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shapespaths.py
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shapespaths.py
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from __future__ import division
#from vpython import vec, mag, norm
from math import sqrt, sin, cos, tan, asin, acos, atan, floor, pi
import platform
try:
if platform.python_implementation() == 'PyPy':
from .vector import vector, mag, norm # use pure python vector for PyPy
else:
from .cyvector import vector, mag, norm
v = vector(0.,0.,0.)
except:
from .vector import vector, mag, norm
vec = vector
# The path and shape objects were designed and implemented by Kadir Haldenbilen
# for Classic VPython 5. Modified by Bruce Sherwood for GlowScript/Jupyter VPython,
# eliminating dependency on Polygon library.
# GlowScript API:
# shape = [2Ds], hole = [2Ds] or shape = [ [shape 2Ds], [hole 2Ds] ]
# Another option for hole is [ [hole1], [hole2], ..... ]
# If hole represents multiple holes, len([hole[0]]) > 1
##################################
## ----------- shapes ------------
##################################
npdefault = 64 # default number of points for a circle. ellipse, and arc
def roundc(cps, roundness=0.1, invert=False, nseg=16):
cp = []
for i in range(len(cps)): cp.append(vec(cps[i][0], cps[i][1], 0)) # convert [x,y] => vec(x,y,0), so can use vector functions
# If points are ordered counterclockwise, vord will be > 0
vord = 0
cp.pop() # remove the final point, which is equal to the initial point
lcp = len(cp)
for i in range(lcp):
i1 = (i + 1) % lcp
i2 = (i + 2) % lcp
v1 = cp[i1] - cp[i]
v2 = cp[i2] - cp[i1]
dv = v1.cross(v2).z
vord += dv
if vord < 0: cp.reverse() # force points to be in counterclockwise order
# Determine shortest side
L = 1e200
for i in range(lcp):
p1 = cp[i]
p2 = cp[(i + 1) % lcp]
lm = mag(p2 - p1)
if (lm < L):
L = lm
r = L * roundness # radius of rounded curve connecting adjacent sides
ncp = [[0,0]] # starting point will be modified later
for i in range(lcp):
v1 = cp[(i+1) % lcp] - cp[i % lcp] # first side
v2 = cp[(i+2) % lcp] - cp[(i+1) % lcp] # next side
theta = v1.diff_angle(v2) # angle of change of direction from first side to next side
d = r*tan(theta/2) # how much to shorten the end of a side and the start of the next
p1 = cp[i] + v1 - d*norm(v1) # end of first side, start of bend
p2 = cp[(i+1) % lcp] + d*norm(v2) # start of next side, end of bend
ncp.append([p1.x, p1.y])
N = norm(v1).cross(norm(v2))
center = p1 + r*norm(N.cross(v1)) # center of circular arc
v = p1 - center
dtheta = theta/(nseg+1)
if N.z < 0: dtheta = -dtheta
if invert:
c = 0.5*(p1 + p2) # midpoint along line connecting p1 and p2
center = c + (c-center) # move center to other side of corner
v = p1 - center
dtheta = -dtheta
for j in range(nseg):
v1 = center + v.rotate(j*dtheta)
ncp.append([v1.x, v1.y])
ncp.append([p2.x, p2.y])
v1 = cp[1] - cp[0]
v1 = cp[0] + d*norm(v1) # start of first side, at end of preceding bend
ncp[0] = [v1.x, v1.y]
return ncp
def rotatecp(cp, pos=[0,0], rotate=0):
sinr = sin(rotate)
cosr = cos(rotate)
xRel = pos[0]
yRel = pos[1]
cpr = []
for i in range(len(cp)):
p = cp[i]
x = p[0]
y = p[1]
newx = x * cosr - y * sinr - xRel * cosr + yRel * sinr + xRel
newy = x * sinr + y * cosr - xRel * sinr - yRel * cosr + yRel
cpr.append([ newx, newy ])
return cpr
def scalecp(cp, xscale=1, yscale=1):
cpr = []
for i in range(len(cp)):
p = cp[i]
cpr.append([ xscale * p[0], yscale * p[1] ])
return cpr
def addpos(cp, pos=[0,0]):
for i in range(len(cp)):
p = cp[i]
p[0] += pos[0]
p[1] += pos[1]
return cp
##The following script has been developed and based on the
##Blender 235 script "Blender Mechanical Gears"
##developed in 2004 by Stefano <S68> Selleri,
##released under the Blender Artistic License (BAL).
##See www.blender.org.
