Copy y2018 python arm visualization to y2023

Signed-off-by: Maxwell Henderson <mxwhenderson@gmail.com>
Change-Id: I0e4c2be36e46ab1d88ba04cfdb8e80f1e88ec5fc
diff --git a/y2023/control_loops/python/graph_generate.py b/y2023/control_loops/python/graph_generate.py
new file mode 100644
index 0000000..046b9dd
--- /dev/null
+++ b/y2023/control_loops/python/graph_generate.py
@@ -0,0 +1,798 @@
+import numpy
+
+# joint_center in x-y space.
+joint_center = (-0.299, 0.299)
+
+# Joint distances (l1 = "proximal", l2 = "distal")
+l1 = 46.25 * 0.0254
+l2 = 43.75 * 0.0254
+
+
+# Convert from x-y coordinates to theta coordinates.
+# orientation is a bool. This orientation is circular_index mod 2.
+# where circular_index is the circular index, or the position in the
+# "hyperextension" zones. "cross_point" allows shifting the place where
+# it rounds the result so that it draws nicer (no other functional differences).
+def to_theta(pt, circular_index, cross_point=-numpy.pi):
+    orient = (circular_index % 2) == 0
+    x = pt[0]
+    y = pt[1]
+    x -= joint_center[0]
+    y -= joint_center[1]
+    l3 = numpy.hypot(x, y)
+    t3 = numpy.arctan2(y, x)
+    theta1 = numpy.arccos((l1**2 + l3**2 - l2**2) / (2 * l1 * l3))
+
+    if orient:
+        theta1 = -theta1
+    theta1 += t3
+    theta1 = (theta1 - cross_point) % (2 * numpy.pi) + cross_point
+    theta2 = numpy.arctan2(y - l1 * numpy.sin(theta1),
+                           x - l1 * numpy.cos(theta1))
+    return numpy.array((theta1, theta2))
+
+
+# Simple trig to go back from theta1, theta2 to x-y
+def to_xy(theta1, theta2):
+    x = numpy.cos(theta1) * l1 + numpy.cos(theta2) * l2 + joint_center[0]
+    y = numpy.sin(theta1) * l1 + numpy.sin(theta2) * l2 + joint_center[1]
+    orient = ((theta2 - theta1) % (2.0 * numpy.pi)) < numpy.pi
+    return (x, y, orient)
+
+
+def get_circular_index(theta):
+    return int(numpy.floor((theta[1] - theta[0]) / numpy.pi))
+
+
+def get_xy(theta):
+    theta1 = theta[0]
+    theta2 = theta[1]
+    x = numpy.cos(theta1) * l1 + numpy.cos(theta2) * l2 + joint_center[0]
+    y = numpy.sin(theta1) * l1 + numpy.sin(theta2) * l2 + joint_center[1]
+    return numpy.array((x, y))
+
+
+# Draw a list of lines to a cairo context.
+def draw_lines(cr, lines):
+    cr.move_to(lines[0][0], lines[0][1])
+    for pt in lines[1:]:
+        cr.line_to(pt[0], pt[1])
+
+
+max_dist = 0.01
+max_dist_theta = numpy.pi / 64
+xy_end_circle_size = 0.01
+theta_end_circle_size = 0.07
+
+
+# Subdivide in theta space.
+def subdivide_theta(lines):
+    out = []
+    last_pt = lines[0]
+    out.append(last_pt)
+    for n_pt in lines[1:]:
+        for pt in subdivide(last_pt, n_pt, max_dist_theta):
+            out.append(pt)
+        last_pt = n_pt
+
+    return out
+
+
+# subdivide in xy space.
+def subdivide_xy(lines, max_dist=max_dist):
+    out = []
+    last_pt = lines[0]
+    out.append(last_pt)
+    for n_pt in lines[1:]:
+        for pt in subdivide(last_pt, n_pt, max_dist):
+            out.append(pt)
+        last_pt = n_pt
+
+    return out
+
+
+def to_theta_with_ci(pt, circular_index):
+    return to_theta_with_circular_index(pt[0], pt[1], circular_index)
+
+
+# to_theta, but distinguishes between
+def to_theta_with_circular_index(x, y, circular_index):
+    theta1, theta2 = to_theta((x, y), circular_index)
+    n_circular_index = int(numpy.floor((theta2 - theta1) / numpy.pi))
+    theta2 = theta2 + ((circular_index - n_circular_index)) * numpy.pi
+    return numpy.array((theta1, theta2))
+
+
+# alpha is in [0, 1] and is the weight to merge a and b.
