Slightly imperfect Python simulation of the "HOOT-NANNY" (or Magic Designer) drawing toy

hootnanny-cleaned_up.py

#!/usr/bin/env python3
# hootnanny.py - simulate Hoot-Nanny / Magic Designer drawing toy
# Currently hard-coded to output figure "25KM" in HP-GL,
#  a simple but somewhat obsolete plotting language.
# Output figures as close to actual sizes as I could manage.
# All dimensions in inches, unfortunately, but HP-GL is bilingual.
# scruss, 2022-02 - code cleanup - 2022-12
# Licence: CC-BY-SA - share freely, but credit me and make your
#                     improvements freely available for all
# -*- coding: utf-8 -*-

from math import sin, cos, sqrt, radians, degrees, atan2


def arm_length(letter):
    """
    each metal arm has pivot holes marked A - R, at 1/4" spacing
    from 5.75 to 1.5". The perpendicular distance from the pivot holes
    to the pencil is 5/16". This doesn't add much to the overall arm
    length, but it's easy to take into account
    """
    if len(letter) > 1 or letter > "R" or letter < "A":
        # wrong input
        return None
    return sqrt(
        (5.75 - (ord(letter) - ord("A")) / 4.0) ** 2 + (5 / 16) ** 2
    )


def angle_setting(deg):
    """
    the hoot-nanny has two smaller gears: one fixed, the other on a movable
    track with a scale 10 to 70 degrees. The indicator isn't the same as the
    angle between the gears: when 40 degrees is indicated, the gears are
    60 degrees apart. So the actual range is 30 to 90 degrees.

    The smaller gears are 1" in diameter (32 teeth) on a 7" PCD
    Each smaller gear has a pivot point for the arms at 3/8" radius
    The large gear is 6" in diameter (192 teeth)
    """
    return 20 + deg


def distance(p1, p2):
    """
    return Euclidean distance between two points in 2d space
    Note that I'm using a two element list to represent [x, y]
    """
    return sqrt((p1[0] - p2[0]) ** 2 + (p1[1] - p2[1]) ** 2)


def epitrochoid(r1, r2, d, theta):
    """
    If you held the paper on the Hoot-Nanny fixed, the smaller
    gears would describe epitrochoids around the larger
    """
    return [
        (r1 + r2) * cos(theta) - d * cos(((r1 + r2) / r2) * theta),
        (r1 + r2) * sin(theta) - d * sin(((r1 + r2) / r2) * theta),
    ]


def nearest_circle_intersection(p0, p1, r0, r1):
    """
    return the intersection point of two circles nearer the origin
    if equidistant, may not return the point you expect
    """
    d = distance(p0, p1)
    a = (r0**2 - r1**2 + d**2) / (2 * d)
    h = sqrt(r0**2 - a**2)
    x2 = p0[0] + a * (p1[0] - p0[0]) / d
    y2 = p0[1] + a * (p1[1] - p0[1]) / d
    p3 = [x2 + h * (p1[1] - p0[1]) / d, y2 - h * (p1[0] - p0[0]) / d]
    p4 = [x2 - h * (p1[1] - p0[1]) / d, y2 + h * (p1[0] - p0[0]) / d]
    if distance(p3, [0, 0]) <= distance(p4, [0, 0]):
        return p3
    else:
        return p4


