diff --git a/y2018/control_loops/python/BUILD b/y2018/control_loops/python/BUILD
index a72c464..5a44834 100644
--- a/y2018/control_loops/python/BUILD
+++ b/y2018/control_loops/python/BUILD
@@ -1,73 +1,87 @@
-package(default_visibility = ['//y2018:__subpackages__'])
+package(default_visibility = ["//y2018:__subpackages__"])
 
 py_binary(
-  name = 'drivetrain',
-  srcs = [
-    'drivetrain.py',
-  ],
-  deps = [
-    '//external:python-gflags',
-    '//external:python-glog',
-    '//frc971/control_loops/python:drivetrain',
-  ],
-  restricted_to = ['//tools:k8'],
+    name = "drivetrain",
+    srcs = [
+        "drivetrain.py",
+    ],
+    restricted_to = ["//tools:k8"],
+    deps = [
+        "//external:python-gflags",
+        "//external:python-glog",
+        "//frc971/control_loops/python:drivetrain",
+    ],
 )
 
 py_binary(
-  name = 'polydrivetrain',
-  srcs = [
-    'polydrivetrain.py',
-    'drivetrain.py',
-  ],
-  deps = [
-    '//external:python-gflags',
-    '//external:python-glog',
-    '//frc971/control_loops/python:polydrivetrain',
-  ],
-  restricted_to = ['//tools:k8'],
+    name = "polydrivetrain",
+    srcs = [
+        "drivetrain.py",
+        "polydrivetrain.py",
+    ],
+    restricted_to = ["//tools:k8"],
+    deps = [
+        "//external:python-gflags",
+        "//external:python-glog",
+        "//frc971/control_loops/python:polydrivetrain",
+    ],
 )
 
 py_library(
-  name = 'polydrivetrain_lib',
-  srcs = [
-    'polydrivetrain.py',
-    'drivetrain.py',
-  ],
-  deps = [
-    '//external:python-gflags',
-    '//external:python-glog',
-    '//frc971/control_loops/python:controls',
-    '//frc971/control_loops/python:drivetrain',
-  ],
-  restricted_to = ['//tools:k8'],
+    name = "polydrivetrain_lib",
+    srcs = [
+        "drivetrain.py",
+        "polydrivetrain.py",
+    ],
+    restricted_to = ["//tools:k8"],
+    deps = [
+        "//external:python-gflags",
+        "//external:python-glog",
+        "//frc971/control_loops/python:controls",
+        "//frc971/control_loops/python:drivetrain",
+    ],
 )
 
 py_test(
-  name = 'polydrivetrain_test',
-  srcs = [
-    'polydrivetrain_test.py',
-  ],
-  deps = [
-    '//external:python-gflags',
-    '//external:python-glog',
-    '//frc971/control_loops/python:polydrivetrain',
-    '//frc971/control_loops/python:controls',
-    ':polydrivetrain_lib',
-  ],
-  restricted_to = ['//tools:k8'],
+    name = "polydrivetrain_test",
+    srcs = [
+        "polydrivetrain_test.py",
+    ],
+    restricted_to = ["//tools:k8"],
+    deps = [
+        ":polydrivetrain_lib",
+        "//external:python-gflags",
+        "//external:python-glog",
+        "//frc971/control_loops/python:controls",
+        "//frc971/control_loops/python:polydrivetrain",
+    ],
 )
 
 py_binary(
-  name = 'intake',
-  srcs = [
-    'intake.py',
-  ],
-  deps = [
-    '//external:python-gflags',
-    '//external:python-glog',
-    '//frc971/control_loops/python:controls',
-  ],
-  restricted_to = ['//tools:k8'],
+    name = "arm_trajectory",
+    srcs = [
+        "arm_trajectory.py",
+        "path_points.py",
+    ],
+    restricted_to = ["//tools:k8"],
+    deps = [
+        "//external:python-gflags",
+        "//external:python-glog",
+        "//frc971/control_loops/python:controls",
+    ],
+)
+
+py_binary(
+    name = "intake",
+    srcs = [
+        "intake.py",
+    ],
+    restricted_to = ["//tools:k8"],
+    deps = [
+        "//external:python-gflags",
+        "//external:python-glog",
+        "//frc971/control_loops/python:controls",
+    ],
 )
 
 cc_binary(
@@ -75,10 +89,10 @@
     srcs = [
         "arm_mpc.cc",
     ],
+    restricted_to = ["//tools:k8"],
     deps = [
         "//third_party/ct",
-        "//third_party/matplotlib-cpp",
         "//third_party/gflags",
+        "//third_party/matplotlib-cpp",
     ],
-    restricted_to = ["//tools:k8"],
 )
diff --git a/y2018/control_loops/python/arm_trajectory.py b/y2018/control_loops/python/arm_trajectory.py
new file mode 100755
index 0000000..0923300
--- /dev/null
+++ b/y2018/control_loops/python/arm_trajectory.py
@@ -0,0 +1,803 @@
+#!/usr/bin/python
+
+import copy
+import numpy
+import path_points
+from matplotlib import pylab
+from frc971.control_loops.python import controls
+
+# This code computes the optimal velocity profile for the arm to follow
+# the path while adhering to constraints.
+#
+# TODO(austin): We shouldn't need to precompute the forwards pass for
+# constraints.  That shold be done dynamically.
+
+
+def RungeKutta(f, x, dt):
+    """4th order RungeKutta integration of F starting at X."""
+    a = f(x)
+    b = f(x + dt / 2.0 * a)
+    c = f(x + dt / 2.0 * b)
+    d = f(x + dt * c)
+    return x + dt * (a + 2.0 * b + 2.0 * c + d) / 6.0
+
+
+class Dynamics(object):
+    def __init__(self, dt):
+        self.dt = dt
+
+        # 1 is the proximal link of the arm
+        # 2 is the distal link of the arm
+        self.l1 = 46.25 * 0.0254
+        self.l2 = 41.80 * 0.0254
+
+        self.m1 = 9.34 / 2.2
+        self.m2 = 9.77 / 2.2
+
+        self.J1 = 2957.05 * 0.0002932545454545454
+        self.J2 = 2824.70 * 0.0002932545454545454
+
+        self.r1 = 21.64 * 0.0254
+        self.r2 = 26.70 * 0.0254
+
+        self.G1 = 140.0
+        self.G2 = 90.0
+
+        # These constants are for a minicim and the double jointed arm as
+        # modeled.
