HP 7475A: Superformula Successes

In the course of running off some Superformula plots, I found what must be my original stash of B-size plotter paper. Although it wasn’t archival paper and has yellowed a bit with age, it’s the smoothest and creamiest paper I’ve touched in quite some time: far nicer than the cheap stuff I picked up while reconditioning the HP 7475A plotter & its assorted pens.

Once in a while, all my errors and omissions cancel out enough to produce interesting results on that historic paper, hereby documented for future reference…

A triangle starburst:

Superformula - triangle burst
Superformula – triangle burst
Superformula - triangle burst - detail
Superformula – triangle burst – detail

A symmetric starburst:

Superformula - starburst
Superformula – starburst
Superformula - starburst - detail
Superformula – starburst – detail

Complex meshed ovals:

Superformula - meshed ovals
Superformula – meshed ovals
Superformula - meshed ovals - details
Superformula – meshed ovals – details

They look better in person, of course. Although inkjet printers produce more accurate results in less time, those old pen plots definitely look better in some sense.

The demo program lets you jam a fixed set of parameters into the plot, so (at least in principle) one could reproduce a plot from the parameters in the lower right corner. Here you go:

The triangle starburst:

Superformula - triangle burst - parameters
Superformula – triangle burst – parameters

The symmetric starburst:

Superformula - starburst - parameters
Superformula – starburst – parameters

The meshed ovals:

Superformula - meshed ovals - parameters
Superformula – meshed ovals – parameters

The current Python / Chiplotle source code as a GitHub gist:

from chiplotle import *
from math import *
from datetime import *
from time import *
from types import *
import random
def superformula_polar(a, b, m, n1, n2, n3, phi):
''' Computes the position of the point on a
superformula curve.
Superformula has first been proposed by Johan Gielis
and is a generalization of superellipse.
see: http://en.wikipedia.org/wiki/Superformula
Tweaked to return polar coordinates
'''
t1 = cos(m * phi / 4.0) / a
t1 = abs(t1)
t1 = pow(t1, n2)
t2 = sin(m * phi / 4.0) / b
t2 = abs(t2)
t2 = pow(t2, n3)
t3 = -1 / float(n1)
r = pow(t1 + t2, t3)
if abs(r) == 0:
return (0, 0)
else:
# return (r * cos(phi), r * sin(phi))
return (r, phi)
def supershape(width, height, m, n1, n2, n3,
point_count=10 * 1000, percentage=1.0, a=1.0, b=1.0, travel=None):
'''Supershape, generated using the superformula first proposed
by Johan Gielis.
- `points_count` is the total number of points to compute.
- `travel` is the length of the outline drawn in radians.
3.1416 * 2 is a complete cycle.
'''
travel = travel or (10 * 2 * pi)
# compute points...
phis = [i * travel / point_count
for i in range(1 + int(point_count * percentage))]
points = [superformula_polar(a, b, m, n1, n2, n3, x) for x in phis]
# scale and transpose...
path = []
for r, a in points:
x = width * r * cos(a)
y = height * r * sin(a)
path.append(Coordinate(x, y))
return Path(path)
# RUN DEMO CODE
if __name__ == '__main__':
override = False
plt = instantiate_plotters()[0]
# plt.write('IN;')
if plt.margins.soft.width < 11000: # A=10365 B=16640
maxplotx = (plt.margins.soft.width / 2) - 100
maxploty = (plt.margins.soft.height / 2) - 150
legendx = maxplotx - 2900
legendy = -(maxploty - 750)
tscale = 0.45
numpens = 4
# prime/10 = number of spikes
m_values = [n / 10.0 for n in [11, 13, 17, 19, 23]]
# ring-ness 0.1 to 2.0, higher is larger
n1_values = [
n / 100.0 for n in range(55, 75, 2) + range(80, 120, 5) + range(120, 200, 10)]
else:
maxplotx = plt.margins.soft.width / 2
maxploty = plt.margins.soft.height / 2
legendx = maxplotx - 3000
legendy = -(maxploty - 900)
tscale = 0.45
numpens = 6
m_values = [n / 10.0 for n in [11, 13, 17, 19, 23, 29, 31,
37, 41, 43, 47, 53, 59]] # prime/10 = number of spikes
# ring-ness 0.1 to 2.0, higher is larger
n1_values = [
n / 100.0 for n in range(15, 75, 2) + range(80, 120, 5) + range(120, 200, 10)]
print " Max: ({},{})".format(maxplotx, maxploty)
# spiky-ness 0.1 to 2.0, higher is spiky-er (mostly)
n2_values = [
n / 100.0 for n in range(10, 60, 2) + range(65, 100, 5) + range(110, 200, 10)]
plt.write(chr(27) + '.H200:') # set hardware handshake block size
plt.set_origin_center()
# scale based on B size characters
plt.write(hpgl.SI(tscale * 0.285, tscale * 0.375))
# slow speed for those abrupt spikes
plt.write(hpgl.VS(10))
while True:
# standard loadout has pen 1 = fine black
plt.write(hpgl.PA([(legendx, legendy)]))
pen = 1
plt.select_pen(pen)
plt.write(hpgl.PA([(legendx, legendy)]))
plt.write(hpgl.LB("Started " + str(datetime.today())))
if override:
m = 4.1
n1_list = [1.15, 0.90, 0.25, 0.59, 0.51, 0.23]
n2_list = [0.70, 0.58, 0.32, 0.28, 0.56, 0.26]
else:
m = random.choice(m_values)
n1_list = random.sample(n1_values, numpens)
n2_list = random.sample(n2_values, numpens)
pen = 1
for n1, n2 in zip(n1_list, n2_list):
n3 = n2
print "{0} - m: {1:.1f}, n1: {2:.2f}, n2=n3: {3:.2f}".format(pen, m, n1, n2)
plt.select_pen(pen)
plt.write(hpgl.PA([(legendx, legendy - 100 * pen)]))
plt.write(
hpgl.LB("Pen {0}: m={1:.1f} n1={2:.2f} n2=n3={3:.2f}".format(pen, m, n1, n2)))
e = supershape(maxplotx, maxploty, m, n1, n2, n3)
plt.write(e)
pen = pen + 1 if (pen % numpens) else 1
pen = 1
plt.select_pen(pen)
plt.write(hpgl.PA([(legendx, legendy - 100 * (numpens + 1))]))
plt.write(hpgl.LB("Ended " + str(datetime.today())))
plt.write(hpgl.PA([(legendx, legendy - 100 * (numpens + 2))]))
plt.write(hpgl.LB("More at https://softsolder.com/?s=7475a&quot;))
plt.select_pen(0)
plt.write(hpgl.PA([(-maxplotx,maxploty)]))
print "Waiting for plotter... ignore timeout errors!"
sleep(40)
while NoneType is type(plt.status):
sleep(5)
print "Load more paper, then ..."
print " ... Press ENTER on the plotter to continue"
plt.clear_digitizer()
plt.digitize_point()
plotstatus = plt.status
while (NoneType is type(plotstatus)) or (0 == int(plotstatus) & 0x04):
plotstatus = plt.status
print "Digitized: " + str(plt.digitized_point)
view raw PlotterShapes.py hosted with ❤ by GitHub

One thought on “HP 7475A: Superformula Successes

  1. Yes, I think they look better in the same sense as vector graphics look better than raster graphics in some situations. This is why I’m breadboarding CRT power supplies, deflection amplifiers, and vector generators.

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