def revolve_x(a):
''' Revolve a part in the XY plane about the X axis. '''
# Y' = +/- sqrt(Y**2 + Z**2)
pos = a.map(Transform('', 'r+qYqZ', '', '', '', ''))
neg = a.map(Transform('', 'nr+qYqZ', '', '', '', ''))
m = max(abs(a.bounds.ymin), abs(a.bounds.ymax))
return Shape((pos | neg).math, a.bounds.xmin, -m, -m, a.bounds.xmax, m, m)
def scale_y(part, y0, sy):
# Y' = y0 + (Y-y0)/sy
return part.map(
Transform(
'X',
'+f%(y0)g/-Yf%(y0)gf%(sy)g' % locals() if y0 else '/Yf%g' % sy,
'X',
'+f%(y0)g*f%(sy)g-Yf%(y0)g' % locals() if y0 else '*Yf%g' % sy))
def scale_x(part, x0, sx):
# X' = x0 + (X-x0)/sx
return part.map(
Transform(
'+f%(x0)g/-Xf%(x0)gf%(sx)g' % locals() if x0 else '/Xf%g' % sx,
'Y',
'+f%(x0)g*f%(sx)g-Xf%(x0)g' % locals() if x0 else '*Xf%g' % sx,
'Y'))
def scale_z(part, z0, sz):
# Z' = z0 + (Y-y0)/sz
# Z = (Z'-z0)*sz + z0
return part.map(
Transform(
'X', 'Y',
'+f%(z0)g/-Zf%(z0)gf%(sz)g' % locals() if z0 else '/Zf%g' % sz,
'X', 'Y',
'+f%(z0)g*f%(sz)g-Zf%(z0)g' % locals() if z0 else '*Zf%g' % sz))
def shear_x_y(part, y0, y1, dx0, dx1):
dx = dx1 - dx0
dy = y1 - y0
# X' = X-dx0-dx*(Y-y0)/dy
# X = X'+dx0+(dx)*(Y-y0)/dy
return part.map(
Transform('--Xf%(dx0)g/*f%(dx)g-Yf%(y0)gf%(dy)g' % locals(), 'Y',
'++Xf%(dx0)g/*f%(dx)g-Yf%(y0)gf%(dy)g' % locals(), 'Y'))
def shear_x_y(part, ymin, ymax, dx0, dx1):
dx = dx1 - dx0
dy = ymax - ymin
# X' = X-dx0-dx*(Y-ymin)/dy
# X = X'+dx0+(dx)*(Y-ymin)/dy
return part.map(
Transform('--Xf%(dx0)g/*f%(dx)g-Yf%(ymin)gf%(dy)g' % locals(), 'Y',
'++Xf%(dx0)g/*f%(dx)g-Yf%(ymin)gf%(dy)g' % locals(), 'Y'))
def reflect_yz(part, y0=0, z0=0):
# Y' = y0 + (Z-z0)
# Z' = z0 + (Y-y0)
# Y = y0 + (Z'-z0)
# Z = z0 + (Y'-y0)
return part.map(
Transform('X', '+f%(y0)g-Zf%(z0)g' % locals(),
'+f%(z0)g-Yf%(y0)g' % locals(), 'X',
'+f%(y0)g-Zf%(z0)g' % locals(),
'+f%(z0)g-Yf%(y0)g' % locals()))
def reflect_xy(part, x0=0, y0=0):
# X' = x0 + (Y-y0)
# Y' = y0 + (X-x0)
# X = x0 + (Y'-y0)
# Y = y0 + (X'-x0)
return part.map(
Transform('+f%(x0)g-Yf%(y0)g' % locals(),
'+f%(y0)g-Xf%(x0)g' % locals(),
'+f%(x0)g-Yf%(y0)g' % locals(),
'+f%(y0)g-Xf%(x0)g' % locals()))
def reflect_xz(part, x0=0, z0=0):
# X' = x0 + (Z-z0)
# Z' = z0 + (X-x0)
# X = x0 + (Z'-z0)
# Z = z0 + (X'-x0)
return part.map(
Transform('+f%(x0)g-Zf%(z0)g' % locals(), 'Y',