+        self.stall_torque = 1.41
+        self.free_speed = (5840.0 / 60.0) * 2.0 * numpy.pi
+        self.stall_current = 89.0
+        self.R = 12.0 / self.stall_current
+
+        self.Kv = self.free_speed / 12.0
+        self.Kt = self.stall_torque / self.stall_current
+
+        self.alpha = self.J1 + self.r1 * self.r1 * \
+            self.m1 + self.l1 * self.l1 * self.m2
+        self.beta = self.l1 * self.r2 * self.m2
+        self.gamma = self.J2 + self.r2 * self.r2 * self.m2
+
+        self.kNumDistalMotors = 2.0
+
+        self.K3 = numpy.matrix(
+            [[self.G1 * self.Kt / self.R, 0.0],
+             [0.0, self.G2 * self.kNumDistalMotors * self.Kt / self.R]])
+        self.K4 = numpy.matrix(
+            [[self.G1 * self.G1 * self.Kt / (self.Kv * self.R), 0.0], [
+                0.0, self.G2 * self.G2 * self.Kt * self.kNumDistalMotors /
+                (self.Kv * self.R)
+            ]])
+
+    def NormilizedMatriciesForState(self, X):
+        """Generate K1-4 for the arm ODE.
+
+        K1 * d^2 theta / dt^2 + K2 * d theta / dt = K3 * V - K4 * d theta/dt
+        """
+
+        s = numpy.sin(X[0, 0] - X[2, 0])
+        c = numpy.cos(X[0, 0] - X[2, 0])
+
+        # K1 * d^2 theta/dt^2 + K2 * d theta/dt = torque
+        K1 = numpy.matrix(
+            [[self.alpha, c * self.beta], [c * self.beta, self.gamma]])
+
+        K2 = numpy.matrix([[0.0, s * self.beta], [-s * self.beta, 0.0]])
+
+        return K1, K2, self.K3, self.K4
+
+    def MatriciesForState(self, X):
+        K1, K2, K3, K4 = self.NormilizedMatriciesForState(X)
+        K2[1, 0] *= X[1, 0]
+        K2[0, 1] *= X[3, 0]
+        return K1, K2, K3, K4
+
+    def ff_u(self, X, omega_t, alpha_t):
+        """Computes the feed forwards U required to track the provided state.
+
+        Args:
+          X, (4, 1) matrix, the state matrix
+          omega_t, (2, 1) matrix, The angular velocities of the two joints.
+          alpha_t, (2, 1) matrix, The angular accelerations of the two joints.
+
+        Returns the voltages required to track the path.
+        """
+        K1, K2, K3, K4 = self.MatriciesForState(X)
+
+        return numpy.linalg.inv(K3) * (
+            K1 * alpha_t + K2 * omega_t + K4 * omega_t)
+
+    def ff_u_distance(self, trajectory, distance):
+        """Computes the feed forward U at the distance on the trajectory.
+
+        Args:
+            trajectory, Trajectory, The trajectory to follow.
+            distance, float, the distance along the trajectory to compute
+              theta, omega and alpha.
+        """
+        theta_t = trajectory.theta(distance)
+        omega_t = trajectory.omega_t(distance)
+        alpha_t = trajectory.alpha_t(distance)
+
+        X = numpy.matrix([[theta_t[0, 0]], [omega_t[0, 0]], [theta_t[1, 0]],
+                          [omega_t[1, 0]]])
+
+        return self.ff_u(X, omega_t, alpha_t)
+
+    def dynamics(self, X, U):
+        """Calculates the dynamics for a double jointed arm.
+
+        Args:
+          X, numpy.matrix(4, 1), The state.  [theta1, omega1, theta2, omega2]
+          U, numpy.matrix(2, 1), The input.  [torque1, torque2]
+
+        Returns:
+          numpy.matrix(4, 1), The derivative of the dynamics.
+        """
+        K1, K2, K3, K4 = self.MatriciesForState(X)
+
+        velocity = numpy.matrix([[X[1, 0]], [X[3, 0]]])
+        torque = K3 * U - K4 * velocity
+
+        accel = numpy.linalg.inv(K1) * (torque - K2 * velocity)
+
+        return numpy.matrix([[X[1, 0]], [accel[0, 0]], [X[3, 0]],
+                             [accel[1, 0]]])
+
+    def unbounded_discrete_dynamics(self, X, U, dt=None):
+        return RungeKutta(lambda startingX: self.dynamics(startingX, U), X,
+                          dt or self.dt)
+
+    def discrete_dynamics(self, X, U, dt=None):
+        assert((U <= (12.0 + 1e-6)).all())
+        return self.unbounded_discrete_dynamics(X, U, dt)
+
+
+def numerical_jacobian_x(fn, X, U, epsilon=1e-4):
+    """Numerically estimates the jacobian around X, U in X.
+
+    Args:
+      fn: A function of X, U.
+      X: numpy.matrix(num_states, 1), The state vector to take the jacobian
+        around.
+      U: numpy.matrix(num_inputs, 1), The input vector to take the jacobian
+        around.
+
+    Returns:
+      numpy.matrix(num_states, num_states), The jacobian of fn with X as the
+        variable.
+    """
+    num_states = X.shape[0]
+    nominal = fn(X, U)
+    answer = numpy.matrix(numpy.zeros((nominal.shape[0], num_states)))
+    # It's more expensive, but +- epsilon will be more reliable
+    for i in range(0, num_states):
+        dX_plus = X.copy()
+        dX_plus[i] += epsilon
+        dX_minus = X.copy()
+        dX_minus[i] -= epsilon
+        answer[:, i] = (fn(dX_plus, U) - fn(dX_minus, U)) / (epsilon * 2.0)
+    return answer
+
+
+def numerical_jacobian_u(fn, X, U, epsilon=1e-4):
+    """Numerically estimates the jacobian around X, U in U.
+
+    Args:
+      fn: A function of X, U.
+      X: numpy.matrix(num_states, 1), The state vector to take the jacobian
+        around.
+      U: numpy.matrix(num_inputs, 1), The input vector to take the jacobian
+        around.
+
+    Returns:
+      numpy.matrix(num_states, num_inputs), The jacobian of fn with U as the
+        variable.
+    """
+    num_states = X.shape[0]
+    num_inputs = U.shape[0]
+    nominal = fn(X, U)
+    answer = numpy.matrix(numpy.zeros((nominal.shape[0], num_inputs)))
+    for i in range(0, num_inputs):
+        dU_plus = U.copy()
+        dU_plus[i] += epsilon
+        dU_minus = U.copy()
+        dU_minus[i] -= epsilon
+        answer[:, i] = (fn(X, dU_plus) - fn(X, dU_minus)) / (epsilon * 2.0)
+    return answer
+
+
+def K_at_state(dynamics, x, u):
+    """Computes the controller gain K at the given X and U."""
+    q_pos = 0.2
+    q_vel = 4.0
+    Q = numpy.matrix(
+        numpy.diag([
+            1.0 / (q_pos**2.0), 1.0 / (q_vel**2.0), 1.0 / (q_pos**2.0), 1.0 / (
+                q_vel**2.0)
+        ]))
+
+    R = numpy.matrix(numpy.diag([1.0 / (12.0**2.0), 1.0 / (12.0**2.0)]))
+
+    final_A = numerical_jacobian_x(dynamics.unbounded_discrete_dynamics, x, u)
+    final_B = numerical_jacobian_u(dynamics.unbounded_discrete_dynamics, x, u)
+
+    return controls.dlqr(final_A, final_B, Q, R)
+
+
+class Trajectory:
+    """This class represents a trajectory in theta space."""
