck1=1e3  #N/m2
qdeck2=2e3   #N/m2
Qbeam=3e3  #N/m
qunifBeam=5e3
qLinDeck2=30 #N/m
Qwheel=5e3  #N
firad=math.radians(31)  #internal friction angle (radians)                   
KearthPress=(1-math.sin(firad))/(1+math.sin(firad))     #Active coefficient of p
densSoil=800       #mass density of the soil (kg/m3)
densWater=1000      #mass density of the water (kg/m3)


#Materials
concrete=EHE_materials.HA30
reinfSteel=EHE_materials.B500S
# concrete=SIA262_materials.c30_37
# reinfSteel=SIA262_materials.B500B

eSize= 0.2     #length of elements

#             *** GEOMETRIC model (points, lines, surfaces) - SETS ***
FEcase= xc.FEProblem()
preprocessor=FEcase.getPreprocessor
Пример #45
0
 def __getCosAndSin(self, angle):
     return math.cos(angle), math.sin(angle)
Пример #46
0
# common functions
def twist_mesh(vertex_list, mesh, Axis, Angle, StartFrom, EndAt):

    StartFrom, EndAt = min(StartFrom, EndAt) / 100.0, max(StartFrom,
                                                          EndAt) / 100.0
    Angle = pi * Angle / 180.0

    def rot_x((x, y, z), angle):
        c = cos(angle)
        s = sin(angle)
        return (x, y * c - z * s, y * s + z * c)

    def rot_y((x, y, z), angle):
        c = cos(angle)
        s = sin(angle)
        return (x * c - z * s, y, x * s + z * c)

    def rot_z((x, y, z), angle):
        c = cos(angle)
        s = sin(angle)
        return (x * c - y * s, x * s + y * s, z)

    if Axis == 'x':
        d = max_x - min_x
        rd = EndAt - StartFrom
        for index, v in enumerate(mesh.verts):
            t = (vertex_list[index][0] - min_x) / d
            if StartFrom <= t <= EndAt:
                ang = Angle * (t - StartFrom) / rd
                v.co[0], v.co[1], v.co[2] = rot_x(vertex_list[index], ang)
def calcula_distancia_do_projetil(v,yo,t):
    a = (v**2)/(2*9.8)
    b = (1+(2*9.8*yo)/(v**2*(math.sin(t))**2))**(1/2)
    c = math.sin(2*t)
    return ((a)*(1+b)*(c))
 def ovector(self, angle):
     return math.cos(angle),math.sin(angle)
Пример #49
0
 def g0(self, L):
     """
     acceleration due to gravity at the elipsoid surface at latitude L
     """
     return 9.7803267715 * (1 + 0.001931851353 * sin(L)**2) / \
         sqrt(1 - 0.0066943800229 * sin(L)**2)
Пример #50
0
# issue 499
data = [1, 2, 3]
data = (item for item in data)
assert list(data) == [1, 2, 3]

# issue 557
from math import sin, log


class N:
    def __float__(self):
        return 42.0


num = N()
assert sin(num) == -0.9165215479156338
assert log(num) == 3.7376696182833684


# issue 560
class Base:
    @classmethod
    def test(cls):
        return cls


class Derived(Base):
    def __init__(self):
        pass

Пример #51
0
import math
import numpy as np
from AirSimClient import *

client = MultirotorClient()
client.confirmConnection()
client.enableApiControl(True)
client.armDisarm(True)
#client.takeoff()
#client.hover()
client.moveToZ(-6, 5)
duration = 1
speed_x = 3
speed_y = 3

pitch, roll, yaw = client.getPitchRollYaw()
vel = client.getVelocity()
vx = math.cos(yaw) * speed_x - math.sin(yaw) * speed_y
vy = math.sin(yaw) * speed_x + math.cos(yaw) * speed_y

drivetrain = DrivetrainType.ForwardOnly
yaw_mode = YawMode(is_rate=False, yaw_or_rate=0)
print(vel.z_val)

client.moveByVelocity(vx=0,
                      vy=0.5,
                      vz=0,
                      duration=duration + 5,
                      drivetrain=drivetrain,
                      yaw_mode=yaw_mode)
print(vel.z_val)
Пример #52
0
def load_data():
    global canvas_extents, sensor_canvas_extents, world_extents, max_scanner_range
    for filename in all_file_names:
        logfile.read(filename)

    global draw_objects
    draw_objects = []
    scale.configure(to=logfile.size() - 1)

