MuesliMix/prototype/circles.py

from casadi import *
import matplotlib.pyplot as plt
import math
import operator

from svg_utils import *


# this function reads and processes data for optimal circle packaging obtained form packomania.com
def read_circle_data(N):
    coords_raw = open('cci/cci{}.txt'.format(N))
    radii_raw = open('cci/radii.txt'.format(N))

    coords_raw = coords_raw.readlines()
    coords_raw = [c.split() for c in coords_raw if c[0] != '#']
    coords = {}
    for c in coords_raw:
        coords[int(c[0])] = (float(c[1]), float(c[2]))

    coords = sort_ccw(coords, (0,0))

    radii_raw = radii_raw.readlines()
    radii_raw = [r.split() for r in radii_raw if r[0] != '#']
    radii = {}
    for r in radii_raw:
        radii[int(r[0])] = float(r[1])

    return radii[N], coords


# this function sorts enclosed circle coordinates counter-clockwise w.r.t. the center point
# TODO: there is a problem when circles are present that are not touching the boundary of the enclosing circle (e.g. N = 7)
def sort_ccw(coords, center):
    a = {}
    for c in coords:
        a[c] = math.atan2(coords[c][1] - center[1], coords[c][0] - center[0])
    a_sort = sorted(a.items(), key=operator.itemgetter(1))

    coords_sort = []
    for a in a_sort:
        coords_sort.append(coords[a[0]])

    return coords_sort


# compute the two tangential points at the circle with center c and radius r intersecting the point p
def compute_tangent_points(p, c, r):
    b = sqrt((p[0] - c[0]) ** 2 + (p[1] - c[1]) ** 2)
    th = acos(r / b)  # angle theta
    d = atan2(p[1] - c[1], p[0] - c[0])  # direction angle of point p from c
    d1 = d + th  # direction angle of point T1 from c
    d2 = d - th  # direction angle of point T2 from c

    T1x = c[0] + r * cos(d1)
    T1y = c[1] + r * sin(d1)
    T2x = c[0] + r * cos(d2)
    T2y = c[1] + r * sin(d2)

    return (T1x, T1y), (T2x, T2y)


class PlateLayout:
    def __init__(self, N, plate_radius):
        self.N = N # number of enclosed circles
        self.plate_radius = plate_radius

    def compute_layout(self):
        # read radius and center coordinates for enclosed circles
        rtilde, coords = read_circle_data(self.N)

        c = (0.0, 0.0)  # center of big circle
        R = 1.0        # radius of big circle

        plt.xlim((-1, 1))
        plt.ylim((-1, 1))
        plt.gca().set_aspect('equal', 'box')

        plt.ion()
        plt.show()

        for p in coords:
            plt.plot(p[0], p[1], 'o')
            circle = plt.Circle(p, rtilde, fill=False)
            plt.gca().add_artist(circle)
        circle = plt.Circle(c, R, fill=False)
        plt.gca().add_artist(circle)

        plt.plot(c[0], c[1], 'o')

        coords_2 = []
        for k in range(0, self.N):
            p1 = coords[k]
            p2 = coords[(k+1) % self.N]

            # midpoint between center of two circles
            m = np.mean([p1, p2], axis=0)

            # vector in direction of midpoint
            v = m - np.array(c)
            v = v/np.linalg.norm(v)
            #plt.plot(m[0], m[1], 'o')


            # optimization problem for computing position and radius for a maximal circle fitting in space between two big circles
            # and being fully contained in enclosing circle
            opti = casadi.Opti()

            r = opti.variable(1)    # radius of new circle
            p = opti.variable(2)    # center of new circle
            lamb = opti.variable(1) # distance of center of new circle to center of enclosing circle

            opti.minimize(-r)
            opti.subject_to(p == c + v * lamb)
            opti.subject_to((p[0] - p1[0])**2 + (p[1] - p1[1])**2 >= (rtilde + r)**2)
            opti.subject_to(R == lamb + r)
            opti.subject_to(r >= 0)
            opti.subject_to(r <= R)

            opti.solver('ipopt')