+
+    def __init__(self, path_step_size):
+        # Points are a list of (theta0, theta1) to follow.  They are not
+        # required to be at any sort of spacing.
+        self.path_points = path_points.points
+        self.path_points = [
+            numpy.matrix([[numpy.pi / 2.0 - x[0]], [numpy.pi / 2.0 - x[1]]])
+            for x in self.path_points
+        ]
+        self.path_step_size = path_step_size
+        self.point_distances = [0.0]
+        last_point = self.path_points[0]
+        for point in self.path_points[1:]:
+            self.point_distances.append(
+                numpy.linalg.norm(point - last_point) +
+                self.point_distances[-1])
+            last_point = point
+        self._length = self.point_distances[-1]
+
+    def theta(self, distance):
+        """Interpolates the angle as a function of distance.
+
+        Note:
+          points before or after the path will get truncated to the ends of the path.
+        """
+        if distance <= 0.0:
+            return self.path_points[0]
+        elif distance >= self._length:
+            return self.path_points[-1]
+        after_index = numpy.searchsorted(
+            self.point_distances, distance, side='right')
+        before_index = after_index - 1
+        return (distance - self.point_distances[before_index]) / (
+            self.point_distances[after_index] -
+            self.point_distances[before_index]) * (
+                self.path_points[after_index] - self.path_points[before_index]
+            ) + self.path_points[before_index]
+
+    def length(self):
+        """Returns the path length in radians."""
+        return self.point_distances[-1]
+
+    def omega(self, distance):
+        """Returns d theta / dd for our path at the specified distance."""
+        after_index = numpy.searchsorted(
+            self.point_distances,
+            min(self.point_distances[-1] - 1e-6, max(0.0, distance)),
+            side='right')
+        before_index = after_index - 1
+        return (self.path_points[after_index] - self.path_points[before_index]
+                ) / (self.point_distances[after_index] -
+                     self.point_distances[before_index])
+
+    def alpha(self, distance):
+        """Returns d^2 theta / dd^2 for our path at the specified distance."""
+        delta = self.path_step_size
+        omega_plus = self.omega(distance + delta)
+        omega_minus = self.omega(distance - delta)
+        return (omega_plus - omega_minus) / (2.0 * delta)
+
+    def curvature_trajectory_pass(self, dynamics, alpha_unitizer,
+                                  distance_array, vmax):
+        """Computes the steady state curvature pass for optimizing our trajectory."""
+        max_dvelocity_unfiltered = []
+        # Pass 0
+        for index, distance in enumerate(distance_array):
+            theta = self.theta(distance)
+            omega = self.omega(distance)
+            alpha = self.alpha(distance)
+            X = numpy.matrix([[theta[0, 0]], [0.0], [theta[1, 0]], [0.0]])
+            K1, K2, K3, K4 = dynamics.NormilizedMatriciesForState(X)
+            omega_square = numpy.matrix(
+                [[omega[0, 0], 0.0], [0.0, omega[1, 0]]])
+            # Here, we can say that
+            #   d^2/dt^2 theta = d^2/dd^2 theta(d) * (d d/dt)^2
+            # Normalize so that the max accel is 1, and take magnitudes. This
+            # gives us the max velocity we can be at each point due to
+            # curvature.
+            vk1 = numpy.linalg.inv(K3) * (
+                K1 * alpha + K2 * omega_square * omega)
+            vk2 = numpy.linalg.inv(K3) * K4 * omega
+            ddots = []
+            for c in [-vmax, vmax]:
+                for a, b in [(vk1[0, 0], vk2[0, 0]), (vk1[1, 0], vk2[1, 0])]:
+                    sqrt_number = b * b - 4.0 * a * c
+                    if sqrt_number > 0:
+                        ddots.append(
+                            (-b + numpy.sqrt(sqrt_number)) / (2.0 * a))
+                        ddots.append(
+                            (-b - numpy.sqrt(sqrt_number)) / (2.0 * a))
+            good_ddots = []
+            for ddot in ddots:
+                U = vk1 * ddot * ddot + vk2 * ddot
+                if (numpy.abs(U) <= vmax + 1e-6).all() and ddot > 0.0:
+                    good_ddots.append(ddot)
+
+            max_dvelocity_unfiltered.append(
+                min(
+                    min(good_ddots),
+                    numpy.sqrt(1.0 / max(
+                        0.001, numpy.linalg.norm(alpha_unitizer * alpha)))))
+
+        return max_dvelocity_unfiltered
+
+    def back_trajectory_pass(self, previous_pass, dynamics, alpha_unitizer,
+                             distance_array, vmax):
+        """Computes the backwards pass for optimizing our trajectory."""
+        max_dvelocity_back_pass = copy.copy(previous_pass)
+        # Now, iterate over the list of velocities and constrain the
+        # acceleration.
+        for index, distance in reversed(list(enumerate(distance_array))):
+            if index == len(distance_array) - 1:
+                continue
+
+            prev_velocity = max_dvelocity_back_pass[index + 1]
+            prev_distance = distance_array[index + 1]
+
+            int_d = 0.0
+            int_vel = prev_velocity
+            num_steps = 10
+            for _ in xrange(num_steps):
+                theta = self.theta(prev_distance - int_d)
+                omega = self.omega(prev_distance - int_d)
+                alpha = self.alpha(prev_distance - int_d)
+
+                X = numpy.matrix([[theta[0, 0]], [0.0], [theta[1, 0]], [0.0]])
+                K1, K2, K3, K4 = dynamics.NormilizedMatriciesForState(X)
+                omega_square = numpy.matrix(
+                    [[omega[0, 0], 0.0], [0.0, omega[1, 0]]])
+
+                k_constant = numpy.linalg.inv(K3) * (
+                    (K1 * alpha + K2 * omega_square * omega
+                     ) * int_vel * int_vel + K4 * omega * int_vel)
+                k_scalar = numpy.linalg.inv(K3) * K1 * omega
+
+                voltage_accel_list = []
+                for c in [-vmax, vmax]:
+                    for a, b in [(k_constant[0, 0], k_scalar[0, 0]),
+                                 (k_constant[1, 0], k_scalar[1, 0])]:
+                        # This time, we are doing the other pass.  So, find all
+                        # the decelerations (and flip them) to find the prior
+                        # velocity.
+                        voltage_accel_list.append((c - a) / b)
+                filtered_voltage_accel_list = []
+                for a in voltage_accel_list:
+                    U = k_constant + k_scalar * a
+                    if a < 0.0 and (numpy.abs(U) <= vmax + 1e-6).all():
+                        filtered_voltage_accel_list.append(a)
+
+                int_accel_t = numpy.sqrt(
+                    max(0.0, 1.0 - (numpy.linalg.norm(alpha_unitizer * alpha) *
+                                    int_vel * int_vel)**
+                        2.0)) / numpy.linalg.norm(alpha_unitizer * omega)
+                if filtered_voltage_accel_list:
+                    # TODO(austin): The max of the list seems right, but I'm
+                    # not seeing many lists with a size > 1, so it's hard to
+                    # tell.  Max is conservative, for sure.