    # Insert: landmarks.
    draw_objects.append(
        Landmarks(logfile.landmarks, world_canvas, canvas_extents,
                  world_extents))

    # Insert: reference trajectory.
    positions = [
        to_world_canvas(pos, canvas_extents, world_extents)
        for pos in logfile.reference_positions
    ]
    draw_objects.append(
        Trajectory(positions,
                   world_canvas,
                   world_extents,
                   canvas_extents,
                   cursor_color="red",
                   background_color="#FFB4B4"))

    # Insert: filtered trajectory.
    if logfile.filtered_positions:
        if len(logfile.filtered_positions[0]) > 2:
            positions = [
                tuple(
                    list(to_world_canvas(pos, canvas_extents, world_extents)) +
                    [pos[2]]) for pos in logfile.filtered_positions
            ]
        else:
            positions = [
                to_world_canvas(pos, canvas_extents, world_extents)
                for pos in logfile.filtered_positions
            ]
        # If there is error ellipses, insert them as well.
        draw_objects.append(
            Trajectory(positions,
                       world_canvas,
                       world_extents,
                       canvas_extents,
                       standard_deviations=logfile.filtered_stddev,
                       cursor_color="blue",
                       background_color="lightblue",
                       position_stddev_color="#8080ff",
                       theta_stddev_color="#c0c0ff"))

    # Insert: scanner data.
    draw_objects.append(
        ScannerData(logfile.scan_data, sensor_canvas, sensor_canvas_extents,
                    max_scanner_range))

    # Insert: detected cylinders, in scanner coord system.
    if logfile.detected_cylinders:
        positions = [[
            to_sensor_canvas(pos, sensor_canvas_extents, max_scanner_range)
            for pos in cylinders_one_scan
        ] for cylinders_one_scan in logfile.detected_cylinders]
        draw_objects.append(Points(positions, sensor_canvas, "#88FF88"))

    # Insert: detected cylinders, transformed into world coord system.
    if logfile.detected_cylinders and logfile.filtered_positions and \
        len(logfile.filtered_positions[0]) > 2:
        positions = []
        for i in xrange(
                min(len(logfile.detected_cylinders),
                    len(logfile.filtered_positions))):
            this_pose_positions = []
            pos = logfile.filtered_positions[i]
            dx = cos(pos[2])
            dy = sin(pos[2])
            for pole in logfile.detected_cylinders[i]:
                x = pole[0] * dx - pole[1] * dy + pos[0]
                y = pole[0] * dy + pole[1] * dx + pos[1]
                p = to_world_canvas((x, y), canvas_extents, world_extents)
                this_pose_positions.append(p)
            positions.append(this_pose_positions)
        draw_objects.append(Points(positions, world_canvas, "#88FF88"))

    # Insert: world objects, cylinders.
    if logfile.world_cylinders:
        positions = [[
            to_world_canvas(pos, canvas_extents, world_extents)
            for pos in cylinders_one_scan
        ] for cylinders_one_scan in logfile.world_cylinders]
        draw_objects.append(Points(positions, world_canvas, "#DC23C5"))

    # Start new canvas and do all background drawing.
    world_canvas.delete(ALL)
    sensor_canvas.delete(ALL)
    for d in draw_objects:
        d.background_draw()
Пример #53
0
import math
import random
import time
import datetime
from datetime import date

print("Sqrt : ",math.sqrt(25))
print("Degrees : ",math.degrees(2))
print("Pi : ",math.pi)
print("Sin : ",math.sin(2))
print("Cos : ",math.cos(0.5))
print("Tan : ",math.tan(0.23))
print("Factorial : ",math.factorial(4))

print("Randint : ",random.randint(0,5))
print("Random : ",random.random())
print("Random * 100 : ",random.random() * 100)
List = [1,4,True,800,"python",27,"hello"]
print("Random Choice : ",random.choice(List))