            init_r = 0.1
            init_lamb = R - init_r
            init_p = c + v * init_lamb

            opti.set_initial(r, init_r)
            opti.set_initial(p, init_p)
            opti.set_initial(lamb, init_lamb)

            sol = opti.solve()

            p = sol.value(p)
            r = sol.value(r)
            lamb = sol.value(lamb)

            print("p = {}".format(p))
            print("r = {}".format(r))
            print("lambda = {}".format(lamb))
            print("v = {}".format(v))

            coords_2.append(p)

            plt.plot(p[0], p[1], 'o')
            circle = plt.Circle(p, r, fill=False)
            plt.gca().add_artist(circle)

        tube1 = {}
        tube2 = {}

        # postprocessing solution:
        # - output radii for circles
        # - output center coordinates, angle w.r.t. origin and distance from origin
        outer_radius = self.plate_radius  # desired plate radius in meters
        tube1_radius = outer_radius * rtilde
        tube2_radius = outer_radius * r

        print("\n------------------")
        print("optimal values")
        print("plate radius  = {:6.3} m = {:6.2f} mm".format(outer_radius / 1000, outer_radius))
        print("big circles:")
        print("  radius = {:6.3} m = {:6.2f} mm".format(tube1_radius / 1000, tube1_radius))
        print("  diameter = {:6.3} m = {:6.2f} mm".format(2 * tube1_radius / 1000, 2 * tube1_radius))
        print("small circles:")
        print("  radius = {:6.3} m = {:6.2f} mm".format(tube2_radius, tube2_radius * 1000))
        print("  diameter = {:6.3} m = {:6.2f} mm".format(2*tube2_radius, 2*tube2_radius * 1000))

        # compute coordinates and various measurements for fixed radii of plate and tubes
        self.target_plate_radius = 160.0
        self.target_center_hole_radius = 7.5
        self.target_radius_1 = 50.5
        self.target_radius_2 = 20.0
        teeth = 200

        D = 2 * self.target_plate_radius
        self.plate_module = D/teeth

        print("plate radius        = {:6.2f} mm".format(self.target_plate_radius))
        print("big circle radius   = {:6.2f} mm".format(self.target_radius_1))
        print("small circle radius = {:6.2f} mm".format(self.target_radius_2))

        print("number of teeth: N = {}".format(teeth))
        print("pitch diameter:  D = {} mm".format(D))
        print("module:          M = {} mm".format(self.plate_module))


        # parameters for dispenser gears
        self.dispenser_module = 1.0
        dispenser_1_target_pitch_diameter_big = 50.0
        dispenser_1_target_pitch_diameter_small = 15.0
        dispenser_1_teeth_big = int(dispenser_1_target_pitch_diameter_big/self.dispenser_module)
        dispenser_1_teeth_small = int(dispenser_1_target_pitch_diameter_small/ self.dispenser_module)

        dispenser_1_pitch_diameter_big = self.dispenser_module * dispenser_1_teeth_big
        dispenser_1_outer_diameter_big = dispenser_1_pitch_diameter_big + 2 * self.dispenser_module
        dispenser_1_pitch_diameter_small = self.dispenser_module * dispenser_1_teeth_small
        dispenser_1_outer_diameter_small = dispenser_1_pitch_diameter_small + 2 * self.dispenser_module

        dispenser_2_target_pitch_diameter_big = 20.0
        dispenser_2_target_pitch_diameter_small = 15.0
        dispenser_2_teeth_big = int(dispenser_2_target_pitch_diameter_big / self.dispenser_module)
        dispenser_2_teeth_small = int(dispenser_2_target_pitch_diameter_small / self.dispenser_module)