+                    int_accel_t = min(-max(filtered_voltage_accel_list),
+                                      int_accel_t)
+
+                integration_step_size = self.path_step_size / float(num_steps)
+                int_d += integration_step_size
+                int_vel = numpy.sqrt(2.0 * int_accel_t * integration_step_size
+                                      + int_vel * int_vel)
+            max_dvelocity_back_pass[index] = min(
+                int_vel, max_dvelocity_back_pass[index])
+        return max_dvelocity_back_pass
+
+    def forward_trajectory_pass(self, previous_pass, dynamics, alpha_unitizer,
+                                distance_array, vmax):
+        """Computes the forward pass for optimizing our trajectory."""
+        max_dvelocity_forward_pass = copy.copy(previous_pass)
+        # Now, iterate over the list of velocities and constrain the
+        # acceleration.
+        for index, distance in enumerate(distance_array):
+            if index == 0:
+                continue
+
+            prev_velocity = max_dvelocity_forward_pass[index - 1]
+            prev_distance = distance_array[index - 1]
+
+            int_d = 0.0
+            int_vel = prev_velocity
+            num_steps = 10
+            for _ in xrange(num_steps):
+                theta = self.theta(prev_distance + int_d)
+                omega = self.omega(prev_distance + int_d)
+                alpha = self.alpha(prev_distance + int_d)
+
+                X = numpy.matrix([[theta[0, 0]], [0.0], [theta[1, 0]], [0.0]])
+                K1, K2, K3, K4 = dynamics.NormilizedMatriciesForState(X)
+                omega_square = numpy.matrix(
+                    [[omega[0, 0], 0.0], [0.0, omega[1, 0]]])
+
+                k_constant = numpy.linalg.inv(K3) * (
+                    (K1 * alpha + K2 * omega_square * omega
+                     ) * int_vel * int_vel + K4 * omega * int_vel)
+                k_scalar = numpy.linalg.inv(K3) * K1 * omega
+                voltage_accel_list = []
+                for c in [-vmax, vmax]:
+                    for a, b in [(k_constant[0, 0], k_scalar[0, 0]),
+                                 (k_constant[1, 0], k_scalar[1, 0])]:
+                        voltage_accel_list.append((c - a) / b)
+
+                int_accel_t = numpy.sqrt(
+                    max(0.0, 1.0 - (numpy.linalg.norm(alpha_unitizer * alpha) *
+                                    int_vel * int_vel)**
+                        2.0)) / numpy.linalg.norm(alpha_unitizer * omega)
+
+                filtered_voltage_accel_list = []
+                for a in voltage_accel_list:
+                    U = k_constant + k_scalar * a
+                    if a > 0.0 and (numpy.abs(U) <= vmax + 1e-6).all():
+                        filtered_voltage_accel_list.append(a)
+
+                if filtered_voltage_accel_list:
+                    # TODO(austin): The max of the list seems right, but I'm not
+                    # seeing many lists with a size > 1, so it's hard to tell.
+                    # Min is conservative, for sure.
+                    int_accel_t = min(
+                        min(filtered_voltage_accel_list), int_accel_t)
+
+                integration_step_size = self.path_step_size / float(num_steps)
+                int_d += integration_step_size
+                int_vel = numpy.sqrt(2.0 * int_accel_t * integration_step_size
+                                      + int_vel * int_vel)
+
+            max_dvelocity_forward_pass[index] = min(
+                int_vel, max_dvelocity_forward_pass[index])
+
+        return max_dvelocity_forward_pass
+
+    def compute_trajectory(self,
+                           dynamics,
+                           alpha_unitizer,
+                           distance_array,
+                           vmax=12.0):
+        self.distance_array = copy.copy(distance_array)
+        self.max_dvelocity_unfiltered = self.curvature_trajectory_pass(
+            dynamics, alpha_unitizer, distance_array, vmax)
+        print 'Finished curvature pass'
+
+        self.max_dvelocity_unfiltered[0] = 0.0
+        self.max_dvelocity_unfiltered[-1] = 0.0
+
+        self.max_dvelocity_back_pass = self.back_trajectory_pass(
+            self.max_dvelocity_unfiltered, dynamics, alpha_unitizer,
+            distance_array, vmax)
+        print 'Finished backwards pass'
+
+        self.max_dvelocity_forward_pass = self.forward_trajectory_pass(
+            self.max_dvelocity_back_pass, dynamics, alpha_unitizer,
+            distance_array, vmax)
+        self.max_dvelocity = self.max_dvelocity_forward_pass
+        print 'Finished forwards pass'
+
+    def get_dvelocity(self, d):
+        """Computes the path distance velocity of the plan as a function of the distance."""
+        after_index = numpy.argmax(self.distance_array > d)
+        before_index = after_index - 1
+        v0 = self.max_dvelocity[before_index]
+        v1 = self.max_dvelocity[after_index]
+        d0 = self.distance_array[before_index]
+        d1 = self.distance_array[after_index]
+        if v0 + v1 > 0:
+            return numpy.sqrt(v0 * v0 + (v1 * v1 - v0 * v0) * (d - d0) / (d1 -
+                                                                          d0))
+        else:
+            return -numpy.sqrt(v0 * v0 + (v1 * v1 - v0 * v0) * (d - d0) / (d1 -
+                                                                           d0))
+
+    def get_dacceleration(self, d):
+        """Computes the path distance acceleration of the plan as a function of the distance."""
+        after_index = numpy.argmax(self.distance_array > d)
+        before_index = after_index - 1
+        v0 = self.max_dvelocity[before_index]
+        v1 = self.max_dvelocity[after_index]
+        d0 = self.distance_array[before_index]
+        d1 = self.distance_array[after_index]
+        return 0.5 * (v1**2.0 - v0**2.0) / (d1 - d0)
+
+    def omega_t(self, d, velocity=None):
+        """Returns d theta/dt at a specified distance."""
+        if d > self._length:
+            return numpy.matrix(numpy.zeros((2, 1)))
+        return self.omega(d) * (velocity or self.get_dvelocity(d))
+
+    def alpha_t(self, d, velocity=None, acceleration=None):
+        """Returns d^2 theta/dt^2 at a specified distance."""