+def alpha_blend(a, b, alpha):
+    """Blends a and b.
+
+    Args:
+      alpha: double, Ratio.  Needs to be in [0, 1] and is the weight to blend a
+          and b.
+    """
+    return b * alpha + (1.0 - alpha) * a
+
+
+def normalize(v):
+    """Normalize a vector while handling 0 length vectors."""
+    norm = numpy.linalg.norm(v)
+    if norm == 0:
+        return v
+    return v / norm
+
+
+# CI is circular index and allows selecting between all the stats that map
+# to the same x-y state (by giving them an integer index).
+# This will compute approximate first and second derivatives with respect
+# to path length.
+def to_theta_with_circular_index_and_derivs(x, y, dx, dy,
+                                            circular_index_select):
+    a = to_theta_with_circular_index(x, y, circular_index_select)
+    b = to_theta_with_circular_index(x + dx * 0.0001, y + dy * 0.0001,
+                                     circular_index_select)
+    c = to_theta_with_circular_index(x - dx * 0.0001, y - dy * 0.0001,
+                                     circular_index_select)
+    d1 = normalize(b - a)
+    d2 = normalize(c - a)
+    accel = (d1 + d2) / numpy.linalg.norm(a - b)
+    return (a[0], a[1], d1[0], d1[1], accel[0], accel[1])
+
+
+def to_theta_with_ci_and_derivs(p_prev, p, p_next, c_i_select):
+    a = to_theta(p, c_i_select)
+    b = to_theta(p_next, c_i_select)
+    c = to_theta(p_prev, c_i_select)
+    d1 = normalize(b - a)
+    d2 = normalize(c - a)
+    accel = (d1 + d2) / numpy.linalg.norm(a - b)
+    return (a[0], a[1], d1[0], d1[1], accel[0], accel[1])
+
+
+# Generic subdivision algorithm.
+def subdivide(p1, p2, max_dist):
+    dx = p2[0] - p1[0]
+    dy = p2[1] - p1[1]
+    dist = numpy.sqrt(dx**2 + dy**2)
+    n = int(numpy.ceil(dist / max_dist))
+    return [(alpha_blend(p1[0], p2[0],
+                         float(i) / n), alpha_blend(p1[1], p2[1],
+                                                    float(i) / n))
+            for i in range(1, n + 1)]
+
+
+# convert from an xy space loop into a theta loop.
+# All segements are expected go from one "hyper-extension" boundary
+# to another, thus we must go backwards over the "loop" to get a loop in
+# x-y space.
+def to_theta_loop(lines, cross_point=-numpy.pi):
+    out = []
+    last_pt = lines[0]
+    for n_pt in lines[1:]:
+        for pt in subdivide(last_pt, n_pt, max_dist):
+            out.append(to_theta(pt, 0, cross_point))
+        last_pt = n_pt
+    for n_pt in reversed(lines[:-1]):
+        for pt in subdivide(last_pt, n_pt, max_dist):
+            out.append(to_theta(pt, 1, cross_point))
+        last_pt = n_pt
+    return out
+
+
+# Convert a loop (list of line segments) into
+# The name incorrectly suggests that it is cyclic.
+def back_to_xy_loop(lines):
+    out = []
+    last_pt = lines[0]
+    out.append(to_xy(last_pt[0], last_pt[1]))
+    for n_pt in lines[1:]:
+        for pt in subdivide(last_pt, n_pt, max_dist_theta):
+            out.append(to_xy(pt[0], pt[1]))
+        last_pt = n_pt
+
+    return out
+
+
+# Segment in angle space.
+class AngleSegment:
+
+    def __init__(self, start, end, name=None, alpha_unitizer=None, vmax=None):
+        """Creates an angle segment.