        dispenser_2_pitch_diameter_big = self.dispenser_module * dispenser_2_teeth_big
        dispenser_2_outer_diameter_big = dispenser_2_pitch_diameter_big + 2 * self.dispenser_module
        dispenser_2_pitch_diameter_small = self.dispenser_module * dispenser_2_teeth_small
        dispenser_2_outer_diameter_small = dispenser_2_pitch_diameter_small + 2 * self.dispenser_module
        print("parameters for dispenser gears:")
        print(" big container:")
        print("  module                      = {}".format(self.dispenser_module))
        print("  pitch diameter big gear     = {}".format(dispenser_1_pitch_diameter_big))
        print("  number of teeth big gear    = {}".format(dispenser_1_teeth_big))
        print("  pitch diameter small gear   = {}".format(dispenser_1_pitch_diameter_small))
        print("  number of teeth small gear  = {}".format(dispenser_1_teeth_small))
        print(" small container:")
        print("  module                      = {}".format(self.dispenser_module))
        print("  pitch diameter big gear     = {}".format(dispenser_2_pitch_diameter_big))
        print("  number of teeth big gear    = {}".format(dispenser_2_teeth_big))
        print("  pitch diameter small gear   = {}".format(dispenser_2_pitch_diameter_small))
        print("  number of teeth small gear  = {}".format(dispenser_2_teeth_small))

        # plot plate
        plt.figure(2)
        plt.plot(0.0, 0.0, 'o')
        circle = plt.Circle((0.0, 0.0), self.target_plate_radius, fill=False)
        plt.gca().add_artist(circle)
        plt.xlim((-self.target_plate_radius*1.1, self.target_plate_radius*1.1))
        plt.ylim((-self.target_plate_radius*1.1, self.target_plate_radius*1.1))
        plt.gca().set_aspect('equal', 'box')

        # plate coordinates
        print("plate coordinates: (x,y) = ({:8.3f}, {:8.3f})".format(0.0, 0.0))

        self.tube_1_coords = {}
        self.tube_2_coords = {}
        self.tube_1_angles = {}
        self.tube_2_angles = {}
        self.tube_1_tangents = {}
        self.tube_1_tangent_angles = {}
        self.tube_1_cuts = {}
        self.tube_2_tangents = {}
        self.tube_2_tangent_angles = {}
        self.tube_2_cuts = {}

        print(" big circle coordinates:")
        for k in range(0,self.N):
            x = coords[k][0] * outer_radius
            y = coords[k][1] * outer_radius

            angle = arctan2(y, x) * 360.0 / (2.0 * math.pi)

            self.tube_1_coords[k] = (x,y)
            self.tube_1_angles[k] = angle

            print("   k = {},  (x,y) = ({:8.3f}, {:8.3f}),  angle = {:8.3f} deg".format(k, x, y, angle))

            circle = plt.Circle((x,y), self.target_radius_1, fill=False)
            plt.gca().add_artist(circle)

        p1 = dispenser_1_pitch_diameter_big
        p2 = dispenser_1_pitch_diameter_small
        a1 = self.dispenser_module
        a2 = self.dispenser_module
        offset_1 = sqrt((p1 / 2 + p2 / 2) ** 2 - (p1 / 2 + a1) ** 2) - p2 / 2 - a2
        print("dispenser 1 offset = {}".format(offset_1))

        print(" big circle tangent points: ")
        for k in range(0, self.N):
            x = coords[k][0] * outer_radius
            y = coords[k][1] * outer_radius

            t1, t2 = compute_tangent_points((0, 0), (x, y), self.target_radius_1)

            angle1_rad = arctan2(t1[1], t1[0])
            angle2_rad = arctan2(t2[1], t2[0])
            angle1_deg = angle1_rad * 360.0 / (2.0 * math.pi)
            angle2_deg = angle2_rad * 360.0 / (2.0 * math.pi)

            self.tube_1_tangents[k] = (t1, t2)
            self.tube_1_tangent_angles[k] = (angle1_deg, angle2_deg)

            print(
            "   k = {},  t1 = ({:8.3f}, {:8.3f}),  angle = {:8.3f} deg\n           t2 = ({:8.3f}, {:8.3f}),  angle "
            "= {:8.3f} deg".format(k, t1[0], t1[1], angle1_deg, t2[0], t2[1], angle2_deg))

            plt.plot(t1[0], t1[1], 'o')
            plt.plot(t2[0], t2[1], 'o')