# this is where I hard-code the "25KM" setting
arm1 = arm_length("K")
arm2 = arm_length("M")
t = angle_setting(25)

# output the figure in HP-GL: it may be old, but it's very simple
# the path steps around a circle once in full degrees
for i in range(360):
    """
    p is the fixed smaller gear path:
     * large radius   = 3"
     * small radius   = 1/2"
     * cam arm length = 3/8"
    """
    p = epitrochoid(3, 1 / 2, 3 / 8, radians(i))
    # q is the movable smaller gear path
    q = epitrochoid(3, 1 / 2, 3 / 8, radians(i - t))
    # pencil holder is where the two arms intersect
    # coordinates of ph are [x, y] in inches (blecch)
    ph = nearest_circle_intersection(p, q, arm1, arm2)
    # scale to HP-GL units: 40 units / mm == 1016 units / inch
    # thanks, Carl Edvard Johansson!
    x = int(1016 * ph[0])
    y = int(1016 * ph[1])
    if i == 0:
        # initialize and plot first point
        print("IN;")  # HP-GL INitialize plotter
        print("SP1;")  # HP-GL Select Pen 1
        print("PU", x, ",", y, ";")  # HP-GL Pen Up (= move) to x, y
        print("PD;")  # HP-GL Pen Down (= plot)
        # save first point to close figure
        first = [x, y]
    else:
        print("PD", x, ",", y, ";")  # HP-GL Pen Down (= plot) to x, y
# close figure
print("PD", first[0], ",", first[1], ";")
# plot is now finished, so pick up pen and put it away
print("PU;")  # HP-GL Pen Up (= pick up pen, if no coordinates)
print("SP0;")  # HP-GL Select Pen 0 (= put the pen away)