+
+        Args:
+          start: (double, double),  The start of the segment in theta1, theta2
+              coordinates in radians
+          end: (double, double),  The end of the segment in theta1, theta2
+              coordinates in radians
+        """
+        self.start = start
+        self.end = end
+        self.name = name
+        self.alpha_unitizer = alpha_unitizer
+        self.vmax = vmax
+
+    def __repr__(self):
+        return "AngleSegment(%s, %s)" % (repr(self.start), repr(self.end))
+
+    def DrawTo(self, cr, theta_version):
+        if theta_version:
+            cr.move_to(self.start[0], self.start[1] + theta_end_circle_size)
+            cr.arc(self.start[0], self.start[1], theta_end_circle_size, 0,
+                   2.0 * numpy.pi)
+            cr.move_to(self.end[0], self.end[1] + theta_end_circle_size)
+            cr.arc(self.end[0], self.end[1], theta_end_circle_size, 0,
+                   2.0 * numpy.pi)
+            cr.move_to(self.start[0], self.start[1])
+            cr.line_to(self.end[0], self.end[1])
+        else:
+            start_xy = to_xy(self.start[0], self.start[1])
+            end_xy = to_xy(self.end[0], self.end[1])
+            draw_lines(cr, back_to_xy_loop([self.start, self.end]))
+            cr.move_to(start_xy[0] + xy_end_circle_size, start_xy[1])
+            cr.arc(start_xy[0], start_xy[1], xy_end_circle_size, 0,
+                   2.0 * numpy.pi)
+            cr.move_to(end_xy[0] + xy_end_circle_size, end_xy[1])
+            cr.arc(end_xy[0], end_xy[1], xy_end_circle_size, 0, 2.0 * numpy.pi)
+
+    def ToThetaPoints(self):
+        dx = self.end[0] - self.start[0]
+        dy = self.end[1] - self.start[1]
+        mag = numpy.hypot(dx, dy)
+        dx /= mag
+        dy /= mag
+
+        return [(self.start[0], self.start[1], dx, dy, 0.0, 0.0),
+                (self.end[0], self.end[1], dx, dy, 0.0, 0.0)]
+
+
+class XYSegment:
+    """Straight line in XY space."""
+
+    def __init__(self, start, end, name=None, alpha_unitizer=None, vmax=None):
+        """Creates an XY segment.
+
+        Args:
+          start: (double, double),  The start of the segment in theta1, theta2
+              coordinates in radians
+          end: (double, double),  The end of the segment in theta1, theta2
+              coordinates in radians
+        """
+        self.start = start
+        self.end = end
+        self.name = name
+        self.alpha_unitizer = alpha_unitizer
+        self.vmax = vmax
+
+    def __repr__(self):
+        return "XYSegment(%s, %s)" % (repr(self.start), repr(self.end))
+
+    def DrawTo(self, cr, theta_version):
+        if theta_version:
+            theta1, theta2 = self.start
+            circular_index_select = int(
+                numpy.floor((self.start[1] - self.start[0]) / numpy.pi))
+            start = get_xy(self.start)
+            end = get_xy(self.end)
+
+            ln = [(start[0], start[1]), (end[0], end[1])]
+            draw_lines(cr, [
+                to_theta_with_circular_index(x, y, circular_index_select)
+                for x, y in subdivide_xy(ln)
+            ])
+            cr.move_to(self.start[0] + theta_end_circle_size, self.start[1])
+            cr.arc(self.start[0], self.start[1], theta_end_circle_size, 0,
+                   2.0 * numpy.pi)
+            cr.move_to(self.end[0] + theta_end_circle_size, self.end[1])
+            cr.arc(self.end[0], self.end[1], theta_end_circle_size, 0,
+                   2.0 * numpy.pi)
+        else:
+            start = get_xy(self.start)
+            end = get_xy(self.end)
+            cr.move_to(start[0], start[1])
+            cr.line_to(end[0], end[1])
+            cr.move_to(start[0] + xy_end_circle_size, start[1])
+            cr.arc(start[0], start[1], xy_end_circle_size, 0, 2.0 * numpy.pi)
+            cr.move_to(end[0] + xy_end_circle_size, end[1])
+            cr.arc(end[0], end[1], xy_end_circle_size, 0, 2.0 * numpy.pi)
+
+    def ToThetaPoints(self):
+        """ Converts to points in theta space via to_theta_with_circular_index_and_derivs"""
+        theta1, theta2 = self.start
+        circular_index_select = int(
+            numpy.floor((self.start[1] - self.start[0]) / numpy.pi))
+        start = get_xy(self.start)
+        end = get_xy(self.end)
+
+        ln = [(start[0], start[1]), (end[0], end[1])]
+
+        dx = end[0] - start[0]
+        dy = end[1] - start[1]
+        mag = numpy.hypot(dx, dy)
+        dx /= mag
+        dy /= mag
+
+        return [
+            to_theta_with_circular_index_and_derivs(x, y, dx, dy,
+                                                    circular_index_select)
+            for x, y in subdivide_xy(ln, 0.01)
+        ]
+
+
+def spline_eval(start, control1, control2, end, alpha):
+    a = alpha_blend(start, control1, alpha)
+    b = alpha_blend(control1, control2, alpha)
+    c = alpha_blend(control2, end, alpha)
+    return alpha_blend(alpha_blend(a, b, alpha), alpha_blend(b, c, alpha),
+                       alpha)
+
+
+def subdivide_spline(start, control1, control2, end):
+    # TODO: pick N based on spline parameters? or otherwise change it to be more evenly spaced?