####################################################################
#CREATES THE BASE INVOLUTE PROFILE
####################################################################
def ToothOutline(n=30, res=1, phi=20, radius=50, addendum=0.4, dedendum=0.5, fradius=0.1, bevel=0.05):
TOOTHGEO = {
'PitchRadius' : radius,
'TeethN' : n,
'PressureAng' : phi,
'Addendum' : addendum,
'Dedendum' : dedendum,
'Fillet' : fradius,
'Bevel' : bevel,
'Resolution' : res,
}
####################################################################
#Basic Math computations: Radii
#
R = {
'Bottom' : TOOTHGEO['PitchRadius'] - TOOTHGEO['Dedendum'] - TOOTHGEO['Fillet'],
'Ded' : TOOTHGEO['PitchRadius'] - TOOTHGEO['Dedendum'],
'Base' : TOOTHGEO['PitchRadius'] * cos(TOOTHGEO['PressureAng']*pi/180.0),
'Bevel' : TOOTHGEO['PitchRadius'] + TOOTHGEO['Addendum'] - TOOTHGEO['Bevel'],
'Add' : TOOTHGEO['PitchRadius'] + TOOTHGEO['Addendum']
}
####################################################################
#Basic Math computations: Angles
#
DiametralPitch = TOOTHGEO['TeethN']/(2*TOOTHGEO['PitchRadius'])
ToothThickness = 1.5708/DiametralPitch
CircularPitch = pi / DiametralPitch
U1 = sqrt((1-cos(TOOTHGEO['PressureAng']*pi/180.0))/
cos(TOOTHGEO['PressureAng']*pi/180.0))
U2 = sqrt(R['Bevel']*R['Bevel']/(R['Ded']*R['Ded'])-1)
ThetaA1 = atan((sin(U1)-U1*cos(U1))/(cos(U1)+U1*sin(U1)))
ThetaA2 = atan((sin(U2)-U2*cos(U2))/(cos(U2)+U2*sin(U2)))
ThetaA3 = ThetaA1 + ToothThickness/(TOOTHGEO['PitchRadius']*2.0)
A = {
'Theta0' : CircularPitch/(TOOTHGEO['PitchRadius']*2.0),
'Theta1' : ThetaA3 + TOOTHGEO['Fillet']/R['Ded'],
'Theta2' : ThetaA3,
'Theta3' : ThetaA3 - ThetaA2,
'Theta4' : ThetaA3 - ThetaA2 - TOOTHGEO['Bevel']/R['Add']
}
####################################################################
# Profiling
#
N = TOOTHGEO['Resolution']
points = []
normals = []
# Top half bottom of tooth
for i in range(2*N):
th = (A['Theta1'] - A['Theta0'])*i/(2*N-1) + A['Theta0']
points.append ([R['Bottom']*cos(th),
R['Bottom']*sin(th)])
normals.append([-cos(th),
-sin(th)])
# Bottom Fillet
xc = R['Ded']*cos(A['Theta1'])
yc = R['Ded']*sin(A['Theta1'])
Aw = pi/2.0 + A['Theta2'] - A['Theta1']
for i in range(N):
th = (Aw)*(i+1)/(N) + pi + A['Theta1']
points.append ([xc + TOOTHGEO['Fillet']*cos(th),
yc + TOOTHGEO['Fillet']*sin(th)])
normals.append([cos(th),
sin(th)])
# Straight part
for i in range(N):
r = (R['Base']-R['Ded'])*(i+1)/(N) + R['Ded']
points.append ([r*cos(A['Theta2']),
r*sin(A['Theta2'])])
normals.append([cos(A['Theta2']-pi/2.0),
sin(A['Theta2']-pi/2.0)])
# Tooth Involute
for i in range(3*N):
r = (R['Bevel'] - R['Base'])*(i+1)/(3*N) + R['Base']
u = sqrt(r*r/(R['Base']*R['Base'])-1)
xp = R['Base']*(cos(u)+u*sin(u))
yp = - R['Base']*(sin(u)-u*cos(u))
points.append ([xp*cos(A['Theta2'])-yp*sin(A['Theta2']),
+xp*sin(A['Theta2'])+yp*cos(A['Theta2'])])
normals.append([-sin(u),
-cos(u)])
# Tooth Bevel
auxth = -u
auxth = auxth + ThetaA3 + pi/2.0
m = tan(auxth)
P0 = points[len(points)-1]
rA = TOOTHGEO['Bevel']/(1-cos(auxth-A['Theta4']))
xc = P0[0] - rA*cos(auxth)
yc = P0[1] - rA*sin(auxth)
for i in range(N):
th = (A['Theta4'] - auxth)*(i+1)/(N) + auxth
points.append ([xc + rA*cos(th),
yc +rA*sin(th)])
normals.append([-cos(th),
-sin(th)])
# Tooth Top
P0 = points[len(points)-1]
A['Theta4'] = atan (P0[1]/P0[0])
Ra = sqrt(P0[0]*P0[0]+P0[1]*P0[1])
for i in range(N):
th = (-A['Theta4'])*(i+1)/(N) + A['Theta4']
points.append ([Ra*cos(th),
Ra*sin(th)])
normals.append([-cos(th),
-sin(th)])