print("Time : ",time.time())
print("Date : ",date.fromtimestamp(454554))
Пример #54
0
 def lla2utm(self, lla):
     """
     Converts lat, lon, alt to Universal Transverse Mercator coordinates
     Input: lla - (lat, lon, alt) in (decimal degrees, decimal degrees, m)
     Output: utm - (easting, northing, upping) in (m, m, m)
         info - (zone, scale factor)
     Algorithm from:
         Snyder, J. P., Map Projections-A Working Manual, U.S. Geol. Surv.
             Prof. Pap., 1395, 1987
     Code segments from pygps project, Russ Nelson
     """
     # Decompose lla
     lat = lla[0]
     lon = lla[1]
     alt = lla[2]
     # Determine the zone number
     zoneNumber = int((lon+180.)/6) + 1
     # Special zone for Norway
     if (56. <= lat < 64.) and (3. <= lon < 12.):
         zoneNumber = 32
     # Special zones for Svalbard
     if 72. <= lat < 84.:
         if 0. <= lon < 9.:
             zoneNumber = 31
         elif 9. <= lon < 21.:
             zoneNumber = 33
         elif 21. <= lon < 33.:
             zoneNumber = 35
         elif 33. <= lon < 42.:
             zoneNumber = 37
     # Format the zone
     zone = "%d%c" % (zoneNumber, self.utmLetterDesignator(lat))
     # Determine longitude origin
     lonOrigin = (zoneNumber - 1) * 6 - 180 + 3
     # Convert to radians
     latRad = geo.deg2rad(lat)
     lonRad = geo.deg2rad(lon)
     lonOriginRad = geo.deg2rad(lonOrigin)
     # Conversion constants
     k0 = 0.9996
     eSquared = self.e**2
     ePrimeSquared = eSquared/(1.-eSquared)
     N = self.a/sqrt(1.-eSquared*sin(latRad)**2)
     T = tan(latRad)**2
     C = ePrimeSquared*cos(latRad)**2
     A = (lonRad - lonOriginRad)*cos(latRad)
     M = self.a*(
         (1. -
             eSquared/4. -
             3.*eSquared**2/64. -
             5.*eSquared**3/256)*latRad -
         (3.*eSquared/8. +
             3.*eSquared**2/32. +
             45.*eSquared**3/1024.)*sin(2.*latRad) +
         (15.*eSquared**2/256. +
             45.*eSquared**3/1024.)*sin(4.*latRad) -
         (35.*eSquared**3/3072.)*sin(6.*latRad))
     M0 = 0.
     # Calculate coordinates
     x = k0*N*(
         A+(1-T+C)*A**3/6. +
         (5.-18.*T+T**2+72.*C-58.*ePrimeSquared)*A**5/120.) + 500000.
     y = k0*(
         M-M0+N*tan(latRad)*(
             A**2/2. +
             (5.-T+9.*C+4.*C**2)*A**4/24. +
             (61.-58.*T+T**2+600.*C-330.*ePrimeSquared)*A**6/720.))
     # Calculate scale factor
     k = k0*(1 +
             (1+C)*A**2/2. +
             (5.-4.*T+42.*C+13.*C**2-28.*ePrimeSquared)*A**4/24. +
             (61.-148.*T+16.*T**2)*A**6/720.)
     utm = [x, y, alt]
     info = [zone, k]
     return utm, info
#       print
#       math
#       'math'
#
# After you have written and run the code to learn the TYPE
# of each of the above, change the above _TODO_ to DONE.
###############################################################################
print(type(3.14))
print(type("hello"))
print(type('hello'))
print(type('a b c'))
print(type(3+3))
print(type("3"+"3"))
print(type(2**100))
print(type(2.0**100))
print(type(math.sin(8)))
print(type(math.sin))
print(type(print))
print(type(math))
print(type('math'))
###############################################################################
#
# DONE: 6.
#   Ensure that no blue bars on the scrollbar-thing to the right remain.
#   Run one more time to be sure that all is still OK.
#
#   Then COMMIT-and-PUSH your work as before:
#     1. Select   VCS   from the menu bar (above).
#     2. Choose  Commit  from the pull-down menu that appears.
#     3. In the  Commit Changes  window that pops up,
#        press the   Commit and Push   button.
Пример #56
0
"""
Пример #57
0
    def __timeout_callback(self, widget):

        self.anicount += 1

        # Pre start animation
        if self.anicount < 42:
            self.glarea.window.invalidate_rect(self.glarea.allocation, False)