+    n = 100
+    for i in range(0, n + 1):
+        yield i / float(n)
+
+
+class SplineSegment:
+
+    def __init__(self,
+                 start,
+                 control1,
+                 control2,
+                 end,
+                 name=None,
+                 alpha_unitizer=None,
+                 vmax=None):
+        self.start = start
+        self.control1 = control1
+        self.control2 = control2
+        self.end = end
+        self.name = name
+        self.alpha_unitizer = alpha_unitizer
+        self.vmax = vmax
+
+    def __repr__(self):
+        return "SplineSegment(%s, %s, %s, %s)" % (repr(
+            self.start), repr(self.control1), repr(
+                self.control2), repr(self.end))
+
+    def DrawTo(self, cr, theta_version):
+        if theta_version:
+            c_i_select = get_circular_index(self.start)
+            start = get_xy(self.start)
+            control1 = get_xy(self.control1)
+            control2 = get_xy(self.control2)
+            end = get_xy(self.end)
+
+            draw_lines(cr, [
+                to_theta(spline_eval(start, control1, control2, end, alpha),
+                         c_i_select)
+                for alpha in subdivide_spline(start, control1, control2, end)
+            ])
+            cr.move_to(self.start[0] + theta_end_circle_size, self.start[1])
+            cr.arc(self.start[0], self.start[1], theta_end_circle_size, 0,
+                   2.0 * numpy.pi)
+            cr.move_to(self.end[0] + theta_end_circle_size, self.end[1])
+            cr.arc(self.end[0], self.end[1], theta_end_circle_size, 0,
+                   2.0 * numpy.pi)
+        else:
+            start = get_xy(self.start)
+            control1 = get_xy(self.control1)
+            control2 = get_xy(self.control2)
+            end = get_xy(self.end)
+
+            draw_lines(cr, [
+                spline_eval(start, control1, control2, end, alpha)
+                for alpha in subdivide_spline(start, control1, control2, end)
+            ])
+
+            cr.move_to(start[0] + xy_end_circle_size, start[1])
+            cr.arc(start[0], start[1], xy_end_circle_size, 0, 2.0 * numpy.pi)
+            cr.move_to(end[0] + xy_end_circle_size, end[1])
+            cr.arc(end[0], end[1], xy_end_circle_size, 0, 2.0 * numpy.pi)
+
+    def ToThetaPoints(self):
+        t1, t2 = self.start
+        c_i_select = get_circular_index(self.start)
+        start = get_xy(self.start)
+        control1 = get_xy(self.control1)
+        control2 = get_xy(self.control2)
+        end = get_xy(self.end)
+
+        return [
+            to_theta_with_ci_and_derivs(
+                spline_eval(start, control1, control2, end, alpha - 0.00001),
+                spline_eval(start, control1, control2, end, alpha),
+                spline_eval(start, control1, control2, end, alpha + 0.00001),
+                c_i_select)
+            for alpha in subdivide_spline(start, control1, control2, end)
+        ]
+
+
+def get_derivs(t_prev, t, t_next):
+    c, a, b = t_prev, t, t_next
+    d1 = normalize(b - a)
+    d2 = normalize(c - a)
+    accel = (d1 + d2) / numpy.linalg.norm(a - b)
+    return (a[0], a[1], d1[0], d1[1], accel[0], accel[1])
+
+
+class ThetaSplineSegment:
+
+    def __init__(self,
+                 start,
+                 control1,
+                 control2,
+                 end,
+                 name=None,
+                 alpha_unitizer=None,
+                 vmax=None):
+        self.start = start
+        self.control1 = control1
+        self.control2 = control2
+        self.end = end
+        self.name = name
+        self.alpha_unitizer = alpha_unitizer
+        self.vmax = vmax
+
+    def __repr__(self):
+        return "ThetaSplineSegment(%s, %s, &s, %s)" % (repr(
+            self.start), repr(self.control1), repr(
+                self.control2), repr(self.end))
+
+    def DrawTo(self, cr, theta_version):
+        if (theta_version):
+            draw_lines(cr, [
+                spline_eval(self.start, self.control1, self.control2, self.end,
+                            alpha)
+                for alpha in subdivide_spline(self.start, self.control1,
+                                              self.control2, self.end)
+            ])
+        else:
+            start = get_xy(self.start)
