File:Roche potential.stl

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Roche_potential.stl(file size: 270 KB, MIME type: application/sla)

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View Roche potential.stl  on viewstl.com

Summary

Description Roche potential of two orbiting bodies, rendered half as a filled surface and half as a open mesh by CMG Lee.
Source Own work
Author Cmglee
Other versions
Lagrangian points equipotential.gif
Lagrangian points equipotential.png
Lagrangian points equipotential.jpg

Python source

#!/usr/bin/env python

header      = 'Roche potential of two orbiting bodies, half-filled-half-open by CMG Lee.'
z_scale     = -20
z_min       = -20
offset      = 0.1
i_xy_max    = 32
i_xy_scale  = 0.05

import re, struct, math
def fmt(string): ## string.format(**vars()) using tags {expression!format} by CMG Lee
 def f(tag): i_sep = tag.rfind('!'); return (re.sub('\.0+$', '', str(eval(tag[1:-1])))
  if (i_sep < 0) else ('{:%s}' % tag[i_sep + 1:-1]).format(eval(tag[1:i_sep])))
 return (re.sub(r'(?<!{){[^{}]+}', lambda m:f(m.group()), string)
         .replace('{{', '{').replace('}}', '}'))
def append(obj, string): return obj.append(fmt(string))
def tabbify(cellss, separator='|'):
 cellpadss = [list(rows) + [''] * (len(max(cellss, key=len)) - len(rows)) for rows in cellss]
 fmts = ['%%%ds' % (max([len(str(cell)) for cell in cols])) for cols in zip(*cellpadss)]
 return '\n'.join([separator.join(fmts) % tuple(rows) for rows in cellpadss])
def hex_rgb(colour): ## convert [#]RGB to #RRGGBB and [#]RRGGBB to #RRGGBB
 return '#%s' % (colour if len(colour) > 4 else ''.join([c * 2 for c in colour])).lstrip('#')
def viscam_colour(colour):
 colour_hex      = hex_rgb(colour)
 colour_top5bits = [int(colour_hex[i:i+2], 16) >> 3 for i in range(1,7,2)]
 return (1 << 15) + (colour_top5bits[0] << 10) + (colour_top5bits[1] << 5) + colour_top5bits[2]
def roundm(x, multiple=1):
 if   (isinstance(x, tuple)): return tuple(roundm(list(x), multiple))
 elif (isinstance(x, list )): return [roundm(x_i, multiple) for x_i in x]
 else: return int(math.floor(float(x) / multiple + 0.5)) * multiple
def flatten(lss): return [l for ls in lss for l in ls]
def rotate(facetss, degs): ## around x then y then z axes
 (deg_x,deg_y,deg_z) = degs
 (sin_x,cos_x) = (math.sin(math.radians(deg_x)), math.cos(math.radians(deg_x)))
 (sin_y,cos_y) = (math.sin(math.radians(deg_y)), math.cos(math.radians(deg_y)))
 (sin_z,cos_z) = (math.sin(math.radians(deg_z)), math.cos(math.radians(deg_z)))
 facet_rotatess = []
 for facets in facetss:
  facet_rotates = []
  for i_point in range(4):
   (x, y, z) = [facets[3 * i_point + i_xyz] for i_xyz in range(3)]
   if (x is None or y is None or z is None):
    facet_rotates += [x, y, z]
   else:
    (y, z) = (y * cos_x - z * sin_x,  y * sin_x + z * cos_x) ## rotate about x
    (x, z) = (x * cos_y + z * sin_y, -x * sin_y + z * cos_y) ## rotate about y
    (x, y) = (x * cos_z - y * sin_z,  x * sin_z + y * cos_z) ## rotate about z
    facet_rotates += [round(value, 9) for value in [x, y, z]]
  facet_rotatess.append(facet_rotates)
 return facet_rotatess
def translate(facetss, ds): ## ds = (dx,dy,dz)
 return [facets[:3] + [facets[3 * i_point + i_xyz] + ds[i_xyz]
                       for i_point in range(1,4) for i_xyz in range(3)]
         for facets in facetss]

def potential(x, y, z, q):
 try: return ((x - q / (1.0 + q)) ** 2 + 2 / ((1 + q) * (x ** 2 + y ** 2 + z ** 2) ** 0.5) +
              y ** 2 + 2 * q / ((1 + q) * ((x - 1) ** 2 + y ** 2 + z ** 2) ** 0.5))
 except ZeroDivisionError: return 9

## Compute elevation data
zss = [[potential(i_x * i_xy_scale, i_y * i_xy_scale, 0, 0.1) - 5
       for i_y in range(-i_xy_max, i_xy_max + 1)] for i_x in range(-i_xy_max, i_xy_max + 1)]