# Mirrors this!
N = len(points)
for i in range(N-1):
P = points[N-2-i]
points.append([P[0],-P[1]])
V = normals[N-2-i]
normals.append([V[0],-V[1]])
return points # ,normals
####################################################################
#CREATES THE BASE RACK PROFILE
####################################################################
def RackOutline(n=30, res=1, phi=20, radius=5, addendum=0.4, dedendum=0.5, fradius=0.1, bevel=0.05):
TOOTHGEO = {
'PitchRadius' : radius,
'TeethN' : n,
'PressureAng' : phi,
'Addendum' : addendum,
'Dedendum' : dedendum,
'Fillet' : fradius,
'Bevel' : bevel,
'Resolution' : res,
}
####################################################################
#Basic Math computations: QUotes
#
X = {
'Bottom' : - TOOTHGEO['Dedendum'] - TOOTHGEO['Fillet'],
'Ded' : - TOOTHGEO['Dedendum'],
'Bevel' : TOOTHGEO['Addendum'] - TOOTHGEO['Bevel'],
'Add' : TOOTHGEO['Addendum']
}
####################################################################
#Basic Math computations: Angles
#
DiametralPitch = TOOTHGEO['TeethN']/(2*TOOTHGEO['PitchRadius'])
ToothThickness = 1.5708/DiametralPitch
CircularPitch = pi / DiametralPitch
Pa = TOOTHGEO['PressureAng']*pi/180.0
yA1 = ToothThickness/2.0
yA2 = (-X['Ded']+TOOTHGEO['Fillet']*sin(Pa))*tan(Pa)
yA3 = TOOTHGEO['Fillet']*cos(Pa)
A = {
'y0' : CircularPitch/2.0,
'y1' : yA1+yA2+yA3,
'y2' : yA1+yA2,
'y3' : yA1 -(X['Add']-TOOTHGEO['Bevel'])*tan(Pa),
'y4' : yA1 -(X['Add']-TOOTHGEO['Bevel'])*tan(Pa)
- cos(Pa)/(1-sin(Pa))*TOOTHGEO['Bevel']
}
####################################################################
# Profiling
#
N = TOOTHGEO['Resolution']
points = []
normals = []
ist = 0
if fradius: ist = 1
# Top half bottom of tooth
for i in range(ist, 2*N):
y = (A['y1'] - A['y0'])*i/(2*N-1) + A['y0']
points.append ([X['Bottom'],
y])
normals.append([-1.0,
-0.0])
# Bottom Fillet
xc = X['Ded']
yc = A['y1']
Aw = pi/2.0 - Pa
for i in range(N):
th = (Aw)*(i+1)/(N) + pi
points.append ([xc + TOOTHGEO['Fillet']*cos(th),
yc + TOOTHGEO['Fillet']*sin(th)])
normals.append([cos(th),
sin(th)])
# Straight part
Xded = X['Ded'] - TOOTHGEO['Fillet']*sin(Pa)
for i in range(4*N):
x = (X['Bevel']-Xded)*(i+1)/(4*N) + Xded
points.append ([x,
yA1-tan(Pa)*x])
normals.append([-sin(Pa),
-cos(Pa)])
# Tooth Bevel
rA = TOOTHGEO['Bevel']/(1-sin(Pa))
xc = X['Add'] - rA
yc = A['y4']
for i in range(N):
th = (-pi/2.0+Pa)*(i+1)/(N) + pi/2.0-Pa
points.append ([xc + rA*cos(th),
yc + rA*sin(th)])
normals.append([-cos(th),
-sin(th)])
# Tooth Top
for i in range(N):
y = -A['y4']*(i+1)/(N) + A['y4']
points.append ([X['Add'],
y])
normals.append([-1.0,
0.0])
# Mirrors this!
N = len(points)
for i in range(N-1):
P = points[N-2-i]
points.append([P[0],-P[1]])
V = normals[N-2-i]
normals.append([V[0],-V[1]])
return points # ,normals
####################################################################
## CREATES THE BASE CROWN INVOLUTE -- NOT CURRENTLY IMPLEMENTED IN GLOWSCRIPT -- GAVE ERRORS
####################################################################
# def CrownOutline(n=30, res=1, phi=20., radius=5.0, addendum=0.4, dedendum=0.5, fradius=0.1, bevel=0.05):
# TOOTHGEO = {
# 'PitchRadius' : radius,
# 'TeethN' : n,
# 'PressureAng' : phi,
# 'Addendum' : addendum,
# 'Dedendum' : dedendum,
# 'Fillet' : fradius,
# 'Bevel' : bevel,
# 'Resolution' : res,
# }
###################################################################
## Basic Math computations: Radii
# R = {
# 'Bottom' : TOOTHGEO['PitchRadius'] * cos(TOOTHGEO['PressureAng']*pi/180.0) ,
# 'Base' : TOOTHGEO['PitchRadius'] * cos(TOOTHGEO['PressureAng']*pi/180.0) + TOOTHGEO['Fillet'],
# 'Ded' : TOOTHGEO['PitchRadius'] + TOOTHGEO['Dedendum']
# }
###################################################################