+            end = get_xy(self.end)
+
+            draw_lines(cr, [
+                get_xy(
+                    spline_eval(self.start, self.control1, self.control2,
+                                self.end, alpha))
+                for alpha in subdivide_spline(self.start, self.control1,
+                                              self.control2, self.end)
+            ])
+
+            cr.move_to(start[0] + xy_end_circle_size, start[1])
+            cr.arc(start[0], start[1], xy_end_circle_size, 0, 2.0 * numpy.pi)
+            cr.move_to(end[0] + xy_end_circle_size, end[1])
+            cr.arc(end[0], end[1], xy_end_circle_size, 0, 2.0 * numpy.pi)
+
+    def ToThetaPoints(self):
+        return [
+            get_derivs(
+                spline_eval(self.start, self.control1, self.control2, self.end,
+                            alpha - 0.00001),
+                spline_eval(self.start, self.control1, self.control2, self.end,
+                            alpha),
+                spline_eval(self.start, self.control1, self.control2, self.end,
+                            alpha + 0.00001))
+            for alpha in subdivide_spline(self.start, self.control1,
+                                          self.control2, self.end)
+        ]
+
+
+tall_box_x = 0.411
+tall_box_y = 0.125
+
+short_box_x = 0.431
+short_box_y = 0.082
+
+ready_above_box = to_theta_with_circular_index(tall_box_x,
+                                               tall_box_y + 0.08,
+                                               circular_index=-1)
+tall_box_grab = to_theta_with_circular_index(tall_box_x,
+                                             tall_box_y,
+                                             circular_index=-1)
+short_box_grab = to_theta_with_circular_index(short_box_x,
+                                              short_box_y,
+                                              circular_index=-1)
+
+# TODO(austin): Drive the front/back off the same numbers a bit better.
+front_high_box = to_theta_with_circular_index(0.378, 2.46, circular_index=-1)
+front_middle3_box = to_theta_with_circular_index(0.700,
+                                                 2.125,
+                                                 circular_index=-1.000000)
+front_middle2_box = to_theta_with_circular_index(0.700,
+                                                 2.268,
+                                                 circular_index=-1)
+front_middle1_box = to_theta_with_circular_index(0.800,
+                                                 1.915,
+                                                 circular_index=-1)
+front_low_box = to_theta_with_circular_index(0.87, 1.572, circular_index=-1)
+back_high_box = to_theta_with_circular_index(-0.75, 2.48, circular_index=0)
+back_middle2_box = to_theta_with_circular_index(-0.700, 2.27, circular_index=0)
+back_middle1_box = to_theta_with_circular_index(-0.800, 1.93, circular_index=0)
+back_low_box = to_theta_with_circular_index(-0.87, 1.64, circular_index=0)
+
+back_extra_low_box = to_theta_with_circular_index(-0.87,
+                                                  1.52,
+                                                  circular_index=0)
+
+front_switch = to_theta_with_circular_index(0.88, 0.967, circular_index=-1)
+back_switch = to_theta_with_circular_index(-0.88, 0.967, circular_index=-2)
+
+neutral = to_theta_with_circular_index(0.0, 0.33, circular_index=-1)
+
+up = to_theta_with_circular_index(0.0, 2.547, circular_index=-1)
+
+front_switch_auto = to_theta_with_circular_index(0.750,
+                                                 2.20,
+                                                 circular_index=-1.000000)
+
+duck = numpy.array([numpy.pi / 2.0 - 0.92, numpy.pi / 2.0 - 4.26])
+
+starting = numpy.array([numpy.pi / 2.0 - 0.593329, numpy.pi / 2.0 - 3.749631])
+vertical_starting = numpy.array([numpy.pi / 2.0, -numpy.pi / 2.0])
+
+self_hang = numpy.array([numpy.pi / 2.0 - 0.191611, numpy.pi / 2.0])
+partner_hang = numpy.array([numpy.pi / 2.0 - (-0.30), numpy.pi / 2.0])
+
+above_hang = numpy.array([numpy.pi / 2.0 - 0.14, numpy.pi / 2.0 - (-0.165)])
+below_hang = numpy.array([numpy.pi / 2.0 - 0.39, numpy.pi / 2.0 - (-0.517)])
+
+up_c1 = to_theta((0.63, 1.17), circular_index=-1)