+        if d > self._length:
+            return numpy.matrix(numpy.zeros((2, 1)))
+        return self.alpha(d) * (
+            (velocity or self.get_dvelocity(d))**2.0) + self.omega(d) * (
+                acceleration or self.get_dacceleration(d))
+
+    def R(self, d, velocity=None):
+        theta_t = self.theta(d)
+        omega_t = self.omega_t(d, velocity=velocity)
+        return numpy.matrix([[theta_t[0, 0]], [omega_t[0, 0]], [theta_t[1, 0]],
+                             [omega_t[1, 0]]])
+
+
+def main():
+    dt = 0.00505
+    path_step_size = 0.01
+    dynamics = Dynamics(dt)
+
+    trajectory = Trajectory(path_step_size)
+    print 'Initialized path'
+
+    distance_array = numpy.arange(0.0, trajectory.length(), path_step_size)
+    theta0_array = []
+    theta1_array = []
+    omega0_array = []
+    omega1_array = []
+    alpha0_array = []
+    alpha1_array = []
+
+    it0 = trajectory.theta(0.0)[0, 0]
+    it1 = trajectory.theta(0.0)[1, 0]
+    io0 = trajectory.omega(0.0)[0, 0]
+    io1 = trajectory.omega(0.0)[1, 0]
+
+    integrated_distance = []
+    integrated_omega0_array = []
+    integrated_omega1_array = []
+    integrated_theta0_array = []
+    integrated_theta1_array = []
+
+    for index, distance in enumerate(distance_array):
+        theta = trajectory.theta(distance)
+        omega = trajectory.omega(distance)
+        alpha = trajectory.alpha(distance)
+
+        theta0_array.append(theta[0, 0])
+        theta1_array.append(theta[1, 0])
+        omega0_array.append(omega[0, 0])
+        omega1_array.append(omega[1, 0])
+        alpha0_array.append(alpha[0, 0])
+        alpha1_array.append(alpha[1, 0])
+
+    # For a consistency check, integrate back up the acceleration and see how
+    # close we got.
+    dd = 0.005
+    for distance in numpy.arange(0.0, trajectory.length(), dd):
+        integrated_distance.append(distance)
+        integrated_omega0_array.append(io0)
+        integrated_omega1_array.append(io1)
+        integrated_theta0_array.append(it0)
+        integrated_theta1_array.append(it1)
+        alpha = trajectory.alpha(distance)
+        it0 += io0 * dd
+        it1 += io1 * dd
+        io0 += alpha[0, 0] * dd
+        io1 += alpha[1, 0] * dd
+
+    print 'Iterated through path'
+
+    # Bounds on the accelerations of the two DOFs.
+    # We'll draw an oval to represent the actual bounds here.
+    alpha0_max = 40.0
+    alpha1_max = 60.0
+
+    alpha_unitizer = numpy.matrix(
+        [[1.0 / alpha0_max, 0.0], [0.0, 1.0 / alpha1_max]])
+
+    # Compute the trajectory taking into account our velocity, acceleration
+    # and voltage constraints.
+    trajectory.compute_trajectory(dynamics, alpha_unitizer, distance_array)
+
+    print 'Computed trajectory'
+
+    # Now, we can get acceleration, velocity, and position as a function of distance.
+    # Acceleration is best effort (derived from the velocities), but velocity
+    # is pretty good.  So, use that to integrate up positions to track.
+
+    t_array = []
+    theta0_goal_t_array = []
+    theta1_goal_t_array = []
+    omega0_goal_t_array = []
+    omega1_goal_t_array = []
+    alpha0_goal_t_array = []
+    alpha1_goal_t_array = []
+    theta0_t_array = []
+    theta1_t_array = []
+    omega0_t_array = []
+    omega1_t_array = []
+    alpha0_t_array = []
+    alpha1_t_array = []
+    distance_t_array = []
+    velocity_t_array = []
+    acceleration_t_array = []
+
+    uff0_array = []
+    uff1_array = []
+    u0_array = []
+    u1_array = []
+    u0_unsaturated_array = []
+    u1_unsaturated_array = []
+
+    last_goal_distance = 0.0
+
+    goal_distance = 0.0
+    goal_velocity = 0.0
+
+    theta_t = trajectory.theta(goal_distance)
+    X = numpy.matrix([[theta_t[0, 0]], [0.0], [theta_t[1, 0]], [0.0]])
+
+    sim_dt = dt
+
+    vmax = 12.0
+
+    print 'Starting simulation'
+    # Now, we can start following the trajectory!
+    for t in numpy.arange(0.0, 1.0, sim_dt):
+        dacceleration = trajectory.get_dacceleration(goal_distance)
+
+        t_array.append(t)
+        theta_t = trajectory.theta(goal_distance)
+        omega_t = trajectory.omega_t(goal_distance, velocity=goal_velocity)
+        alpha_t = trajectory.alpha_t(goal_distance, velocity=goal_velocity)
+
+        theta0_goal_t_array.append(theta_t[0, 0])
+        theta1_goal_t_array.append(theta_t[1, 0])
+        omega0_goal_t_array.append(omega_t[0, 0])
+        omega1_goal_t_array.append(omega_t[1, 0])
+        alpha0_goal_t_array.append(alpha_t[0, 0])
+        alpha1_goal_t_array.append(alpha_t[1, 0])
+        theta0_t_array.append(X[0, 0])
+        omega0_t_array.append(X[1, 0])
+        theta1_t_array.append(X[2, 0])
+        omega1_t_array.append(X[3, 0])
+
+        distance_t_array.append(goal_distance)
+        velocity_t_array.append(goal_velocity)
+        acceleration_t_array.append(dacceleration)
+
+        U_ff = dynamics.ff_u_distance(trajectory, goal_distance)
+        K = K_at_state(dynamics, X, U_ff)
+        R = trajectory.R(goal_distance, velocity=goal_velocity)
+        U = U_ff + K * (R - X)
+
+        # Ok, now we know if we are staturated or not.  If we are, time to
+        # search between here and our previous goal either until we find a
+        # state where we aren't saturated, or we are really close to our
+        # starting point.
+        if (numpy.abs(U) > vmax).any():
+            # Saturated.  Let's do a binary search.
+            print "Saturated."
+            fraction_along_path = 0.5
+            step_size = 0.5
+            while step_size > 0.01:
+                saturation_goal_distance = (
+                    (goal_distance - last_goal_distance
+                     ) * fraction_along_path + last_goal_distance)
+
+                U_ff = dynamics.ff_u_distance(trajectory, saturation_goal_distance)
+                R = trajectory.R(saturation_goal_distance)
+                U = U_ff + K * (R - X)
+                step_size = step_size * 0.5
+                if (numpy.abs(U) > vmax).any():
+                    fraction_along_path -= step_size
+                else:
+                    fraction_along_path += step_size
+            print "Fraction", fraction_along_path
+            goal_distance = ((goal_distance - last_goal_distance) *
+                             fraction_along_path + last_goal_distance)
+            goal_velocity = trajectory.get_dvelocity(goal_distance)
+            dacceleration = trajectory.get_dacceleration(goal_distance)
+
+        u0_unsaturated_array.append(U[0, 0])
+        u1_unsaturated_array.append(U[1, 0])
+
+        # Now, artifically clip the available voltage.
+        U = numpy.clip(U, -10.0, 10.0)
+
+        xdot = dynamics.dynamics(X, U)
+        alpha0_t_array.append(xdot[1, 0])
+        alpha1_t_array.append(xdot[3, 0])
+
+        uff0_array.append(U_ff[0, 0])
+        uff1_array.append(U_ff[1, 0])
+        u0_array.append(U[0, 0])
+        u1_array.append(U[1, 0])
+
+        # Push our dynamics forwards.