km25.hpgl

IN;
SP1;
PU 29 , -1052 ;
PD;
PD 55 , -1107 ;
PD 87 , -1158 ;
PD 124 , -1203 ;
PD 164 , -1244 ;
PD 209 , -1278 ;
PD 256 , -1305 ;
PD 306 , -1325 ;
PD 358 , -1338 ;
PD 411 , -1342 ;
PD 464 , -1337 ;
PD 516 , -1324 ;
PD 568 , -1302 ;
PD 617 , -1272 ;
PD 664 , -1233 ;
PD 708 , -1186 ;
PD 748 , -1131 ;
PD 783 , -1069 ;
PD 814 , -1001 ;
PD 839 , -927 ;
PD 859 , -848 ;
PD 874 , -765 ;
PD 883 , -680 ;
PD 886 , -593 ;
PD 883 , -506 ;
PD 875 , -420 ;
PD 863 , -335 ;
PD 845 , -254 ;
PD 823 , -177 ;
PD 797 , -105 ;
PD 768 , -38 ;
PD 736 , 20 ;
PD 702 , 72 ;
PD 667 , 116 ;
PD 630 , 153 ;
PD 594 , 181 ;
PD 558 , 200 ;
PD 523 , 212 ;
PD 490 , 215 ;
PD 460 , 211 ;
PD 433 , 200 ;
PD 410 , 181 ;
PD 391 , 156 ;
PD 376 , 126 ;
PD 367 , 91 ;
PD 363 , 51 ;
PD 365 , 9 ;
PD 372 , -36 ;
PD 386 , -83 ;
PD 406 , -131 ;
PD 431 , -178 ;
PD 462 , -226 ;
PD 498 , -271 ;
PD 540 , -315 ;
PD 586 , -355 ;
PD 636 , -392 ;
PD 689 , -424 ;
PD 746 , -451 ;
PD 805 , -474 ;
PD 865 , -490 ;
PD 926 , -501 ;
PD 986 , -505 ;
PD 1046 , -503 ;
PD 1104 , -494 ;
PD 1160 , -479 ;
PD 1211 , -458 ;
PD 1259 , -430 ;
PD 1301 , -397 ;
PD 1338 , -358 ;
PD 1367 , -314 ;
PD 1390 , -266 ;
PD 1405 , -214 ;
PD 1412 , -159 ;
PD 1410 , -101 ;
PD 1400 , -41 ;
PD 1381 , 20 ;
PD 1354 , 82 ;
PD 1318 , 143 ;
PD 1274 , 204 ;
PD 1222 , 263 ;
PD 1164 , 320 ;
PD 1100 , 374 ;
PD 1030 , 424 ;
PD 957 , 470 ;
PD 880 , 512 ;
PD 801 , 548 ;
PD 722 , 579 ;
PD 643 , 605 ;
PD 565 , 624 ;
PD 489 , 638 ;
PD 418 , 646 ;
PD 350 , 648 ;
PD 288 , 644 ;
PD 232 , 636 ;
PD 182 , 623 ;
PD 140 , 605 ;
PD 105 , 584 ;
PD 77 , 559 ;
PD 58 , 533 ;
PD 47 , 504 ;
PD 43 , 475 ;
PD 47 , 445 ;
PD 59 , 417 ;
PD 78 , 389 ;
PD 104 , 363 ;
PD 136 , 340 ;
PD 174 , 320 ;
PD 217 , 304 ;
PD 265 , 293 ;
PD 316 , 286 ;
PD 370 , 284 ;
PD 427 , 287 ;
PD 484 , 296 ;
PD 542 , 310 ;
PD 600 , 329 ;
PD 657 , 354 ;
PD 712 , 385 ;
PD 764 , 420 ;
PD 813 , 460 ;
PD 857 , 504 ;
PD 896 , 551 ;
PD 931 , 602 ;
PD 959 , 654 ;
PD 980 , 709 ;
PD 995 , 764 ;
PD 1002 , 820 ;
PD 1002 , 875 ;
PD 994 , 928 ;
PD 979 , 979 ;
PD 956 , 1027 ;
PD 926 , 1070 ;
PD 888 , 1109 ;
PD 844 , 1143 ;
PD 793 , 1171 ;
PD 735 , 1192 ;
PD 673 , 1206 ;
PD 605 , 1213 ;
PD 534 , 1213 ;
PD 460 , 1205 ;
PD 383 , 1190 ;
PD 304 , 1168 ;
PD 226 , 1140 ;
PD 147 , 1105 ;
PD 71 , 1064 ;
PD -3 , 1018 ;
PD -74 , 968 ;
PD -140 , 915 ;
PD -202 , 859 ;
PD -258 , 801 ;
PD -307 , 743 ;
PD -350 , 685 ;
PD -386 , 627 ;
PD -414 , 572 ;
PD -434 , 519 ;
PD -448 , 469 ;
PD -454 , 424 ;
PD -453 , 383 ;
PD -445 , 347 ;
PD -432 , 317 ;
PD -413 , 293 ;
PD -389 , 275 ;
PD -362 , 264 ;
PD -331 , 260 ;
PD -297 , 262 ;
PD -262 , 272 ;
PD -226 , 288 ;
PD -190 , 311 ;
PD -155 , 341 ;
PD -121 , 376 ;
PD -89 , 417 ;
PD -60 , 463 ;
PD -35 , 513 ;
PD -13 , 567 ;
PD 2 , 625 ;
PD 14 , 685 ;
PD 21 , 746 ;
PD 22 , 809 ;
PD 18 , 872 ;
PD 7 , 934 ;
PD -7 , 994 ;
PD -29 , 1052 ;
PD -55 , 1107 ;
PD -87 , 1158 ;
PD -124 , 1203 ;
PD -164 , 1244 ;
PD -209 , 1278 ;
PD -256 , 1305 ;
PD -306 , 1325 ;
PD -358 , 1338 ;
PD -411 , 1342 ;
PD -464 , 1337 ;