        #print self.glarea.allocation

        self.cnt += 1
        if self.cnt >= 1000:
            self.cnt = 0

        if not self.enable:
            return True

        self.angle += 1.0
        if (self.angle >= 360.0):
            self.angle2 -= 360.0

        self.angle2 += 2.0
        if (self.angle2 >= 360.0):
            self.angle2 -= 360.0

        self.angle3 += 3.0
        if (self.angle >= 360.0):
            self.angle -= 360.0

        self.angle5 += 5.0
        if (self.angle5 >= 360.0):
            self.angle5 -= 360.0

        self.angle7 += 7.0
        if (self.angle7 >= 360.0):
            self.angle7 -= 360.0

        if  self.cnt % 50 == 0:
            self.twinkle += 1

        if  self.twinkle % 2 == 0:
            self.starcol += 0.02
        else:
            self.starcol -= 0.02

        t = self.angle * math.pi / 180.0
        if t > math.pi:
            t = 2.0 * math.pi - t

        t2 = self.angle * math.pi / 180.0

        self.pos_y   = 2.0 * (math.sin (t) + 0.4 * math.sin (3.0*t)) - 1.0
        self.pos_y2  = 2.0 * (math.sin (t))

        self.pos_x  = 2.0 * (math.sin (t/2)) - 1
        self.pos_x2  = 2.0 * (math.sin (t2/2)) - 1

        # Invalidate whole window.
        self.glarea.window.invalidate_rect(self.glarea.allocation, False)

        # Update window synchronously (fast).
        #self.glarea.window.process_updates(False)

        return True
Пример #58
0
def nodeRotate(self, ox, oy, angle):
  angle = radians(angle)
  newX = ox + (self.position.x-ox)*cos(angle) - (self.position.y-oy)*sin(angle)
  newY = oy + (self.position.x-ox)*sin(angle) + (self.position.y-oy)*cos(angle)
  self.position = (round(newX,2), round(newY,2))
Пример #59
0
def drawStar(x=dimention / 2, y=dimention / 3, a=dimention):
    glBegin(GL_POLYGON)
    R = a / 5
    r = R * math.sqrt(2) * math.cos(math.pi * 72 / 180)

    for n in range(5):
        # glVertex2f(x + R * math.cos(math.pi * (90 + 72 * n) / 180),
        #            y + R * math.sin(math.pi * (90 + 72 * n) / 180))
        glVertex2f(x + r * math.cos(math.pi * (126 + 72 * n) / 180),
                   y + r * math.sin(math.pi * (126 + 72 * n) / 180))
    glEnd()
    '''The for loop result was not turn out as expectation
    Thus, I have to draw separate 1 pentagon and 5 triangles
    '''
    glBegin(GL_TRIANGLES)
    glVertex2f(x + r * math.cos(math.pi * (126 + 72 * 4) / 180),
               y + r * math.sin(math.pi * (126 + 72 * 4) / 180))
    glVertex2f(x + R * math.cos(math.pi * (90 + 72 * 0) / 180),
               y + R * math.sin(math.pi * (90 + 72 * 0) / 180))
    glVertex2f(x + r * math.cos(math.pi * (126 + 72 * 0) / 180),
               y + r * math.sin(math.pi * (126 + 72 * 0) / 180))
    glEnd()

    glBegin(GL_TRIANGLES)
    glVertex2f(x + r * math.cos(math.pi * (126 + 72 * 0) / 180),
               y + r * math.sin(math.pi * (126 + 72 * 0) / 180))
    glVertex2f(x + R * math.cos(math.pi * (90 + 72 * 1) / 180),
               y + R * math.sin(math.pi * (90 + 72 * 1) / 180))
    glVertex2f(x + r * math.cos(math.pi * (126 + 72 * 1) / 180),
               y + r * math.sin(math.pi * (126 + 72 * 1) / 180))
    glEnd()

    glBegin(GL_TRIANGLES)
    glVertex2f(x + r * math.cos(math.pi * (126 + 72 * 1) / 180),
               y + r * math.sin(math.pi * (126 + 72 * 1) / 180))
    glVertex2f(x + R * math.cos(math.pi * (90 + 72 * 2) / 180),
               y + R * math.sin(math.pi * (90 + 72 * 2) / 180))
    glVertex2f(x + r * math.cos(math.pi * (126 + 72 * 2) / 180),
               y + r * math.sin(math.pi * (126 + 72 * 2) / 180))
    glEnd()