+        X = dynamics.discrete_dynamics(X, U, sim_dt)
+
+        if abs(goal_distance - trajectory.length()) < 1e-2:
+            # If we go backwards along the path near the goal, snap us to the
+            # end point or we'll never actualy finish.
+            if dacceleration * sim_dt + goal_velocity < 0.0:
+                goal_distance = trajectory.length()
+
+        last_goal_distance = goal_distance
+        goal_distance += goal_velocity * sim_dt + 0.5 * dacceleration * sim_dt * sim_dt
+        goal_velocity = min(
+            trajectory.get_dvelocity(goal_distance),
+            goal_velocity + dacceleration * sim_dt)
+        goal_velocity = trajectory.get_dvelocity(goal_distance)
+
+    print 'Finished simulation'
+    pylab.figure()
+    pylab.title("Trajecotry")
+    pylab.plot(theta0_array, theta1_array, label="desired path")
+    pylab.plot(theta0_t_array, theta1_t_array, label="actual path")
+
+    pylab.figure()
+    pylab.title("Path derivitives")
+    pylab.plot(distance_array, theta0_array, label="theta0")
+    pylab.plot(distance_array, theta1_array, label="theta1")
+    pylab.plot(distance_array, omega0_array, label="omega0")
+    pylab.plot(distance_array, omega1_array, label="omega1")
+    pylab.plot(distance_array, alpha0_array, label="alpha0")
+    pylab.plot(distance_array, alpha1_array, label="alpha1")
+
+    pylab.plot(integrated_distance, integrated_omega0_array, label='iomega0')
+    pylab.plot(integrated_distance, integrated_omega1_array, label='iomega1')
+    pylab.plot(integrated_distance, integrated_theta0_array, label='itheta0')
+    pylab.plot(integrated_distance, integrated_theta1_array, label='itheta1')
+    pylab.legend()
+
+    pylab.figure()
+    pylab.title("Path Velocity Plan")
+    pylab.plot(
+        distance_array, trajectory.max_dvelocity_unfiltered, label="pass0")
+    pylab.plot(
+        distance_array, trajectory.max_dvelocity_forward_pass, label="passf")
+    pylab.plot(
+        distance_array, trajectory.max_dvelocity_back_pass, label="passb")
+    pylab.legend()
+
+    pylab.figure()
+    pylab.title("Path Velocity Plan")
+    pylab.plot(t_array, alpha0_goal_t_array, label="alpha0_t_goal")
+    pylab.plot(t_array, alpha0_t_array, label="alpha0_t")
+    pylab.plot(t_array, alpha1_goal_t_array, label="alpha1_t_goal")
+    pylab.plot(t_array, alpha1_t_array, label="alpha1_t")
+    pylab.plot(t_array, distance_t_array, label="distance_t")
+    pylab.plot(t_array, velocity_t_array, label="velocity_t")
+    pylab.plot(t_array, acceleration_t_array, label="acceleration_t")
+    pylab.legend()
+
+    pylab.figure()
+    pylab.title("Angular Velocities")
+    pylab.plot(t_array, omega0_goal_t_array, label="omega0_t_goal")
+    pylab.plot(t_array, omega0_t_array, label="omega0_t")
+    pylab.plot(t_array, omega1_goal_t_array, label="omega1_t_goal")
+    pylab.plot(t_array, omega1_t_array, label="omega1_t")
+    pylab.legend()
+
+    pylab.figure()
+    pylab.title("Voltages")
+    pylab.plot(t_array, u0_unsaturated_array, label="u0_full")
+    pylab.plot(t_array, u0_array, label="u0")
+    pylab.plot(t_array, uff0_array, label="uff0")
+    pylab.plot(t_array, u1_unsaturated_array, label="u1_full")
+    pylab.plot(t_array, u1_array, label="u1")
+    pylab.plot(t_array, uff1_array, label="uff1")
+    pylab.legend()
+
+    pylab.figure()
+    pylab.title("Angles")
+    pylab.plot(t_array, theta0_goal_t_array, label="theta0_t_goal")
+    pylab.plot(t_array, theta0_t_array, label="theta0_t")
+    pylab.plot(t_array, theta1_goal_t_array, label="theta1_t_goal")
+    pylab.plot(t_array, theta1_t_array, label="theta1_t")
+    pylab.legend()
+
+    pylab.show()
+
+
+if __name__ == '__main__':
+    main()
diff --git a/y2018/control_loops/python/path_points.py b/y2018/control_loops/python/path_points.py
new file mode 100644
index 0000000..99ef123
--- /dev/null
+++ b/y2018/control_loops/python/path_points.py
@@ -0,0 +1,10 @@
+#!/usr/bin/python
+
+# Path points from Parker.
+# Points in (theta0, theta1) of the boundry of the safe region.