## Basic Math computations: Angles
# DiametralPitch = TOOTHGEO['TeethN']/(2*TOOTHGEO['PitchRadius'])
# ToothThickness = 1.5708/DiametralPitch
# CircularPitch = pi / DiametralPitch
# U1 = sqrt((1-cos(TOOTHGEO['PressureAng']*pi/180.0))/
# cos(TOOTHGEO['PressureAng']*pi/180.0))
# U2 = sqrt(R['Ded']*R['Ded']/(R['Base']*R['Base'])-1)
# ThetaA1 = atan((sin(U1)-U1*cos(U1))/(cos(U1)+U1*sin(U1)))
# ThetaA2 = atan((sin(U2)-U2*cos(U2))/(cos(U2)+U2*sin(U2)))
# ThetaA3 = ThetaA1 + ToothThickness/(TOOTHGEO['PitchRadius']*2.0)
# A = {
# 'Theta0' : CircularPitch/(TOOTHGEO['PitchRadius']*2.0),
# 'Theta1' : (ThetaA3 + TOOTHGEO['Fillet']/R['Base']),
# 'Theta2' : ThetaA3,
# 'Theta3' : ThetaA3 - ThetaA2,
# 'Theta4' : ThetaA3 - ThetaA2 - TOOTHGEO['Bevel']/R['Ded']
# }
# M = A['Theta0']
# A['Theta0'] = 0
# A['Theta1'] = A['Theta1']-M
# A['Theta2'] = A['Theta2']-M
# A['Theta3'] = A['Theta3']-M
# A['Theta4'] = A['Theta4']-M
###################################################################
## Profiling
# N = TOOTHGEO['Resolution']
# apoints = []
# anormals = []
## Top half top of tooth
# for i in range(2*N):
# th = (A['Theta1'] - A['Theta0'])*i/(2*N-1) + A['Theta0']
# apoints.append ([R['Bottom']*cos(th),
# R['Bottom']*sin(th)])
# anormals.append([cos(th),
# sin(th)])
## Bottom Bevel
# xc = R['Base']*cos(A['Theta1'])
# yc = R['Base']*sin(A['Theta1'])
# Aw = pi/2.0 + A['Theta2'] - A['Theta1']
# for i in range(N):
# th = (Aw)*(i+1)/(N) + pi + A['Theta1']
# apoints.append ([xc + TOOTHGEO['Fillet']*cos(th),
# yc + TOOTHGEO['Fillet']*sin(th)])
# anormals.append([-cos(th),
# -sin(th)])
## Tooth Involute
# for i in range(4*N):
# r = (R['Ded'] - R['Base'])*(i+1)/(4*N) + R['Base']
# u = sqrt(r*r/(R['Base']*R['Base'])-1)
# xp = R['Base']*(cos(u)+u*sin(u))
# yp = - R['Base']*(sin(u)-u*cos(u))
# apoints.append ([xp*cos(A['Theta2'])-yp*sin(A['Theta2']),
# +xp*sin(A['Theta2'])+yp*cos(A['Theta2'])])
# anormals.append([sin(u),
# cos(u)])
## Tooth Bevel
# auxth = -u
# auxth = auxth + ThetaA3 + pi/2.0
# m = tan(auxth)
# P0 = apoints[len(apoints)-1]
# rA = TOOTHGEO['Bevel']/(1-cos(auxth-A['Theta4']))
# xc = P0[0] - rA*cos(auxth)
# yc = P0[1] - rA*sin(auxth)
# for i in range(N):
# th = (A['Theta4'] - auxth)*(i+1)/(N) + auxth
# apoints.append ([xc + rA*cos(th),
# yc +rA*sin(th)])
# anormals.append([cos(th),
# sin(th)])
## Tooth Top
# P0 = apoints[len(apoints)-1]
# A['Theta4'] = atan (P0[1]/P0[0])
# Ra = sqrt(P0[0]*P0[0]+P0[1]*P0[1])
# for i in range(N):
# th = (-M - A['Theta4'])*(i+1)/(N) + A['Theta4']
# apoints.append ([Ra*cos(th),
# Ra*sin(th)])
# anormals.append([cos(th),
# sin(th)])
# points = []
# normals = []
# N = len(apoints)
# for i in range(N):
# points.append(apoints[N-1-i])
# normals.append(anormals[N-1-i])
## Mirrors this!
# N = len(points)
# for i in range(N-1):
# P = points[N-2-i]
# points.append([P[0],-P[1]])
# V = normals[N-2-i]
# normals.append([V[0],-V[1]])
# return points #,normals process nromals later
class shape_object(object):
def rframe(self, pos=[0,0], width=1, height=None, rotate=0, thickness=None,
roundness=0, invert=False, scale=1, xscale=1, yscale=1):
if height is None:
height = width
if thickness is None: thickness = min(height, width) * .2
else: thickness = min(height, width) * thickness * 2
outer = self.rectangle(pos=pos, width=width, height=height)
inner = self.rectangle(pos=pos, width=width - thickness, height=height - thickness)
if rotate != 0:
outer = rotatecp(outer, pos=pos, rotate=rotate)
inner = rotatecp(inner, pos=pos, rotate=rotate)
if xscale != 1 or yscale != 1:
outer = scalecp(outer, xscale=xscale, yscale=yscale)
inner = scalecp(inner, xscale=xscale, yscale=yscale)
if roundness > 0:
outer = roundc(outer, roundness=roundness, invert=invert)
inner = roundc(inner, roundness=roundness, invert=invert)
return [ outer, inner ]
def rectangle(self, pos=[0,0], width=1, height=None, rotate=0, thickness=0,
roundness=0, invert=False, scale=1, xscale=1, yscale=1):
if height is None:
height = width
if thickness == 0:
cp = []
w2 = width / 2
h2 = height / 2
cp = [ [ w2, -h2 ], [ w2, h2 ], [ -w2, h2 ], [ -w2, -h2 ], [ w2, -h2 ] ]
cp = addpos(cp, pos=pos)
if rotate != 0: cp = rotatecp(cp, pos, rotate)
if scale != 1: xscale = yscale = scale
if xscale != 1 or yscale != 1: cp = scalecp(cp, xscale, yscale)
if roundness > 0: cp = roundc(cp, roundness=roundness, invert=invert)
else:
cp = self.rframe(pos=pos, width=width, height=height, rotate=rotate, thickness=thickness,
roundness=roundness, invert=invert, scale=scale, xscale=xscale, yscale=yscale)
return cp
def cross(self, pos=[0,0], width=1, rotate=0, thickness=0.2,