'+f%(z0)g-Xf%(x0)g' % locals(),
'+f%(x0)g-Zf%(z0)g' % locals(), 'Y',
'+f%(z0)g-Xf%(x0)g' % locals()))
def scale_xy(part, x0, y0, sxy):
# X' = x0 + (X-x0)/sx
# Y' = y0 + (Y-y0)/sy
# X = (X'-x0)*sx + x0
# Y = (Y'-y0)*sy + y0
return part.map(
Transform(
'+f%(x0)g/-Xf%(x0)gf%(sxy)g' % locals() if x0 else '/Xf%g' % sxy,
'+f%(y0)g/-Yf%(y0)gf%(sxy)g' % locals() if y0 else '/Yf%g' % sxy,
'+f%(x0))g*f%(sxy)g-Xf%(x0)g' % locals() if x0 else '*Xf%g' % sxy,
'+f%(y0)g*f%(sxy)g-Yf%(y0)g' % locals() if y0 else '*Yf%g' % sxy))
def scale_z_r(part, x0, y0, z0, r0, s0, r1, s1):
dr = r1 - r0
# Z' = z0 + (Z-z0)*dr/((s1-s0)*sqrt((X-x0)^2+(Y-y0)^2)-s1*r0+s0*r1)
# Z = z0 + (Z'-z0)*((s1-s0)*sqrt((X-x0)^2+(Y-y0)^2)-s1*r0+s0*r1)/dr
return part.map(
Transform(
'X', 'Y',
'+f%(z0)g/*-Zf%(z0)gf%(dr)g+-*-f%(s1)gf%(s0)gr+q-Xf%(x0)gq-Yf%(y0)g*f%(s1)gf%(r0)g*f%(s0)gf%(r1)g'
% locals(), 'X', 'Y',
'+f%(z0)g/*-Zf%(z0)g+-*-f%(s1)gf%(s0)gr+q-Xf%(x0)gq-Yf%(y0)g*f%(s1)gf%(r0)g*f%(s0)gf%(r1)gf%(dr)g'
% locals()))
def rotate(part, angle, x0=0, y0=0):
p = move(part, -x0, -y0, 0)
angle *= math.pi / 180
ca, sa = math.cos(angle), math.sin(angle)
nca, nsa = math.cos(-angle), math.sin(-angle)
return move(
p.map(
Transform('+*f%(ca)gX*f%(sa)gY' % locals(),
'+*f%(nsa)gX*f%(ca)gY' % locals(),
'+*f%(nca)gX*f%(nsa)gY' % locals(),
'+*f%(sa)gX*f%(nca)gY' % locals())), x0, y0, 0)
def scale_cos_x_y(part, x0, y0, y1, amp, off, t0, t1):
dy = y1 - y0
t0 = math.radians(t0)
t1 = math.radians(t1)
# X' = x0 + (X-x0)/(off+amp*math.cos(theta0+(theta1-theta0)*(Y-y0)/dy))
# X = x0 + (X'-x0)*(off+amp*math.cos(theta0+(theta1-theta0)*(Y-y0)/dy))
return part.map(
Transform(
'/+f%(x0)g-Xf%(x0)g+f%(off)g*f%(amp)gc+f%(t0)g/*-f%(t1)gf%(t0)g-Yf%(y0)gf%(dy)g'
% locals(), 'Y',
'*+f%(x0)g-Xf%(x0)g+f%(off)g*f%(amp)gc+f%(t0)g/*-f%(t1)gf%(t0)g-Yf%(y0)gf%(dy)g'
% locals(), 'Y'))
def scale_xy(part, x0, y0, sx, sy=None):
# X' = x0 + (X-x0)/sx
# Y' = y0 + (Y-y0)/sy
# X = (X'-x0)*sx + x0
# Y = (Y'-y0)*sy + y0
if sy is None:
sy = sx
return part.map(
Transform('+f%(x0)g/-Xf%(x0)gf%(sx)g' % locals(),
'+f%(y0)g/-Yf%(y0)gf%(sy)g' % locals(),
'+f%(x0)g*f%(sx)g-Xf%(x0)g' % locals(),
'+f%(y0)g*f%(sy)g-Yf%(y0)g' % locals()))
def rotate_x(part, angle, y0=0, z0=0):
p = move(part, 0, -y0, -z0)
angle *= math.pi / 180
ca, sa = math.cos(angle), math.sin(angle)