            ## compute position of cut for dispenser gear
            # vector pointing from center in direction of tangent point
            v = np.array([math.cos(angle1_rad), math.sin(angle1_rad)])

            cut_center = np.array(t1) - v * (offset_1 + dispenser_1_outer_diameter_small/2.0)
            self.tube_1_cuts[k] = {}
            self.tube_1_cuts[k]['center'] = cut_center
            self.tube_1_cuts[k]['tangent_point'] = t1
            self.tube_1_cuts[k]['angle_deg'] = angle1_deg
            self.tube_1_cuts[k]['length'] = dispenser_1_outer_diameter_small
            self.tube_1_cuts[k]['width'] = 5.0

            plt.plot(cut_center[0], cut_center[1], 'o')


            pass


        print(" small circle coordinates:")
        for k in range(0,self.N):
            x = coords_2[k][0] * outer_radius
            y = coords_2[k][1] * outer_radius

            angle = arctan2(y, x) * 360.0 / (2.0 * math.pi)

            self.tube_2_coords[k] = (x, y)
            self.tube_2_angles[k] = angle

            print("   k = {},  (x,y) = ({:8.3f}, {:8.3f}),  angle = {:8.3f} deg".format(k, x, y, angle))

            circle = plt.Circle((x, y), self.target_radius_2, fill=False)
            plt.gca().add_artist(circle)

        p1 = dispenser_2_pitch_diameter_big
        p2 = dispenser_2_pitch_diameter_small
        a1 = self.dispenser_module
        a2 = self.dispenser_module
        offset_2 = sqrt((p1 / 2 + p2 / 2) ** 2 - (p1 / 2 + a1) ** 2) - p2 / 2 - a2
        print("dispenser 2 offset = {}".format(offset_2))

        print(" small circle tangent points: ")
        for k in range(0, self.N):
            x = coords_2[k][0] * outer_radius
            y = coords_2[k][1] * outer_radius

            t1, t2 = compute_tangent_points((0, 0), (x, y), self.target_radius_2)
            angle1_rad = arctan2(t1[1], t1[0])
            angle2_rad = arctan2(t2[1], t2[0])
            angle1_deg = angle1_rad * 360.0 / (2.0 * math.pi)
            angle2_deg = angle2_rad * 360.0 / (2.0 * math.pi)
            self.tube_2_tangents[k] = (t1, t2)
            self.tube_2_tangent_angles[k] = (angle1_deg, angle2_deg)

            print("   k = {},  t1 = ({:8.3f}, {:8.3f}),  angle = {:8.3f} deg\n           t2 = ({:8.3f}, {:8.3f}),  angle "
                  "= {:8.3f} deg".format(k, t1[0], t1[1], angle1_deg, t2[0], t2[1], angle2_deg))

            plt.plot(t1[0], t1[1], 'o')
            plt.plot(t2[0], t2[1], 'o')

            ## compute position of cut for dispenser gear
            # vector pointing from center in direction of tangent point
            v = np.array([math.cos(angle1_rad), math.sin(angle1_rad)])

            cut_center = np.array(t1) + v * (offset_2 + dispenser_2_outer_diameter_small/2.0)
            self.tube_2_cuts[k] = {}
            self.tube_2_cuts[k]['center'] = cut_center
            self.tube_2_cuts[k]['tangent_point'] = t1
            self.tube_2_cuts[k]['angle_deg'] = angle1_deg
            self.tube_2_cuts[k]['length'] = dispenser_2_outer_diameter_small
            self.tube_2_cuts[k]['width'] = 5.0

            plt.plot(cut_center[0], cut_center[1], 'o')

            pass
    pass


    """
    input: file = svg with plate gear centered at (0,0)
    """
    def generate_svg(self, file):

        f = open(file)
        f_lines = f.readlines()
        f.close()


        circle_found = False
        for k in range(len(f_lines)):
            current_line = f_lines[k]

            if 'transform' in current_line:
                # rotate gear such that teeth match the cut lines
                index = current_line.find('"\n')
                f_lines[k] = current_line[0:index] + " rotate(0.9)" + current_line[-2:]

            if 'd="m ' in current_line:
                # remove center whole drawn by gear-dev
                gear_data = current_line
                index = gear_data.find('z') # end of path containing gear outline coordinates

                f_lines[k] = gear_data[0:index+1] + gear_data[-2:]


            if '<circle' in current_line:
                circle_found = True

            if circle_found and 'r=' in current_line:
                # adjust center hole radius
                f_lines[k] = '       r="{}mm"\n'.format(self.target_center_hole_radius)