+points_bounary = ([1.8577014383575772, -1.7353804562372057], [1.8322288438826315, -1.761574570216062], [1.7840339881582052, -1.8122752826851365], [1.7367354460218392, -1.863184376466228], [1.69054633425053, -1.9140647421906793], [1.6456590387358871, -1.9646939485526782], [1.6022412524081968, -2.0148691793459164], [1.5604334435784202, -2.0644108218872432], [1.5203477477575325, -2.1131646494909866], [1.4820681545944325, -2.1610026706370666], [1.4456517763321752, -2.207822815007094], [1.4111309389855604, -2.253547685496041], [1.3785158286698027, -2.298122627340264], [1.3477974448369014, -2.3415133576238922], [1.318950649522341, -2.3837033700108243], [1.2919371475531436, -2.4246912899477153], [1.266708279449626, -2.464488312575651], [1.2432075513427807, -2.5031158147261996], [1.2213728618107609, -2.5406031969824228], [1.2011384131259828, -2.5769859833310096], [1.1824363142639513, -2.61230418457078], [1.165197896140849, -2.64660091671642], [1.149354767212547, -2.6799212560849437], [1.134839641107821, -2.712311307404836], [1.121586968578607, -2.7438174590386177], [1.1095334047223224, -2.774485799309971], [1.09861813993779, -2.8043616692157007], [1.088783119985477, -2.8334893289039758], [1.079973177230731, -2.861911717797479], [1.0721360919151535, -2.8896702908486835], [1.065222599283597, -2.916804915950962], [1.0591863556764607, -2.943353819884641], [1.0539838743128325, -2.969353572295195], [1.049574439440948, -2.9948390990606946], [1.0459200058000553, -3.01984371800932], [1.0429850888932353, -3.044399191310831], [1.0407366503803421, -3.0685357900111128], [1.039143981929867, -3.092282367132034], [1.0381785900853944, -3.1156664365461078], [1.0378140840766794, -3.1387142554815886], [1.038026068010855, -3.1614509090414518], [1.0387920384931424, -3.1839003955494407], [1.0400912884293725, -3.2060857118856374], [1.0419048175385754, -3.2280289382581637], [1.0442152499395827, -3.2497513220895704], [1.047006759060362, -3.2712733608874625], [1.050265000044113, -3.2926148841283163], [1.0513266200838918, -3.2986722862692828], [0.6882849734317291, -3.2986722862692828], [0.6882849734317291, -2.40847516476558], [0.8062364039734171, -2.2816832357742984], [0.9846964491122989, -2.0749837238115147], [1.080856081125841, -1.9535526052833936], [1.1403399741223543, -1.8700303125904767], [1.1796460643255697, -1.8073338252603661], [1.206509908068604, -1.7574623871869075], [1.225108933139178, -1.7160975113819317], [1.237917343016644, -1.6806816402603253], [1.2465009152225068, -1.6495957958330445], [1.251901644035212, -1.6217619064422375], [1.2548410275662123, -1.5964327471863136], [1.2558349967266738, -1.5730732293972975], [1.2552624664807475, -1.551289614657788], [1.2534080548485127, -1.5307854126408047], [1.2504896957865235, -1.5113328783804112], [1.2466770509718135, -1.492754008779478], [1.2421041193998992, -1.4749075280685116], [1.236878076935188, -1.457679763958034], [1.231085601347444, -1.4409781183381307], [1.2247974811461413, -1.4247263085140511], [1.2180720288351026, -1.408860841660136], [1.2109576458572935, -1.3933283641188086], [1.2034947755974974, -1.378083641634472], [1.1957174082841977, -1.363088001457586], [1.1876542532510088, -1.3483081171759035], [1.179329661157153, -1.3337150510329991], [1.1707643560768641, -1.3192834919003447], [1.1385726725405734, -1.3512941162901886], [1.1061744838535637, -1.3828092440478137], [1.0736355415504857, -1.4137655512448706], [1.0410203155384732, -1.444102884084807], [1.0083912519665894, -1.4737649313813326], [0.975808099297045, -1.5026998012630925], [0.9433273192311136, -1.5308604887780404], [0.941597772428203, -1.50959779639341], [0.9392183822389457, -1.488861961175901], [0.9362399962318921, -1.4685999567644576], [0.9327074201772598, -1.448764371832554], [0.9286602163651203, -1.4293126388801052], [0.9241333769591611, -1.410206381002334], [0.9191578939466147, -1.3914108561164176], [0.9137612431353617, -1.3728944819981919], [0.9079677963791273, -1.3546284285619337], [0.9017991735984072, -1.3365862662768213], [0.8952745440670551, -1.3187436615861219], [0.888410884742945, -1.3010781117818295], [0.8812232020507231, -1.2835687130679965], [0.8737247224089426, -1.2661959565824437], [0.8659270558807739, -1.2489415479874506], [0.8578403365760008, -1.2317882469234374], [0.8810761292150717, -1.2118184809610988], [0.9041762360363244, -1.1914283310662528], [0.9271196683064211, -1.1706361926784383], [0.949885054142765, -1.1494613527499984], [0.9724507572661958, -1.1279238910069835], [0.9947950004998649, -1.1060445714951375], [1.0168959923240788, -1.0838447258650978], [1.0387320546908576, -1.0613461300367468], [1.0602817502430675, -1.0385708760262022], [1.0815240070740941, -1.0155412408147642], [1.102438239206001, -0.9922795541836177], [1.123004461055328, -0.9688080674301042], [1.1432033942926907, -0.9451488248218312], [1.1630165656794818, -0.9213235395370803], [1.1824263946752058, -0.8973534756890716], [1.2014162698440272, -0.8732593378443982], [1.2199706133398625, -0.8490611692304734], [1.2380749330068292, -0.8247782595916947], [1.2557158618869284, -0.800429063408306], [1.2728811851714203, -0.776031128944234], [1.2895598548592355, -0.7516010383486005], [1.3057419925890068, -0.7271543588072293], [1.3214188812865908, -0.702705604531139], [1.3365829464142562, -0.6782682091832445], [1.351227727719687, -0.6538545081853449], [1.365347842462401, -0.6294757302167044], [1.3789389411433586, -0.6051419971134862], [1.391997656782351, -0.5808623313043475], [1.4045215487801634, -0.5566446698699925], [1.4165090423718034, -0.5324958842910054], [1.4279593646268474, -0.5084218049460658], [1.4388724778869602, -0.4844272494383845], [1.449249011452494, -0.460516053858597], [1.4590901922431447, -0.4366911061340692], [1.468397775065033, -0.4129543806643518], [1.4771739730209745, -0.38930697349737264], [1.485421388504271, -0.36574913735813025], [1.4931429451209484, -0.3422803158986589], [1.5003418207921726, -0.3188991765927855], [1.5070213821985838, -0.2956036417497373], [1.513185120641734, -0.2723909171654731], [1.5188365893149296, -0.24925751796822435], [1.5239793418959948, -0.22619929124396096], [1.5286168722972349, -0.2032114350471563], [1.5327525553319497, -0.1802885134112242], [1.5363895879810432, -0.15742446697009113], [1.5395309308654115, -0.1346126187862511], [1.5421792494481048, -0.11184567494963411], [1.5443368544016174, -0.0891157194637005], [1.5460056404769755, -0.06641420286771664], [1.5471870230984175, -0.043731923953761714], [1.547881871775246, -0.021059003819238205], [1.5480904392645911, 0.0016151486553661097], [1.547812285227133, 0.024301881005710235], [1.5470461928818935, 0.047013352405288866], [1.5457900768723736, 0.06976260156314103], [1.5440408801865422, 0.09256362934244797], [1.5417944575035705, 0.11543149864415554], [1.5390454417383017, 0.13838245474060726], [1.5357870897759938, 0.16143407007284788], [1.5320111023738603, 0.18460541860588778], [1.5277074118667517, 0.20791728625864334], [1.5228639295308124, 0.23139242581719505], [1.5174662420569858, 0.25505586728497265], [1.5114972433117844, 0.27893529808946027], [1.5049366830391921, 0.30306153234932315], [1.4977606078174102, 0.32746909510770755], [1.4899406605544634, 0.35219695697813347], [1.4814431917184283, 0.37728946847450484], [1.4722281161523716, 0.40279756372788583], [1.4622474200998372, 0.4287803341537376], [1.4514431778273647, 0.45530712040457033], [1.4397448652396179, 0.48246034696312606], [1.427065639662639, 0.5103394485717625], [1.4132970536897833, 0.5390664502570618], [1.3983013135749314, 0.5687941401756967], [1.3818995257862978, 0.5997184788509978], [1.3638530549860057, 0.6320982830132342], [1.3438323057823602, 0.6662881915757862], [1.3213606855701236, 0.7027978462604986], [1.2957042956404132, 0.7424084023365868], [1.2656247456808565, 0.786433646353686], [1.2287034601894442, 0.8374338794107618], [1.1786904071656892, 0.902017503822168], [1.0497616572686415, 1.0497616572686426], [0.9097522267255194, 1.1864251300690412], [0.8484431816837388, 1.2397127624624213], [0.8000049977037023, 1.2791960970308718], [0.7581818853313602, 1.3114777786351866], [0.7205493452982701, 1.3391121846078957], [0.6882849734317291, 1.3617105524217008], [0.6882849734317291, 2.356194490192345], [1.3376784164442164, 2.356194490192345], [1.3516056511178856, 2.3360528189227487], [1.3708660530144583, 2.308792458458483], [1.3913233553973305, 2.2804469909122105], [1.4131687110627962, 2.2508089759388485], [1.436656614785, 2.219604401551449], [1.4621380338543308, 2.18645769238238], [1.4901198983671067, 2.1508288797419346], [1.5213822452925796, 2.111889875368928], [1.5572408030205178, 2.0682471032649676], [1.6002650085871786, 2.0171829478543404], [1.657096323745671, 1.9516778011159774], [1.7977393629734166, 1.7977393629734166], [1.8577014383575772, 1.7364646168980775], [1.8577014383575772, -1.7353804562372057])
+
+# Test data set in terms of (theta0, theta1) of a motion from Parker.