    glBegin(GL_TRIANGLES)
    glVertex2f(x + r * math.cos(math.pi * (126 + 72 * 2) / 180),
               y + r * math.sin(math.pi * (126 + 72 * 2) / 180))
    glVertex2f(x + R * math.cos(math.pi * (90 + 72 * 3) / 180),
               y + R * math.sin(math.pi * (90 + 72 * 3) / 180))
    glVertex2f(x + r * math.cos(math.pi * (126 + 72 * 3) / 180),
               y + r * math.sin(math.pi * (126 + 72 * 3) / 180))
    glEnd()

    glBegin(GL_TRIANGLES)
    glVertex2f(x + r * math.cos(math.pi * (126 + 72 * 3) / 180),
               y + r * math.sin(math.pi * (126 + 72 * 3) / 180))
    glVertex2f(x + R * math.cos(math.pi * (90 + 72 * 4) / 180),
               y + R * math.sin(math.pi * (90 + 72 * 4) / 180))
    glVertex2f(x + r * math.cos(math.pi * (126 + 72 * 4) / 180),
               y + r * math.sin(math.pi * (126 + 72 * 4) / 180))
    glEnd()
Пример #60
0
def rotatebot(rot_angle):
    global yaw

    # create Twist object
    twist = Twist()
    # set up Publisher to cmd_vel topic
    pub = rospy.Publisher('cmd_vel', Twist, queue_size=10)
    # set the update rate to 1 Hz
    rate = rospy.Rate(1)

    # get current yaw angle
    current_yaw = np.copy(yaw)
    # log the info
    rospy.loginfo(['Current: ' + str(math.degrees(current_yaw))])
    # we are going to use complex numbers to avoid problems when the angles go from
    # 360 to 0, or from -180 to 180
    c_yaw = complex(math.cos(current_yaw), math.sin(current_yaw))
    # calculate desired yaw
    target_yaw = current_yaw + math.radians(rot_angle)
    # convert to complex notation
    c_target_yaw = complex(math.cos(target_yaw), math.sin(target_yaw))
    rospy.loginfo(['Desired: ' + str(math.degrees(cmath.phase(c_target_yaw)))])
    # divide the two complex numbers to get the change in direction
    c_change = c_target_yaw / c_yaw
    # get the sign of the imaginary component to figure out which way we have to turn
    c_change_dir = np.sign(c_change.imag)
    # set linear speed to zero so the TurtleBot rotates on the spot
    twist.linear.x = 0.0
    # set the direction to rotate
    twist.angular.z = c_change_dir * rotate_speed
    # start rotation
    pub.publish(twist)

    # we will use the c_dir_diff variable to see if we can stop rotating
    c_dir_diff = c_change_dir
    # rospy.loginfo(['c_change_dir: ' + str(c_change_dir) + ' c_dir_diff: ' + str(c_dir_diff)])
    # if the rotation direction was 1.0, then we will want to stop when the c_dir_diff
    # becomes -1.0, and vice versa
    while (c_change_dir * c_dir_diff > 0):
        # get current yaw angle
        current_yaw = np.copy(yaw)
        # get the current yaw in complex form
        c_yaw = complex(math.cos(current_yaw), math.sin(current_yaw))
        rospy.loginfo('While Yaw: %f Target Yaw: %f',
                      math.degrees(current_yaw), math.degrees(target_yaw))
        # get difference in angle between current and target
        c_change = c_target_yaw / c_yaw
        # get the sign to see if we can stop
        c_dir_diff = np.sign(c_change.imag)
        # rospy.loginfo(['c_change_dir: ' + str(c_change_dir) + ' c_dir_diff: ' + str(c_dir_diff)])
        rospy.loginfo(['test'])
        angle_to_go = abs(target_yaw - current_yaw)
        twist.linear.x = 0.0
        twist.angular.z = c_change_dir * rotate_speed * (angle_to_go / pi)
        pub.publish(twist)
        rate.sleep()
        if math.degrees(target_yaw) - 10 <= math.degrees(
                current_yaw) <= math.degrees(target_yaw) + 10:
            break

    rospy.loginfo(['End Yaw: ' + str(math.degrees(current_yaw))])
    rospy.loginfo(['exits loop'])
    # set the rotation speed to 0
    twist.angular.z = 0.0
    # stop the rotation
    time.sleep(1)
    pub.publish(twist)