+up_c2 = to_theta((0.65, 1.62), circular_index=-1)
+
+front_high_box_c1 = to_theta((0.63, 1.04), circular_index=-1)
+front_high_box_c2 = to_theta((0.50, 1.60), circular_index=-1)
+
+front_middle2_box_c1 = to_theta((0.41, 0.83), circular_index=-1)
+front_middle2_box_c2 = to_theta((0.52, 1.30), circular_index=-1)
+
+front_middle1_box_c1 = to_theta((0.34, 0.82), circular_index=-1)
+front_middle1_box_c2 = to_theta((0.48, 1.15), circular_index=-1)
+
+#c1: (1.421433, -1.070254)
+#c2: (1.434384, -1.057803
+ready_above_box_c1 = numpy.array([1.480802, -1.081218])
+ready_above_box_c2 = numpy.array([1.391449, -1.060331])
+
+front_switch_c1 = numpy.array([1.903841, -0.622351])
+front_switch_c2 = numpy.array([1.903841, -0.622351])
+
+
+sparse_front_points = [
+    (front_high_box, "FrontHighBox"),
+    (front_middle2_box, "FrontMiddle2Box"),
+    (front_middle3_box, "FrontMiddle3Box"),
+    (front_middle1_box, "FrontMiddle1Box"),
+    (front_low_box, "FrontLowBox"),
+    (front_switch, "FrontSwitch"),
+]  # yapf: disable
+
+sparse_back_points = [
+    (back_high_box, "BackHighBox"),
+    (back_middle2_box, "BackMiddle2Box"),
+    (back_middle1_box, "BackMiddle1Box"),
+    (back_low_box, "BackLowBox"),
+    (back_extra_low_box, "BackExtraLowBox"),
+]  # yapf: disable
+
+def expand_points(points, max_distance):
+    """Expands a list of points to be at most max_distance apart
+
+    Generates the paths to connect the new points to the closest input points,
+    and the paths connecting the points.
+
+    Args:
+      points, list of tuple of point, name, The points to start with and fill
+          in.
+      max_distance, float, The max distance between two points when expanding
+          the graph.
+
+    Return:
+      points, edges
+    """
+    result_points = [points[0]]
+    result_paths = []
+    for point, name in points[1:]:
+        previous_point = result_points[-1][0]
+        previous_point_xy = get_xy(previous_point)
+        circular_index = get_circular_index(previous_point)
+
+        point_xy = get_xy(point)
+        norm = numpy.linalg.norm(point_xy - previous_point_xy)
+        num_points = int(numpy.ceil(norm / max_distance))
+        last_iteration_point = previous_point
+        for subindex in range(1, num_points):
+            subpoint = to_theta(alpha_blend(previous_point_xy, point_xy,
+                                            float(subindex) / num_points),
+                                circular_index=circular_index)
+            result_points.append(
+                (subpoint, '%s%dof%d' % (name, subindex, num_points)))
+            result_paths.append(
+                XYSegment(last_iteration_point, subpoint, vmax=6.0))
+            if (last_iteration_point != previous_point).any():
+                result_paths.append(XYSegment(previous_point, subpoint))
+            if subindex == num_points - 1:
+                result_paths.append(XYSegment(subpoint, point, vmax=6.0))
+            else:
+                result_paths.append(XYSegment(subpoint, point))
+            last_iteration_point = subpoint
+        result_points.append((point, name))
+
+    return result_points, result_paths
+
+
+front_points, front_paths = expand_points(sparse_front_points, 0.06)
+back_points, back_paths = expand_points(sparse_back_points, 0.06)
+
+points = [(ready_above_box, "ReadyAboveBox"),
+          (tall_box_grab, "TallBoxGrab"),
+          (short_box_grab, "ShortBoxGrab"),
+          (back_switch, "BackSwitch"),
+          (neutral, "Neutral"),
+          (up, "Up"),
+          (above_hang, "AboveHang"),
+          (below_hang, "BelowHang"),
+          (self_hang, "SelfHang"),
+          (partner_hang, "PartnerHang"),
+          (front_switch_auto, "FrontSwitchAuto"),
+          (starting, "Starting"),
+          (duck, "Duck"),
+          (vertical_starting, "VerticalStarting"),
+] + front_points + back_points  # yapf: disable
+
+duck_c1 = numpy.array([1.337111, -1.721008])
+duck_c2 = numpy.array([1.283701, -1.795519])
+
+ready_to_up_c1 = numpy.array([1.792962, 0.198329])
+ready_to_up_c2 = numpy.array([1.792962, 0.198329])
+
+front_switch_auto_c1 = numpy.array([1.792857, -0.372768])
+front_switch_auto_c2 = numpy.array([1.861885, -0.273664])
+
+# We need to define critical points so we can create paths connecting them.