## Add facets
facetss = []
for  y in range(len(zss[0]) - 1):
 for x in range(len(zss   ) - 1):
  (x0, y0) = (x - i_xy_max, y - i_xy_max)
  (x1, y1) = (x0 + 1, y0 + 1)
  z00 = zss[x    ][y    ] * z_scale
  z01 = zss[x    ][y + 1] * z_scale
  z11 = zss[x + 1][y + 1] * z_scale
  z10 = zss[x + 1][y    ] * z_scale
  if (y0 >= 0):
   if (z01 >= z_min and z10 >= z_min and z11 >= z_min):
    facetss.append([None,0,0,  x0,y1,z01,  x1,y1,z11,  x1 - offset,y1 - offset,z11])
    facetss.append([None,0,0,  x1,y0,z10,  x1,y1,z11,  x1 - offset,y1 - offset,z11])
  elif (abs(z00 - z11) < abs(z01 - z10)):
   if (z11 >= z_min or z10 >= z_min or z00 >= z_min):
    facetss.append([None,0,0,  x1,y1,z11,  x0,y0,z00,  x1,y0,z10])
   if (z00 >= z_min or z01 >= z_min or z11 >= z_min):
    facetss.append([None,0,0,  x0,y0,z00,  x1,y1,z11,  x0,y1,z01])
  else:
   if (z10 >= z_min or z00 >= z_min or z01 >= z_min):
    facetss.append([None,0,0,  x1,y0,z10,  x0,y1,z01,  x0,y0,z00])
   if (z01 >= z_min or z11 >= z_min or z10 >= z_min):
    facetss.append([None,0,0,  x0,y1,z01,  x1,y0,z10,  x1,y1,z11])
  # sys.stdout.write(chr(int(math.ceil(zss[x][y] * 0.1)) + 32))
 # print('')
# facetss += [facets[0: 5] + [max(0, facets[ 5] - thickness)] +
#             facets[9:11] + [max(0, facets[11] - thickness)] +
#             facets[6: 8] + [max(0, facets[ 8] - thickness)] for facets in facetss]
facetss = rotate(facetss, (0, 0, 180))

## Calculate normals
for facets in facetss:
 if (facets[0] is None or facets[1] is None or facets[2] is None):
  us      = [facets[i_xyz + 9] - facets[i_xyz + 6] for i_xyz in range(3)]
  vs      = [facets[i_xyz + 6] - facets[i_xyz + 3] for i_xyz in range(3)]
  normals = [us[1]*vs[2] - us[2]*vs[1], us[2]*vs[0] - us[0]*vs[2], us[0]*vs[1] - us[1]*vs[0]]
  normal_length = sum([component * component for component in normals]) ** 0.5
  facets[:3] = [-round(component / normal_length, 10) for component in normals]

# print(tabbify([['N%s'  % (xyz   )                   for xyz in list('xyz')] +
#                ['%s%d' % (xyz, n) for n in range(3) for xyz in list('XYZ')] + ['RGB']] + facetss))
## Compile STL
outss = ([[('STL\n\n%-73s\n\n' % (header[:73])).encode('utf-8'), struct.pack('<L',len(facetss))]] +
         [[struct.pack('<f',float(value)) for value in facets[:12]] +
          [struct.pack('<H',0 if (len(facets) <= 12) else
                            viscam_colour(facets[12]))] for facets in facetss])
out   = b''.join([bytes(out) for outs in outss for out in outs])
# out += ('\n\n## Python script to generate STL\n\n%s\n' % (open(__file__).read())).encode('utf-8')
print("# bytes:%d\t# facets:%d\ttitle:\"%-73s\"" % (len(out), len(facetss), header[:73]))
with open(__file__[:__file__.rfind('.')] + '.stl', 'wb') as f_out: f_out.write(out)

Licensing

Wikimedia Foundation
The uploader of this file has agreed to the Wikimedia Foundation 3D patent license: This file and any 3D objects depicted in the file are both my own work. I hereby grant to each user, maker, or distributor of the object depicted in the file a worldwide, royalty-free, fully-paid-up, nonexclusive, irrevocable and perpetual license at no additional cost under any patent or patent application I own now or in the future, to make, have made, use, offer to sell, sell, import, and distribute this file and any 3D objects depicted in the file that would otherwise infringe any claims of any patents I hold now or in the future.

Please note that in the event of any differences in meaning or interpretation between the original English version of this license and a translation, the original English version takes precedence.
I, the copyright holder of this work, hereby publish it under the following licences:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International licence.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the licence, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible licence as the original.
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation Licence, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the licence is included in the section entitled GNU Free Documentation Licence.
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File history

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Date/TimeDimensionsUserComment
current07:56, 14 March 2022 (270 KB)wikimediacommons>CmgleeFlip and rotate to match File:Lagrangian_points_equipotential.png

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