roundness=0, invert=False, scale=1, xscale=1, yscale=1):
wtp = (width + thickness) / 2
w2 = width / 2
t2 = thickness / 2
cp = [ [ w2, -t2 ], [ w2, t2 ], [ t2, t2 ], [ t2, w2 ], [ -t2, w2 ], [ -t2, t2 ], [ -w2, t2 ],
[ -w2, -t2 ], [ -t2, -t2 ], [ -t2, -w2 ], [ t2, -w2 ], [ t2, -t2 ], [ w2, -t2 ] ]
cp = addpos(cp, pos=pos)
if rotate != 0: cp = rotatecp(cp, pos=pos, rotate=rotate)
if scale != 1: xscale = yscale = scale
if xscale != 1 or yscale != 1: cp = scalecp(cp, xscale=xscale, yscale=yscale)
if roundness > 0: cp = roundc(cp, roundness=roundness, invert=invert)
return cp
def trframe(self, pos=[0,0], width=2, height=1, top=None, rotate=0, thickness=None,
roundness=0, invert=False, scale=1, xscale=1, yscale=1):
if top is None: top = width / 2
if thickness is None:
thickness = min(height, top) * .2
else:
thickness = min(height, top) * thickness * 2
outer = self.trapezoid(pos=pos, width=width, height=height, top=top)
angle = atan((width - top) / 2 / height)
db = thickness / cos(angle)
inner = self.trapezoid(pos=pos, width=width - db - thickness * tan(angle),
height=height - thickness, top=top - (db - thickness * tan(angle)))
outer = addpos(outer, pos=pos)
inner = addpos(inner, pos=pos)
if rotate != 0:
outer = rotatecp(outer, pos=pos, rotate=rotate)
inner = rotatecp(inner, pos=pos, rotate=rotate)
if scale != 1: xscale = yscale = scale
if xscale != 1 or yscale != 1:
outer = scalecp(outer, xscale=xscale, yscale=yscale)
inner = scalecp(inner, xscale=xscale, yscale=yscale)
if roundness > 0:
outer = roundc(outer, roundness=roundness, invert=invert)
inner = roundc(inner, roundness=roundness, invert=invert)
return [ outer, inner ]
def trapezoid(self, pos=[0,0], width=2, height=1, top=None, rotate=0, thickness=0,
roundness=0, invert=False, scale=1, xscale=1, yscale=1):
w2 = width / 2
h2 = height / 2
if top is None: top = w2
t2 = top / 2
if thickness == 0:
cp = [ [ w2, -h2 ], [ t2, h2 ], [ -t2, h2 ], [ -w2, -h2 ], [ w2, -h2 ] ]
cp = addpos(cp, pos=pos)
if rotate != 0: cp = rotatecp(cp, pos=pos, rotate=rotate)
if scale != 1: xscale = yscale = scale
if xscale != 1 or yscale != 1: cp = scalecp(cp, xscale=xscale, yscale=yscale)
if roundness > 0: cp = roundc(cp, roundness=roundness, invert=invert)
else:
cp = self.trframe(pos=pos, width=width, height=height, top=top, rotate=rotate, thickness=thickness,
roundness=roundness, invert=invert, scale=scale, xscale=xscale, yscale=yscale)
return cp
def circframe(self, pos=[0,0], radius=0.5, np=npdefault, rotate=0, iradius=None,
angle1=0, angle2=2*pi, scale=1, xscale=1, yscale=1):
thickness = 0
if iradius is None: iradius = radius * .8
outer = self.circle(pos=pos, radius=radius, np=np, rotate=rotate, iradius=iradius,
angle1=angle1, angle2=angle2, scale=scale, xscale=xscale, yscale=yscale)
if angle1 == 0 and angle2 == 2*pi:
radius = iradius
inner = self.circle(pos=pos, radius=radius, np=np, rotate=rotate, thickness=thickness,
angle1=angle1, angle2=angle2, scale=scale, xscale=xscale, yscale=yscale)
else:
t = radius - iradius
angle = (angle1 + angle2)/2 # pos and center lie on this line
offset = t/sin((angle2-angle1)/2)
corner = [pos[0]+offset*cos(angle), pos[1]+offset*sin(angle)]
dangle = asin(t/iradius)
angle1 = angle1 + dangle
angle2 = angle2 - dangle
radius = iradius
inner = self.circle(pos=pos, radius=radius, np=np, rotate=rotate, thickness=thickness, corner=corner,
angle1=angle1, angle2=angle2, scale=scale, xscale=xscale, yscale=yscale)
if rotate != 0:
outer = rotatecp(outer, pos=pos, rotate=rotate)
inner = rotatecp(inner, pos=pos, rotate=rotate)
if scale != 1: xscale = yscale = scale
if xscale != 1 or yscale != 1:
outer = scalecp(outer, xscale=xscale, yscale=yscale)
inner = scale(inner, xscale=xscale, yscale=yscale)
return [ outer, inner ]
def circle(self, pos=[0,0], radius=0.5, np=npdefault, rotate=0, thickness=0, corner=None, iradius=None,
angle1=0, angle2=2*pi, scale=1, xscale=1, yscale=1):
if corner is None: corner = pos # where the two straight edges meet
cp = []
if thickness > 0:
iradius = radius - radius*thickness
cp = self.circframe(pos=pos, radius=radius, np=np, rotate=rotate, iradius=iradius,
angle1=angle1, angle2=angle2, scale=scale, xscale=xscale, yscale=yscale)