+# TODO(austin): Attach velocities to the slow ones.
+ready_to_back_low_c1 = numpy.array([2.524325, 0.046417])
+
+neutral_to_back_low_c1 = numpy.array([2.381942, -0.070220])
+
+tall_to_back_low_c1 = numpy.array([2.603918, 0.088298])
+tall_to_back_low_c2 = numpy.array([1.605624, 1.003434])
+
+tall_to_back_high_c2 = numpy.array([1.508610, 0.946147])
+
+# If true, only plot the first named segment
+isolate = False
+
+long_alpha_unitizer = numpy.matrix([[1.0 / 17.0, 0.0], [0.0, 1.0 / 17.0]])
+
+neutral_to_back_c1 = numpy.array([0.702527, -2.618276])
+neutral_to_back_c2 = numpy.array([0.526914, -3.109691])
+
+named_segments = [
+    ThetaSplineSegment(neutral, neutral_to_back_c1, neutral_to_back_c2,
+                       back_switch, "BackSwitch"),
+    ThetaSplineSegment(neutral,
+                       neutral_to_back_low_c1,
+                       tall_to_back_high_c2,
+                       back_high_box,
+                       "NeutralBoxToHigh",
+                       alpha_unitizer=long_alpha_unitizer),
+    ThetaSplineSegment(neutral, neutral_to_back_low_c1, tall_to_back_high_c2,
+                       back_middle2_box, "NeutralBoxToMiddle2",
+                       long_alpha_unitizer),
+    ThetaSplineSegment(neutral, neutral_to_back_low_c1, tall_to_back_low_c2,
+                       back_middle1_box, "NeutralBoxToMiddle1",
+                       long_alpha_unitizer),
+    ThetaSplineSegment(neutral, neutral_to_back_low_c1, tall_to_back_low_c2,
+                       back_low_box, "NeutralBoxToLow", long_alpha_unitizer),
+    ThetaSplineSegment(ready_above_box, ready_to_back_low_c1,
+                       tall_to_back_high_c2, back_high_box, "ReadyBoxToHigh",
+                       long_alpha_unitizer),
+    ThetaSplineSegment(ready_above_box, ready_to_back_low_c1,
+                       tall_to_back_high_c2, back_middle2_box,
+                       "ReadyBoxToMiddle2", long_alpha_unitizer),
+    ThetaSplineSegment(ready_above_box, ready_to_back_low_c1,
+                       tall_to_back_low_c2, back_middle1_box,
+                       "ReadyBoxToMiddle1", long_alpha_unitizer),
+    ThetaSplineSegment(ready_above_box, ready_to_back_low_c1,
+                       tall_to_back_low_c2, back_low_box, "ReadyBoxToLow",
+                       long_alpha_unitizer),
+    ThetaSplineSegment(short_box_grab, tall_to_back_low_c1,
+                       tall_to_back_high_c2, back_high_box, "ShortBoxToHigh",
+                       long_alpha_unitizer),
+    ThetaSplineSegment(short_box_grab, tall_to_back_low_c1,
+                       tall_to_back_high_c2, back_middle2_box,
+                       "ShortBoxToMiddle2", long_alpha_unitizer),
+    ThetaSplineSegment(short_box_grab, tall_to_back_low_c1,
+                       tall_to_back_low_c2, back_middle1_box,
+                       "ShortBoxToMiddle1", long_alpha_unitizer),
+    ThetaSplineSegment(short_box_grab, tall_to_back_low_c1,
+                       tall_to_back_low_c2, back_low_box, "ShortBoxToLow",
+                       long_alpha_unitizer),
+    ThetaSplineSegment(tall_box_grab, tall_to_back_low_c1,
+                       tall_to_back_high_c2, back_high_box, "TallBoxToHigh",
+                       long_alpha_unitizer),
+    ThetaSplineSegment(tall_box_grab, tall_to_back_low_c1,
+                       tall_to_back_high_c2, back_middle2_box,
+                       "TallBoxToMiddle2", long_alpha_unitizer),
+    ThetaSplineSegment(tall_box_grab, tall_to_back_low_c1, tall_to_back_low_c2,
+                       back_middle1_box, "TallBoxToMiddle1",
+                       long_alpha_unitizer),
+    ThetaSplineSegment(tall_box_grab, tall_to_back_low_c1, tall_to_back_low_c2,