        # delete last line with </svg> command
        f_lines.remove(f_lines[-1])

        # output plate as svg
        # text = svg_circle(0, 'plate', (0,0), self.target_plate_radius)
        # f_lines = f_lines + text

        output_all = False
        if output_all:
            f_lines = self.output_whole(f_lines)
        else:
            f_lines = self.output_segment(f_lines, 2)

        f_lines.append('</svg>\n')

        # write new svg image
        fw = open('output.svg', 'w')
        fw.writelines(f_lines)
        fw.close()

        pass


    def output_segment(self, f_lines, k):
        # k = which segment?
        k_next = (k + 1) % self.N

        # center hole
        a = self.tube_1_angles[k]
        a = a / 360.0 * 2.0 * np.pi
        vunit = np.array([np.cos(a), np.sin(a)])
        p1 = vunit * self.target_center_hole_radius

        a2 = self.tube_1_angles[k_next]
        a2 = a2 / 360.0 * 2.0 * np.pi
        vunit2 = np.array([np.cos(a2), np.sin(a2)])
        p2 = vunit2 * self.target_center_hole_radius

        f_lines += svg_arc(p1, p2, self.target_center_hole_radius, 0, 1)

        # big circles arcs
        f_lines += svg_half_circle(k, 'big circle', self.tube_1_coords[k], self.target_radius_1, self.tube_1_angles[k])
        f_lines += svg_half_circle(k_next, 'big circle', self.tube_1_coords[k_next], self.target_radius_1,
                               self.tube_1_angles[k_next], orientation_flag=0)

        # small circle
        f_lines += svg_circle(k, 'small circle', self.tube_2_coords[k], self.target_radius_2)

        # gear pos for big circle
        f_lines += svg_gear_marking(self.tube_1_tangents[k_next], self.tube_1_coords[k_next])

        # cutout rectangle for big circles
        f_lines += svg_rectangle(k_next, 'cut', self.tube_1_cuts[k_next])

        # gear pos for small circle
        f_lines += svg_gear_marking(self.tube_2_tangents[k], self.tube_2_coords[k])

        # cutout rectangle for small circles
        f_lines += svg_rectangle(k, 'cut', self.tube_2_cuts[k])

        # first segment border
        f_lines += svg_segment_border_inner(self.tube_1_angles[k], self.target_center_hole_radius,
                                           self.tube_1_coords[k], self.target_radius_1)
        f_lines += svg_segment_border_outer(self.tube_1_angles[k], self.target_plate_radius, self.plate_module,
                                          self.tube_1_coords[k], self.target_radius_1)

        # second segment border
        f_lines += svg_segment_border_inner(self.tube_1_angles[k_next], self.target_center_hole_radius,
                                            self.tube_1_coords[k_next], self.target_radius_1)
        f_lines += svg_segment_border_outer(self.tube_1_angles[k_next], self.target_plate_radius, self.plate_module,
                                 self.tube_1_coords[k_next], self.target_radius_1)


        # find outmost points for segment cut lines
        # in addition we rotate the points by 0.9 degrees because we also rotated the gear path
        # by this amount above
        r_pitch_minus_module = self.target_plate_radius - self.plate_module
        a1 = (self.tube_1_angles[k] - 0.9) / 360.0 * 2.0 * np.pi
        vunit1 = np.array([np.cos(a1), np.sin(a1)])
        outer_point_1 = vunit1 * r_pitch_minus_module

        a2 = (self.tube_1_angles[k_next] - 0.9) / 360.0 * 2.0 * np.pi
        vunit2 = np.array([np.cos(a2), np.sin(a2)])
        outer_point_2 = vunit2 * r_pitch_minus_module