nca, nsa = math.cos(-angle), math.sin(-angle)
return move(
p.map(
Transform('', '+*f%(ca)gY*f%(sa)gZ' % locals(),
'+*f%(nsa)gY*f%(ca)gZ' % locals(), 'X',
'+*f%(nca)gY*f%(nsa)gZ' % locals(),
'+*f%(sa)gY*f%(nca)gZ' % locals())), 0, y0, z0)
def shear_cos_x_y(part, y0, y1, amp, off, t0, t1):
dy = y1 - y0
t0 = math.radians(t0)
t1 = math.radians(t1)
# X' = X-(off+amp*math.cos(theta0+(theta1-theta0)*(Y-y0)/dy))
# X = X'+(off+amp*math.cos(theta0+(theta1-theta0)*(Y-y0)/dy))
return part.map(
Transform(
'-X+f%(off)g*f%(amp)gc+f%(t0)g/*-f%(t1)gf%(t0)g-Yf%(y0)gf%(dy)g' %
locals(), 'Y',
'+X+f%(off)g*f%(amp)gc+f%(t0)g/*-f%(t1)gf%(t0)g-Yf%(y0)gf%(dy)g' %
locals(), 'Y'))
def shear_xy_z(part, zmin, zmax, dx0, dy0, dx1, dy1):
dx = dx1 - dx0
dy = dy1 - dy0
dz = zmax - zmin
# X' = X-dx0-dx*(Z-zmin)/dz
# Y' = Y-dy0-dy*(Z-zmin)/dz
# X = X'+dx0+(dx)*(Y-ymin)/dy
# Y = Y'+dy0+(dy)*(Y-ymin)/dy
return part.map(
Transform('--Xf%(dx0)g/*f%(dx)g-Zf%(zmin)gf%(dz)g' % locals(),
'--Yf%(dy0)g/*f%(dy)g-Zf%(zmin)gf%(dz)g' % locals(),
'++Xf%(dx0)g/*f%(dx)g-Zf%(zmin)gf%(dz)g' % locals(),
'++Yf%(dy0)g/*f%(dy)g-Zf%(zmin)gf%(dz)g' % locals()))
def repel(part, x, y, z, r):
# Shift the part so that it is centered
part = move(part, -x, -y, -z)
# exponential fallout value
# x*(1 - exp(-sqrt(x**2 + y**2 + z**2) / r))
d = '-f1xn/r++qXqYqZf%g' % r
p = part.map(Transform('*X' + d, '*Y' + d, '*Z' + d, '', '', ''))
b = r / math.e
return move(
Shape(p.math, part.bounds.xmin - b, part.bounds.ymin - b,
part.bounds.zmin - b, part.bounds.xmax + b, part.bounds.ymax + b,
part.bounds.zmax + b), x, y, z)
def scale_xyz(part, x0, y0, z0, sx, sy, sz):
# X' = x0 + (X-x0)/sx
# Y' = y0 + (Y-y0)/sy
# Z' = z0 + (Z-z0)/sz
# X = x0 + (X'-x0)*sx
# Y = y0 + (Y'-y0)*sy
# Z = z0 + (Z'-z0)*sz
return part.map(
Transform('+f%(x0)g/-Xf%(x0)gf%(sx)g' % locals(),
'+f%(y0)g/-Yf%(y0)gf%(sy)g' % locals(),
'+f%(z0)g/-Zf%(z0)gf%(sz)g' % locals(),
'+f%(x0)g*-Xf%(x0)gf%(sx)g' % locals(),
'+f%(y0)g*-Yf%(y0)gf%(sy)g' % locals(),
'+f%(z0)g*-Zf%(z0)gf%(sz)g' % locals()))
def taper_x_y(part, x0, y0, y1, s0, s1):
dy = y1 - y0
ds = s1 - s0
s0y1 = s0 * y1
s1y0 = s1 * y0
# X'=x0+(X-x0)*(y1-y0)/(Y*(s1-s0)+s0*y1-s1*y0))
# X=(X'-x0)*(Y*(s1-s0)+s0*y1-s1*y0)/(y1-y0)+x0
return part.map(
Transform(
'+f%(x0)g/*-Xf%(x0)gf%(dy)g-+*Yf%(ds)gf%(s0y1)gf%(s1y0)g' %