else:
if angle1 != 0 or angle2 != 2 *pi:
cp.append([ corner[0], corner[1] ])
seg = 2 * pi / np
nseg = int(floor(abs((angle2 - angle1) / seg + .5)))
seg = (angle2 - angle1) / nseg
if angle1 != 0 or angle2 != 2 * pi: nseg += 1
c = radius * cos(angle1)
s = radius * sin(angle1)
dc = cos(seg)
ds = sin(seg)
x0 = pos[0]
y0 = pos[1]
cp.append([ x0 + c, y0 + s ])
for i in range(nseg-1):
c2 = c * dc - s * ds
s2 = s * dc + c * ds
cp.append([ x0 + c2, y0 + s2 ])
c = c2
s = s2
cp.append(cp[0])
if rotate != 0: cp = rotatecp(cp, pos=pos, rotate=rotate)
if scale != 1: xscale = yscale = scale
if xscale != 1 or yscale != 1: cp = scalecp(cp, xscale=xscale, yscale=yscale)
return cp
def arc(self, pos=[0,0], radius=0.5, np=npdefault, rotate=0, thickness=None,
angle1=0, angle2=2*pi, scale=1, xscale=1, yscale=1, path=False):
if thickness is None: thickness = .01 * radius
cp = [] # outer arc
cpi = [] # inner arc
seg = 2 * pi / np
nseg = int(floor(abs(angle2 - angle1) / seg) + 1)
seg = (angle2 - angle1) / nseg
for i in range(nseg+1):
x = cos(angle1 + i * seg)
y = sin(angle1 + i * seg)
cp.append([radius * x + pos[0], radius * y + pos[1]])
if not path: cpi.append([(radius - thickness) * x + pos[0],
(radius - thickness) * y + pos[1]])
if not path:
cpi.reverse()
for i in range(len(cpi)): cp.append(cpi[i])
cp.append(cp[0])
if rotate != 0: cp = rotatecp(cp, pos, rotate)
if scale != 1: xscale = yscale = scale
if xscale != 1 or yscale != 1: scalecp(cp, xscale, yscale)
return cp
def ellipse(self, pos=[0,0], width=1, height=None, np=npdefault, rotate=0, thickness=0,
angle1=0, angle2=2*pi, scale=1, xscale=1, yscale=1):
if height is None: height = .5 * width
yscale *= height/width
radius = width
return self.circle(pos=pos, radius=radius, np=np, rotate=rotate,
angle1=angle1, angle2=angle2, scale=scale, xscale=xscale, yscale=yscale)
# line is not called by paths.line()
def line(self, pos=[0,0], width=1, height=None, np=2, rotate=0, thickness=None,
start=[0,0], end=[0,1], scale=1, xscale=1, yscale=1):
v = vec(end[0] - start[0], end[1] - start[1], 0)
if thickness is None: thickness = .01 * mag(v)
dv = thickness * norm(vec(0, 0, 1).cross(v))
dx = dv.x
dy = dv.y
cp = [] # outer line
cpi = [] # inner line
vstart = vec(start[0], start[1], 0)
v = vec(end[0]-start[0], end[1]-start[1], 0)
vline = v/(floor(np-1))
for i in range(np):
v = i*vline
x = start[0] + v.x
y = start[1] + v.y
cp.append([x + pos[0], y + pos[1]])
cpi.append([x + pos[0] + dx, y + pos[1] + dy])
cpi.reverse()
for i in range(len(cpi)): cp.append(cpi[i])
cp.append(cp[0])
if rotate != 0: cp = rotatecp(cp, pos, rotate)
if scale != 1: xscale = yscale = scale
if xscale != 1 or yscale != 1: scalecp(cp, xscale, yscale)
return cp
def nframe(self, pos=[0,0], length=1, rotate=0, thickness=None, np=3,
roundness=0, invert=False, scale=1, xscale=1, yscale=1):
if thickness is None:
thickness = length * .1
else:
thickness = length * thickness
outer = self.ngon(pos=pos, np=np, length=length)
angle = pi * (.5 - 1 / np)
length2 = length - 2 * thickness / tan(angle)
inner = self.ngon(pos=pos, np=np, length=length2)
if rotate != 0:
outer = rotatecp(outer, pos, rotate)
inner = rotatecp(inner, pos, rotate)
if scale != 1: xscale = yscale = scale
if xscale != 1 or yscale != 1:
outer = scale(outer, xscale, yscale)
inner = scale(inner, xscale, yscale)
if roundness > 0:
outer = roundc(outer, roundness=roundness, invert=invert)
inner = roundc(inner, roundness=roundness, invert=invert)
return [ outer, inner ]
def ngon(self, pos=[0,0], length=1, rotate=0, thickness=0, np=None,
roundness=0, invert=False, scale=1, xscale=1, yscale=1):
cp = []
if np is None: raise AttributeError("must specify np for ngon shape")
if np < 3: raise AttributeError("number of sides can not be less than 3")
angle = 2 * pi / np
radius = length / 2 / sin(angle / 2)
if thickness == 0:
seg = 2 * pi / np
angle = 0
for i in range(np):
x = radius * cos(angle) + pos[0]
y = radius * sin(angle) + pos[1]
cp.append([ x, y ])
angle += seg
cp.append(cp[0])
if rotate != 0: cp = rotatecp(cp, pos, rotate)
if scale != 1: xscale = yscale = scale
if xscale != 1 or yscale != 1: scalecp(cp, xscale, yscale)