+                       back_low_box, "TallBoxToLow", long_alpha_unitizer),
+    SplineSegment(neutral, ready_above_box_c1, ready_above_box_c2,
+                  ready_above_box, "ReadyToNeutral"),
+    XYSegment(ready_above_box, tall_box_grab, "ReadyToTallBox", vmax=6.0),
+    XYSegment(ready_above_box, short_box_grab, "ReadyToShortBox", vmax=6.0),
+    XYSegment(tall_box_grab, short_box_grab, "TallToShortBox", vmax=6.0),
+    SplineSegment(neutral, ready_above_box_c1, ready_above_box_c2,
+                  tall_box_grab, "TallToNeutral"),
+    SplineSegment(neutral, ready_above_box_c1, ready_above_box_c2,
+                  short_box_grab, "ShortToNeutral"),
+    SplineSegment(neutral, up_c1, up_c2, up, "NeutralToUp"),
+    SplineSegment(neutral, front_high_box_c1, front_high_box_c2,
+                  front_high_box, "NeutralToFrontHigh"),
+    SplineSegment(neutral, front_middle2_box_c1, front_middle2_box_c2,
+                  front_middle2_box, "NeutralToFrontMiddle2"),
+    SplineSegment(neutral, front_middle1_box_c1, front_middle1_box_c2,
+                  front_middle1_box, "NeutralToFrontMiddle1"),
+]
+
+unnamed_segments = [
+    SplineSegment(neutral, front_switch_auto_c1, front_switch_auto_c2,
+                  front_switch_auto),
+    SplineSegment(tall_box_grab, ready_to_up_c1, ready_to_up_c2, up),
+    SplineSegment(short_box_grab, ready_to_up_c1, ready_to_up_c2, up),
+    SplineSegment(ready_above_box, ready_to_up_c1, ready_to_up_c2, up),
+    ThetaSplineSegment(duck, duck_c1, duck_c2, neutral),
+    SplineSegment(neutral, front_switch_c1, front_switch_c2, front_switch),
+    XYSegment(ready_above_box, front_low_box),
+    XYSegment(ready_above_box, front_switch),
+    XYSegment(ready_above_box, front_middle1_box),
+    XYSegment(ready_above_box, front_middle2_box),
+    XYSegment(ready_above_box, front_middle3_box),
+    SplineSegment(ready_above_box, ready_to_up_c1, ready_to_up_c2,
+                  front_high_box),
+    AngleSegment(starting, vertical_starting),
+    AngleSegment(vertical_starting, neutral),
+    XYSegment(neutral, front_low_box),
+    XYSegment(up, front_high_box),
+    XYSegment(up, front_middle2_box),
+    XYSegment(front_middle3_box, up),
+    XYSegment(front_middle3_box, front_high_box),
+    XYSegment(front_middle3_box, front_middle2_box),
+    XYSegment(front_middle3_box, front_middle1_box),
+    XYSegment(up, front_middle1_box),
+    XYSegment(up, front_low_box),
+    XYSegment(front_high_box, front_middle2_box),
+    XYSegment(front_high_box, front_middle1_box),
+    XYSegment(front_high_box, front_low_box),
+    XYSegment(front_middle2_box, front_middle1_box),
+    XYSegment(front_middle2_box, front_low_box),
+    XYSegment(front_middle1_box, front_low_box),
+    XYSegment(front_switch, front_low_box),
+    XYSegment(front_switch, up),
+    XYSegment(front_switch, front_high_box),
+    AngleSegment(up, back_high_box),
+    AngleSegment(up, back_middle2_box),
+    AngleSegment(up, back_middle1_box),
+    AngleSegment(up, back_low_box),
+    XYSegment(back_high_box, back_middle2_box),
+    XYSegment(back_high_box, back_middle1_box),
+    XYSegment(back_high_box, back_low_box),
+    XYSegment(back_middle2_box, back_middle1_box),
+    XYSegment(back_middle2_box, back_low_box),
+    XYSegment(back_middle1_box, back_low_box),
+    AngleSegment(up, above_hang),
+    AngleSegment(above_hang, below_hang),
+    AngleSegment(up, below_hang),
+    AngleSegment(up, self_hang),
+    AngleSegment(up, partner_hang),
+] + front_paths + back_paths
+
+segments = []
+if isolate:
+    segments += named_segments[:isolate]
+else:
+    segments += named_segments + unnamed_segments