locals(), 'Y',
'+f%(x0)g*-Xf%(x0)g/-+*Yf%(ds)gf%(s0y1)gf%(s1y0)gf%(dy)g' %
locals(), 'Y'))
def shear_cos_xy_z(part, z0, z1, ampx, offx, ampy, offy, t0, t1):
dz = z1 - z0
t0 = math.radians(t0)
t1 = math.radians(t1)
# X' = X-(offx+ampx*math.cos(theta0+(theta1-theta0)*(Z-z0)/dz))
# X = X'+(offx+ampx*math.cos(theta0+(theta1-theta0)*(Z-z0)/dz))
# Y' = Y-(offy+ampy*math.cos(theta0+(theta1-theta0)*(Z-z0)/dz))
# Y = Y'+(offy+ampy*math.cos(theta0+(theta1-theta0)*(Z-z0)/dz))
return part.map(
Transform(
'-X+f%(offx)g*f%(ampx)gc+f%(t0)g/*-f%(t1)gf%(t0)g-Zf%(z0)gf%(dz)g'
% locals(),
'-Y+f%(offy)g*f%(ampy)gc+f%(t0)g/*-f%(t1)gf%(t0)g-Zf%(z0)gf%(dz)g'
% locals(), 'Z',
'+X+f%(offx)g*f%(ampx)gc+f%(t0)g/*-f%(t1)gf%(t0)g-Zf%(z0)gf%(dz)g'
% locals(),
'+Y+f%(offy)g*f%(ampy)gc+f%(t0)g/*-f%(t1)gf%(t0)g-Zf%(z0)gf%(dz)g'
% locals(), 'Z'))
def scale_cos_xy_z(part, x0, y0, z0, z1, amp, off, t0, t1):
dz = z1 - z0
t0 = math.radians(t0)
t1 = math.radians(t1)
# X' = x0 + (X-x0)/(off+amp*math.cos(theta0+(theta1-theta0)*(Z-z0)/dz))
# X = x0 + (X'-x0)*(off+amp*math.cos(theta0+(theta1-theta0)*(Z-z0)/dz))
# Y' = y0 + (Y-y0)/(off+amp*math.cos(theta0+(theta1-theta0)*(Z-z0)/dz))
# Y = y0 + (Y'-y0)*(off+amp*math.cos(theta0+(theta1-theta0)*(Z-z0)/dz))
return part.map(
Transform(
'/+f%(x0)g-Xf%(x0)g+f%(off)g*f%(amp)gc+f%(t0)g/*-f%(t1)gf%(t0)g-Zf%(z0)gf%(dz)g'
% locals(),
'/+f%(y0)g-Yf%(y0)g+f%(off)g*f%(amp)gc+f%(t0)g/*-f%(t1)gf%(t0)g-Zf%(z0)gf%(dz)g'
% locals(), 'Z',
'*+f%(x0)g-Xf%(x0)g+f%(off)g*f%(amp)gc+f%(t0)g/*-f%(t1)gf%(t0)g-Zf%(z0)gf%(dz)g'
% locals(),
'*+f%(y0)g-Yf%(y0)g+f%(off)g*f%(amp)gc+f%(t0)g/*-f%(t1)gf%(t0)g-Zf%(z0)gf%(dz)g'
% locals(), 'Z'))
def taper_xy_z(part, x0, y0, z0, z1, s0, s1):
dz = z1 - z0
# X' = x0 +(X-x0)*dz/(s1*(Z-z0) + s0*(z1-Z))
# Y' = y0 +(Y-y0)*dz/(s1*(Z-z0) + s0*(z1-Z))
# X = (X' - x0)*(s1*(Z-z0) + s0*(z1-Z))/dz + x0
# Y = (Y' - y0)*(s1*(Z-z0) + s0*(z1-Z))/dz + y0
return part.map(
Transform(
'+f%(x0)g/*-Xf%(x0)gf%(dz)g+*f%(s1)g-Zf%(z0)g*f%(s0)g-f%(z1)gZ' %
locals(),
'+f%(y0)g/*-Yf%(y0)gf%(dz)g+*f%(s1)g-Zf%(z0)g*f%(s0)g-f%(z1)gZ' %
locals(), '',
'+/*-Xf%(x0)g+*f%(s1)g-Zf%(z0)g*f%(s0)g-f%(z1)gZf%(dz)gf%(x0)g' %
locals(),
'+/*-Yf%(y0)g+*f%(s1)g-Zf%(z0)g*f%(s0)g-f%(z1)gZf%(dz)gf%(y0)g' %
locals(), ''))
def twist_xy_z(part, x, y, z0, z1, t0, t1):