if roundness > 0: cp = roundc(cp, roundness=roundness, invert=invert)
else:
cp = self.nframe(pos=pos, length=length, rotate=rotate, thickness=thickness, np=np,
roundness=roundness, invert=invert, scale=scale, xscale=xscale, yscale=yscale)
return cp
def triangle(self, pos=[0,0], length=1, rotate=0, thickness=0,
roundness=0, invert=False, scale=1, xscale=1, yscale=1):
return self.ngon(pos=pos, np=3, length=length, rotate=rotate-pi/6,
roundness=roundness, invert=invert, scale=scale,
xscale=xscale, yscale=yscale, thickness=thickness)
def pentagon(self, pos=[0,0], length=1, rotate=0, thickness=0,
roundness=0, invert=False, scale=1, xscale=1, yscale=1):
return self.ngon(pos=pos, np=5, length=length, rotate=rotate-pi/10,
roundness=roundness, invert=invert, scale=scale,
xscale=xscale, yscale=yscale, thickness=thickness)
def hexagon(self, pos=[0,0], length=1, rotate=0, thickness=0,
roundness=0, invert=False, scale=1, xscale=1, yscale=1):
return self.ngon(pos=pos, np=6, length=length, rotate=rotate,
roundness=roundness, invert=invert, scale=scale,
xscale=xscale, yscale=yscale, thickness=thickness)
def octagon(self, pos=[0,0], length=1, rotate=0, thickness=0,
roundness=0, invert=False, scale=1, xscale=1, yscale=1):
return self.ngon(pos=pos, np=8, length=length, rotate=rotate+pi/8,
roundness=roundness, invert=invert, scale=scale,
xscale=xscale, yscale=yscale, thickness=thickness)
def sframe(self, pos=[0,0], rotate=0, thickness=None, radius=1, n=5, iradius=None,
roundness=0, invert=False, scale=1, xscale=1, yscale=1):
if iradius is None:
iradius = .5 * radius
if thickness is None:
thickness = .2 * radius
else:
thickness = thickness * 2 * iradius
outer = self.star(pos=pos, n=n, radius=radius, iradius=iradius)
inner = self.star(pos=pos, n=n, radius=radius - thickness, iradius=(radius - thickness) * iradius / radius)
if rotate != 0:
outer = rotatecp(outer, pos, rotate)
inner = rotatecp(inner, pos, rotate)
if scale != 1: xscale = yscale = scale
if xscale != 1 or yscale != 1:
outer = scale(outer, xscale, yscale)
inner = scale(inner, xscale, yscale)
if roundness > 0:
outer = roundc(outer, roundness=roundness, invert=invert)
inner = roundc(inner, roundness=roundness, invert=invert)
return [ outer, inner ]
def star(self, pos=[0,0], rotate=0, thickness=0, radius=1, n=5, iradius=None,
roundness=0, invert=False, scale=1, xscale=1, yscale=1):
## radius is from center to outer point of the star
## iradius is from center to inner corners of the star
if iradius is None: iradius = radius * .5
if thickness == 0:
cp = []
dtheta = pi / n
theta = 0
for i in range(2*n+1):
if i % 2 == 0:
cp.append([ -radius * sin(theta), radius * cos(theta) ])
else:
cp.append([ -iradius * sin(theta), iradius * cos(theta) ])
theta += dtheta
cp = addpos(cp, pos)
cp[-1] = cp[0] # take care of possible rounding errors
if rotate != 0: cp = rotatecp(cp, pos, rotate)
if scale != 1: xscale = yscale = scale
if xscale != 1 or yscale != 1: scalecp(cp, xscale, yscale)
if roundness > 0: cp = roundc(cp, roundness=roundness, invert=invert)
else:
cp = self.sframe(pos=pos, rotate=rotate, thickness=thickness, radius=radius, iradius=iradius,
n=n, roundness=roundness, invert=invert, scale=scale, xscale=xscale, yscale=yscale)
return cp
def points(self, pos=[], rotate=0, path=False, roundness=0, invert=False, scale=1, xscale=1, yscale=1):
cp = pos
closed = cp[-1][0] == cp[0][0] and cp[-1][1] == cp[0][1]
if not closed and not path: cp.append(cp[0])
if len(cp) > 0 and rotate != 0: cp = rotatecp(cp, [0,0], rotate)
if scale != 1: xscale = yscale = scale
if xscale != 1 or yscale != 1: scalecp(cp, xscale, yscale)
if roundness > 0: cp = roundc(cp, roundness=roundness, invert=invert)
return cp
def gear(self, pos=[0,0], n=20, radius=1, phi=20, addendum=None, dedendum=None,
fradius=None, rotate=0, scale=1, res=1, bevel=0):
if addendum is None: addendum = 0.08*radius
if dedendum is None: dedendum = 0.1*radius
if fradius is None: fradius = 0.02*radius
tooth = ToothOutline(n=n, res=res, phi=phi, radius=radius,
addendum=addendum, dedendum=dedendum, fradius=fradius, bevel=0)
g = []
for i in range(n):
rotan = -i * 2 * pi / n
rtooth = []
for j in range(len(tooth)):