PD -516 , 1324 ;
PD -568 , 1302 ;
PD -617 , 1272 ;
PD -664 , 1233 ;
PD -708 , 1186 ;
PD -748 , 1131 ;
PD -783 , 1069 ;
PD -814 , 1001 ;
PD -839 , 927 ;
PD -859 , 848 ;
PD -874 , 765 ;
PD -883 , 680 ;
PD -886 , 593 ;
PD -883 , 506 ;
PD -875 , 420 ;
PD -863 , 335 ;
PD -845 , 254 ;
PD -823 , 177 ;
PD -797 , 105 ;
PD -768 , 38 ;
PD -736 , -20 ;
PD -702 , -72 ;
PD -667 , -116 ;
PD -630 , -153 ;
PD -594 , -181 ;
PD -558 , -200 ;
PD -523 , -212 ;
PD -490 , -215 ;
PD -460 , -211 ;
PD -433 , -200 ;
PD -410 , -181 ;
PD -391 , -156 ;
PD -376 , -126 ;
PD -367 , -91 ;
PD -363 , -51 ;
PD -365 , -9 ;
PD -372 , 36 ;
PD -386 , 83 ;
PD -406 , 131 ;
PD -431 , 178 ;
PD -462 , 226 ;
PD -498 , 271 ;
PD -540 , 315 ;
PD -586 , 355 ;
PD -636 , 392 ;
PD -689 , 424 ;
PD -746 , 451 ;
PD -805 , 474 ;
PD -865 , 490 ;
PD -926 , 501 ;
PD -986 , 505 ;
PD -1046 , 503 ;
PD -1104 , 494 ;
PD -1160 , 479 ;
PD -1211 , 458 ;
PD -1259 , 430 ;
PD -1301 , 397 ;
PD -1338 , 358 ;
PD -1367 , 314 ;
PD -1390 , 266 ;
PD -1405 , 214 ;
PD -1412 , 159 ;
PD -1410 , 101 ;
PD -1400 , 41 ;
PD -1381 , -20 ;
PD -1354 , -82 ;
PD -1318 , -143 ;
PD -1274 , -204 ;
PD -1222 , -263 ;
PD -1164 , -320 ;
PD -1100 , -374 ;
PD -1030 , -424 ;
PD -957 , -470 ;
PD -880 , -512 ;
PD -801 , -548 ;
PD -722 , -579 ;
PD -643 , -605 ;
PD -565 , -624 ;
PD -489 , -638 ;
PD -418 , -646 ;
PD -350 , -648 ;
PD -288 , -644 ;
PD -232 , -636 ;
PD -182 , -623 ;
PD -140 , -605 ;
PD -105 , -584 ;
PD -77 , -559 ;
PD -58 , -533 ;
PD -47 , -504 ;
PD -43 , -475 ;
PD -47 , -445 ;
PD -59 , -417 ;
PD -78 , -389 ;
PD -104 , -363 ;
PD -136 , -340 ;
PD -174 , -320 ;
PD -217 , -304 ;
PD -265 , -293 ;
PD -316 , -286 ;
PD -370 , -284 ;
PD -427 , -287 ;
PD -484 , -296 ;
PD -542 , -310 ;
PD -600 , -329 ;
PD -657 , -354 ;
PD -712 , -385 ;
PD -764 , -420 ;
PD -813 , -460 ;
PD -857 , -504 ;
PD -896 , -551 ;
PD -931 , -602 ;
PD -959 , -654 ;
PD -980 , -709 ;
PD -995 , -764 ;
PD -1002 , -820 ;
PD -1002 , -875 ;
PD -994 , -928 ;
PD -979 , -979 ;
PD -956 , -1027 ;
PD -926 , -1070 ;
PD -888 , -1109 ;
PD -844 , -1143 ;
PD -793 , -1171 ;
PD -735 , -1192 ;
PD -673 , -1206 ;
PD -605 , -1213 ;
PD -534 , -1213 ;
PD -460 , -1205 ;
PD -383 , -1190 ;
PD -304 , -1168 ;
PD -226 , -1140 ;
PD -147 , -1105 ;
PD -71 , -1064 ;
PD 3 , -1018 ;
PD 74 , -968 ;
PD 140 , -915 ;
PD 202 , -859 ;
PD 258 , -801 ;
PD 307 , -743 ;
PD 350 , -685 ;
PD 386 , -627 ;
PD 414 , -572 ;
PD 434 , -519 ;
PD 448 , -469 ;
PD 454 , -424 ;
PD 453 , -383 ;
PD 445 , -347 ;
PD 432 , -317 ;
PD 413 , -293 ;
PD 389 , -275 ;
PD 362 , -264 ;
PD 331 , -260 ;
PD 297 , -262 ;
PD 262 , -272 ;
PD 226 , -288 ;
PD 190 , -311 ;
PD 155 , -341 ;
PD 121 , -376 ;
PD 89 , -417 ;
PD 60 , -463 ;
PD 35 , -513 ;
PD 13 , -567 ;
PD -2 , -625 ;
PD -14 , -685 ;
PD -21 , -746 ;
PD -22 , -809 ;
PD -18 , -872 ;
PD -7 , -934 ;
PD 7 , -994 ;
PD 29 , -1052 ;
PU;
SP0;

km25.svg

code to go with Slightly imperfect Hoot-Nanny/Magic Designer simulation – We Saw a Chicken …, as requested by Sandra Z. Keith

SVG created by importing km25.hpgl into Inkscape