# First, we'll move and scale so that the relevant part of the model
# is at x=y=0 and scaled so that z is between 0 and 1.
p1 = scale_z(move(part, -x, -y, -z0), 0, 1.0 / (z1 - z0))
t0 = math.pi * t0 / 180.0
t1 = math.pi * t1 / 180.0
# X' = X*cos(t1*z + t0*(1-z)) + Y*sin(t1*z + t0*(1-z))
# Y' = -X*sin(t1*z + t0*(1-z)) + Y*cos(t1*z + t0*(1-z))
# X = X*cos(t1*z + t0*(1-z)) - Y*sin(t1*z + t0*(1-z))
# Y = X*sin(t1*z + t0*(1-z)) + Y*cos(t1*z + t0*(1-z))
p2 = p1.map(
Transform(
'+*Xc+*f%(t1)gZ*f%(t0)g-f1Z*Ys+*f%(t1)gZ*f%(t0)g-f1Z' % locals(),
'+n*Xs+*f%(t1)gZ*f%(t0)g-f1Z*Yc+*f%(t1)gZ*f%(t0)g-f1Z' % locals(),
'-*Xc+*f%(t1)gZ*f%(t0)g-f1Z*Ys+*f%(t1)gZ*f%(t0)g-f1Z' % locals(),
'+*Xs+*f%(t1)gZ*f%(t0)g-f1Z*Yc+*f%(t1)gZ*f%(t0)g-f1Z' % locals()))
return move(scale_z(p2, 0, z1 - z0), x, y, z0)
def cylinder_y_wrap(part, radius):
tx = "(X / %(radius)f)" % locals()
tz = "(Z / %(radius)f)" % locals()
dist = "(sqrt( (%(tx)s)**2 + (%(tz)s)**2 ))" % locals()
angle = "(atan2( %(tx)s, %(tz)s ))" % locals()
Xfn = "=%(angle)s * %(radius)f;" % locals()
Yfn = "_"
Zfn = "=(%(dist)s - 1) * %(radius)f;" % locals()
angle = "(X / %(radius)f)" % locals()
r = "(%(radius)f + Z)" % locals()
sina = "(sin(%(angle)s))" % locals()
cosa = "(cos(%(angle)s))" % locals()
Xfn_inv = "=%(r)s * %(sina)s;" % locals()
Yfn_inv = ""
Zfn_inv = "=%(r)s * %(cosa)s;" % locals()
return part.map(Transform(Xfn, Yfn, Zfn, Xfn_inv, Yfn_inv, Zfn_inv))
def move(part, dx, dy, dz=0):
return part.map(
Transform('-Xf%g' % dx, '-Yf%g' % dy, '-Zf%g' % dz, '+Xf%g' % dx,
'+Yf%g' % dy, '+Zf%g' % dz))
def reflect_x(part, x0=0):
# X' = 2*x0-X
# X = 2*x0-X'
return part.map(Transform('-*f2f%gX' % x0, '', '-*f2f%gX' % x0, ''))
def shear_x_z(part, z0, z1, dx0, dx1):
# X' = X-dx0-(dx1-dx0)*(Z-z0)/(z1-z0)
# X = X'+dx0+(dx1-dx0)*(Z-z0)/(z1-z0)
return part.map(
Transform('--Xf%(dx0)g/*f%(dx)g-Zf%(z0)gf%(dz)g' % locals(), '', '',
'++Xf%(dx0))g/*f%(dx)g-Zf%(z0)gf%(dz)g' % locals(), '', ''))
def reflect_y(part, y0=0):
# Y' = 2*y0-Y
return part.map(Transform('', '-*f2f%gY' % y0, '', '-*f2f%gY' % y0))
def reflect_z(part, z0=0):
# Z' = 2*z0-Z
return part.map(Transform('', '', '-*f2f%gZ' % z0, '', '',
'-*f2f%gZ' % z0))