+# This is an example box lift profile.
+points = \
+[(1.3583511559969876, 0.99753029519739866), (1.3588773085542218, 0.99689357539323031), (1.3594016528242854, 0.99625874660952929), (1.3599242059738952, 0.99562579070357471), (1.3604449848987077, 0.99499468981909267), (1.3609640062292812, 0.99436542637995251), (1.3614812863368515, 0.99373798308406303), (1.3619968413389616, 0.99311234289742323), (1.3625106871049333, 0.99248848904833997), (1.3630228392611743, 0.99186640502181722), (1.3635333131963545, 0.99124607455408753), (1.3640421240664473, 0.99062748162728298), (1.3645492867996074, 0.99001061046427996), (1.3650548161009484, 0.989395445523651), (1.3655587264571691, 0.98878197149477332), (1.3660610321410793, 0.98817017329304824), (1.366561747215977, 0.98756003605527409), (1.3670608855399395, 0.98695154513510985), (1.3675584607699935, 0.98634468609867032), (1.368054486366149, 0.98573944472026087), (1.3685489755953899, 0.98513580697816161), (1.3690419415355004, 0.98453375905058238), (1.3695333970788255, 0.98393328731168894), (1.3700233549359311, 0.98333437832773474), (1.3705118276391728, 0.98273701885328935), (1.3709988275461686, 0.9821411958275682), (1.3714843668431982, 0.98154689637084092), (1.3719684575484949, 0.98095410778095005), (1.372451111515482, 0.9803628175298944), (1.3729323404359173, 0.97977301326050226), (1.3734121558429573, 0.9791846827831947), (1.3738905691141534, 0.97859781407281943), (1.3743675914743774, 0.97801239526555861), (1.3748432339986687, 0.97742841465592001), (1.3753175076150201, 0.97684586069379165), (1.3757904231070981, 0.97626472198156999), (1.3762619911168867, 0.97568498727136177), (1.3767322221472984, 0.97510664546222892), (1.3772011265646764, 0.97452968559754061), (1.3776687146012927, 0.97395409686233581), (1.3781349963577458, 0.97337986858078729), (1.3785999818053263, 0.97280699021370376), (1.3790636807883221, 0.97223545135609235), (1.3795261030262633, 0.97166524173478552), (1.3799872581161319, 0.97109635120610804), (1.3804471555345117, 0.97052876975360336), (1.3809058046396876, 0.96996248748581537), (1.3813632146736996, 0.9693974946341174), (1.3818193947643636, 0.96883378155057709), (1.3822743539272269, 0.96827133870589066), (1.3827281010674923, 0.96771015668734772), (1.3831806449819073, 0.96715022619683577), (1.3836319943605933, 0.96659153804890752), (1.3840821577888462, 0.96603408316887773), (1.384531143748907, 0.96547785259095098), (1.3849789606216714, 0.96492283745641638), (1.3854256166883818, 0.96436902901185939), (1.3858711201322809, 0.96381641860741352), (1.3863154790402232, 0.96326499769505758), (1.3867587014042524, 0.96271475782694982), (1.3872007951231566, 0.9621656906537821), (1.3876417680039816, 0.96161778792318331), (1.3880816277635084, 0.96107104147815625), (1.3885203820297187, 0.96052544325552958), (1.3889580383432047, 0.9599809852844674), (1.3893946041585732, 0.95943765968498684), (1.3898300868458122, 0.9588954586665116), (1.3902644936916158, 0.95835437452647454), (1.3906978319007086, 0.95781439964891557), (1.391130108597129, 0.95727552650312697), (1.3915613308254784, 0.95673774764233388), (1.3919915055521646, 0.95620105570237857), (1.3924206396666072, 0.9556654434004469), (1.3928487399824174, 0.95513090353382335), (1.3932758132385734, 0.95459742897864763), (1.3937018661005407, 0.95406501268872934), (1.3941269051614098, 0.95353364769434956), (1.3945509369429736, 0.95300332710111813), (1.3949739678968074, 0.95247404408883463), (1.3953960044053257, 0.95194579191037165), (1.3958170527828155, 0.95141856389058277), (1.3962371192764369, 0.95089235342524325), (1.3966562100672304, 0.95036715397998872), (1.3970743312710887, 0.94984295908928573), (1.3974914889397141, 0.94931976235542159), (1.3979076890615474, 0.94879755744752148), (1.3983229375627051, 0.94827633810055956), (1.3987372403078675, 0.94775609811441885), (1.3991506031011811, 0.94723683135293879), (1.3995630316871122, 0.94671853174301324), (1.3999745317513179, 0.94620119327366892), (1.4003851089214745, 0.94568480999519156), (1.4007947687681055, 0.9451693760182498), (1.4012035168053885, 0.94465488551304311), (1.4016113584919534, 0.94414133270845779), (1.4020182992316501, 0.94362871189125619), (1.4024243443743325, 0.94311701740524856), (1.4028294992165957, 0.9426062436505126), (1.4032337690025205, 0.94209638508260862), (1.403637158924397, 0.94158743621181351), (1.4040396741234407, 0.94107939160236465), (1.4044413196904877, 0.94057224587172517), (1.4048421006666869, 0.94006599368985244), (1.4052420220441713, 0.93956062977848886), (1.4056410887667239, 0.93905614891045819), (1.4060393057304355, 0.93855254590896953), (1.4064366777843365, 0.93804981564695122), (1.4068332097310297, 0.93754795304638205), (1.407228906327318, 0.93704695307762553), (1.4076237722848024, 0.93654681075880208), (1.4080178122704829, 0.93604752115515), (1.4084110309073541, 0.93554907937839893), (1.4088034327749721, 0.93505148058616916), (1.4091950224100316, 0.93455471998136341), (1.4095858043069214, 0.934058792811577), (1.4099757829182771, 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