p = tooth[j]
x = p[0]
y = p[1]
rx = x * cos(rotan) - y * sin(rotan) + pos[0]
ry = x * sin(rotan) + y * cos(rotan) + pos[1]
rtooth.append([rx, ry])
g.extend(rtooth)
if scale != 1: g = scalecp(g, scale, scale)
if rotate != 0: g = rotatecp(g, pos, rotate)
pts = []
i = 0
while i < len(g):
### must eliminate neighboring repeated points and collinear points; poly2tri.js chokes on them
g1 = g[i]
pts.append(g1)
if i == len(g)-1: break
g2 = g[i+1]
if i < len(g)-2:
g3 = g[i+2]
# check for a-b-a instance of collinear points
if abs(g3[0]-g1[0]) < .001*radius and abs(g3[1]-g1[1]) < .001*radius: i += 2
g2 = g[i]
if abs(g1[0] - g2[0]) < .001*radius and abs(g1[1] - g2[1]) < .001*radius:
i += 1
if abs(g1[0] - g2[0]) < .001*radius and abs(g1[1] - g2[1]) < .001*radius:
i += 1
i += 1
g1 = pts[0]
g2 = pts[-1]
if not (g1[0] == g2[0] and g1[1] == g2[1]): pts.append(g1)
return pts
def rackgear(self, pos=(0,0), n=30, radius=5., phi=20., addendum=0.4, dedendum=0.5,
fradius=0.1, rotate=0, scale=1.0, length=10*pi, res=1, bevel=0.05, depth=(0.4+0.6+0.1)):
if addendum is None: addendum = 0.08*radius
if dedendum is None: dedendum = 0.1*radius
if fradius is None: fradius = 0.02*radius
tooth = RackOutline(n=n, res=res, phi=phi, radius=radius,
addendum=addendum, dedendum=dedendum, fradius=fradius, bevel=bevel)
toothl = tooth[0][1] - tooth[-1][1]
nt = int(floor(length / toothl))
flength = nt * toothl
g = []
lastx = lasty = 1e9
for i in range(nt):
ntooth = []
for j in range(len(tooth)):
p = tooth[j]
x = p[0]
y = p[1]
if x == lastx or y == lasty: continue
nx = x + pos[0]
ny = -i * toothl + y + pos[1]
ntooth.append([nx, ny])
lastx = x
lasty = y
g.extend(ntooth)
g.append([g[-1][0] - depth, g[-1][1]])
g.append([g[0][0] - depth, g[0][1]])
g.append(g[0])
left = 1e9
right = -1e9
bottom = 1e9
top = -1e9
for i in range(len(g)):
g1 = g[i]
x = g1[0]
y = g1[1]
if x < left: left = x
if x > right: right = x
if y < bottom: bottom = y
if y > top: top = y
center = [ (left + right) / 2, (bottom + top) / 2 ]
dx = pos[0] - center[0]
dy = pos[1] - center[1]
g2 = []
for i in range(len(g)):
temp = g[i]
g2.append([ temp[0] + dx, temp[1] + dy ])
if scale != 1: g2 = scalecp(g2, scale, scale)
if rotate != 0: g2 = rotatecp(g2, pos, rotate)
a1 = g2[0]
a2 = g2[-1]
if not a1[0] == a2[0] and a1[1] == a2[1]: g2.append(a1)
return g2
def convert(pos=(0,0,0), up=(0,1,0), points=None, closed=True):
pos = vector(pos)
up = norm(vector(up))
up0 = vector(0,1,0)
angle = acos(up.dot(up0))
reorient = (angle > 0.0)
axis = up0.cross(up)
pts = []
for pt in points:
newpt = vector(pt[0],0,-pt[1])
if reorient: newpt = newpt.rotate(angle=angle, axis=axis)
pts.append(pos+newpt)
if closed and not pts[-1].equals(pts[0]): pts.append(pts[0])
return pts
class path_object(object):
def rectangle(self, pos=vec(0,0,0), width=6, height=None, rotate=0.0, thickness=None,
roundness=0.0, invert=False, scale=1.0, xscale=1.0, yscale=1.0, up=vec(0,1,0)):
if height == None: height = width
if thickness is not None:
raise AttributeError("Thickness is not allowed in a rectangular path")
c = shapes.rectangle(width=width, height=height, rotate=rotate, thickness=0,
roundness=roundness, invert=invert, scale=scale, xscale=xscale, yscale=yscale)
return convert(pos=pos, up=up, points=c)
def cross(self, pos=vec(0,0,0), width=5, thickness=2, rotate=0.0,
roundness=0.0, invert=False, scale=1.0, xscale=1.0, yscale=1.0, up=vec(0,1,0)):
c = shapes.cross(width=width, rotate=rotate, thickness=thickness,
roundness=roundness, invert=invert, scale=scale, xscale=xscale, yscale=yscale)
return convert(pos=pos, up=up, points=c)
def trapezoid(self, pos=vec(0,0,0), width=6, height=3, top=None, rotate=0.0, thickness=None,
roundness=0.0, invert=False, scale=1.0, xscale=1.0, yscale=1.0, up=vec(0,1,0)):
if height == None: height = width
if thickness is not None:
raise AttributeError("Thickness is not allowed in a trapezoidal path")
c = shapes.trapezoid(width=width, height=height, top=top, rotate=rotate, thickness=0,
roundness=roundness, invert=invert, scale=scale, xscale=xscale, yscale=yscale)
return convert(pos=pos, up=up, points=c)
def circle(self, pos=vec(0,0,0), radius=3, np=32, thickness=None,