        # truncate gear path
        for j in range(len(f_lines)):
            current_line = f_lines[j]

            if 'd="m ' in current_line:
                # remove center whole drawn by gear-dev
                gear_data = current_line
                index_start = gear_data.find('m') # end of path containing gear outline coordinates
                index_end = gear_data.find('z')
                coordinates_data_raw = gear_data[index_start+1:index_end].split()

                c_running = np.array([float(v) for v in coordinates_data_raw[0].split(',')])
                coordinates = [c_running]
                for c in coordinates_data_raw[1:]:
                    dv = np.array([float(v) for v in c.split(',')])
                    c_running = c_running + dv
                    coordinates.append(c_running)
                    pass

                # find nodes on gear path with minimal distance to segment cuts
                dist_1 = [np.linalg.norm(c - outer_point_1 * svg_scale) for c in coordinates]
                dist_2 = [np.linalg.norm(c - outer_point_2 * svg_scale) for c in coordinates]

                min_dist_index_1 = np.argmin(dist_1)
                min_dist_index_2 = np.argmin(dist_2)

                if min_dist_index_2 > min_dist_index_1:
                    coordinates = coordinates[min_dist_index_1:min_dist_index_2+1]
                else:
                    coordinates = coordinates[min_dist_index_1:] + coordinates[0:min_dist_index_2]

                coordinates_data_raw_new = "".join(['{},{} '.format(c[0], c[1]) for c in coordinates])

                # keep only those nodes from the gear path that are between the segment cuts
                gear_data_new = gear_data[0:index_start] + "M " + coordinates_data_raw_new + gear_data[index_end+1:]
                f_lines[j] = gear_data_new

        return f_lines

    def output_whole(self, f_lines):
        # output big circles as svg
        for k, c in self.tube_1_coords.items():
            text = svg_circle(k, 'big circle', c, self.target_radius_1)
            f_lines = f_lines + text
            pass

        # output small circles as svg
        for k, c in self.tube_2_coords.items():
            text = svg_circle(k, 'small circle', c, self.target_radius_2)
            f_lines = f_lines + text
            pass

        # gear markings for big cirlces and small circles
        for k, c in self.tube_1_tangents.items():
            circle_midpoint = self.tube_1_coords[k]
            v = np.array(c[0]) - np.array(circle_midpoint)
            v = v/np.linalg.norm(v)

            marking_length = 5.0

            p1 = c[0]
            p2 = c[0] + v * marking_length

            text = svg_line(p1, p2)
            f_lines = f_lines + text

        for k, c in self.tube_2_tangents.items():
            circle_midpoint = self.tube_2_coords[k]
            v = np.array(c[0]) - np.array(circle_midpoint)
            v = v/np.linalg.norm(v)

            marking_length = 5.0

            p1 = c[0]
            p2 = c[0] + v * marking_length

            text = svg_line(p1, p2)
            f_lines = f_lines + text
            pass

        # output cuts for big circles
        for k, c in self.tube_1_cuts.items():
            text = svg_rectangle(k, 'cut', c['center'], c['length'], c['width'], c['angle_deg'])
            f_lines = f_lines + text
            pass

        # output cuts for small circles
        for k, c in self.tube_2_cuts.items():
            text = svg_rectangle(k, 'cut', c['center'], c['length'], c['width'], c['angle_deg'])
            f_lines = f_lines + text
            pass

        # lines for manufacturing out of multiple pieces
        for k, a in self.tube_1_angles.items():
            a = a/360.0 * 2.0 * np.pi
            r1 = np.linalg.norm(np.array(self.tube_1_coords[k])) - self.target_radius_1
            vunit = np.array([np.cos(a), np.sin(a)])
            p1 = vunit * self.target_center_hole_radius
            p2 = vunit * r1
            text = svg_line(p1, p2, 0.1)
            f_lines = f_lines + text

            r2 = np.linalg.norm(np.array(self.tube_1_coords[k])) + self.target_radius_1
            p3 = vunit * r2
            r3 = self.target_plate_radius - self.plate_module
            p4 = vunit * r3
            text = svg_line(p3, p4, 0.1)
            f_lines = f_lines + text

            pass

        return f_lines