#
# bearing.cad
#

#
# define limits and parameters
#

cad_xmin = -.7
cad_xmax = .7
cad_ymin = -.7
cad_ymax = .7
cad_zmin = -.2
cad_zmax = .2
cad_rx = 30
cad_rz = 45
cad_units = 'in' # coordinates units
cad_bit_depth = '1' # bit depth
cad_npts = 250
cad_nx = cad_npts # x points to render
cad_ny = cad_npts # y points to render
cad_nz = 100 # z points to render

#
# define shapes and transformation
#

def sphere(x0, y0, z0, r):
   string = "(((X-x0)**2 + (Y-y0)**2 + (Z-z0)**2) <= r**2)"
   string = replace(string,'x0',str(x0))
   string = replace(string,'y0',str(y0))
   string = replace(string,'z0',str(z0))
   string = replace(string,'r',str(r))
   return string

def cylinder(x0, y0, z0, z1, r):
   string = "(((X-x0)**2 + (Y-y0)**2 <= r**2) & (Z >= z0) & (Z <= z1))"
   string = replace(string,'x0',str(x0))
   string = replace(string,'y0',str(y0))
   string = replace(string,'z0',str(z0))
   string = replace(string,'z1',str(z1))
   string = replace(string,'r',str(r))
   return string

def cube(x0, x1, y0, y1, z0, z1):
   string = "((X >= x0) & (X <= x1) & (Y >= y0) & (Y <= y1) & (Z >= z0) & (Z <= z1))"
   string = replace(string,'x0',str(x0))
   string = replace(string,'x1',str(x1))
   string = replace(string,'y0',str(y0))
   string = replace(string,'y1',str(y1))
   string = replace(string,'z0',str(z0))
   string = replace(string,'z1',str(z1))
   return string

def translate(string,dx,dy,dz):
   string = replace(string,'X','(X-'+str(dx)+')')
   string = replace(string,'Y','(Y-'+str(dy)+')')
   string = replace(string,'Z','(Z-'+str(dz)+')')
   return string   

def union(string1, string2):
   string = "(string1) | (string2)"
   string = replace(string,'string1',string1)
   string = replace(string,'string2',string2)
   return string

def intersect(string1, string2):
   string = "(string1) & (string2)"
   string = replace(string,'string1',string1)
   string = replace(string,'string2',string2)
   return string

def subtract(string1, string2):
   string = "(string1) & ~(string2)"
   string = replace(string,'string1',string1)
   string = replace(string,'string2',string2)
   return string

def rotate_x(string, theta):
   string = replace(string,'Y','(cos(theta)*Y+sin(theta)*z)')
   string = replace(string,'Z','(-sin(theta)*Y+cos(theta)*z)')
   string = replace(string,'z','Z')
   string = replace(string,'theta',theta)
   return string

def rotate_y(string, theta):
   string = replace(string,'X','(cos(theta)*X+sin(theta)*z)')
   string = replace(string,'Z','(-sin(theta)*X+cos(theta)*z)')
   string = replace(string,'z','Z')
   string = replace(string,'theta',theta)
   return string

def rotate_z(string, theta):
   string = replace(string,'X','(cos(theta)*X+sin(theta)*y)')
   string = replace(string,'Y','(-sin(theta)*X+cos(theta)*y)')
   string = replace(string,'y','Y')
   string = replace(string,'theta',theta)
   return string

#
# Amy Sun's bearing
#

origin_x = 0
origin_y = 0

height = 0.25
wall = 0.10
OD = 1.0 
O_r = OD / 2

OD_O = cylinder(origin_x, origin_y, -height/2, height/2, O_r + wall/2)
OD_I = cylinder(origin_x, origin_y, -height/2, height/2, O_r - wall/2)
OD = subtract(OD_O,OD_I)

ID = 0.5
I_r = ID / 2
ID_O = cylinder(origin_x, origin_y, -height/2, height/2, I_r + wall/2)
ID_I = cylinder(origin_x, origin_y, -height/2, height/2, I_r - wall/2)
ID = subtract(ID_O,ID_I)

cage = union(OD,ID)

# race radius
R_r = ((O_r - I_r) / 2) + I_r

# bearing radius 
bearing_diameter = .40
#b_r = bearing_diameter/2
b_r = bearing_diameter/4.

race_O = cylinder(origin_x, origin_y, -(height/2.)/3., (height/2.)/3., R_r+b_r)
race_I = cylinder(origin_x, origin_y, -(height/2.)/3., (height/2.)/3., R_r-b_r)
race = subtract(race_O,race_I)

frame = union(OD,ID)
outer_part = subtract(frame,race)

#bearings

# num balls
Nb = 6.

ball1 = sphere(cos(2*pi/Nb)*R_r, sin(2*pi/Nb)*R_r, 0, b_r)
ball2 = sphere(cos(2*2*pi/Nb)*R_r, sin(2*2*pi/Nb)*R_r, 0, b_r)
ball3 = sphere(cos(3*2*pi/Nb)*R_r, sin(3*2*pi/Nb)*R_r, 0, b_r)
ball4 = sphere(cos(4*2*pi/Nb)*R_r, sin(4*2*pi/Nb)*R_r, 0, b_r)
ball5 = sphere(cos(5*2*pi/Nb)*R_r, sin(5*2*pi/Nb)*R_r, 0, b_r)
ball6 = sphere(cos(6*2*pi/Nb)*R_r, sin(6*2*pi/Nb)*R_r, 0, b_r)
balls = union(ball1,ball2)
balls = union(balls,ball3)
balls = union(balls,ball4)
balls = union(balls,ball5)
balls = union(balls,ball6)

bearing = union(outer_part,balls)

cutaway_bearing = subtract(bearing,cube(0,2,-2,0,-2,2))

#
# assign part to SAT_function
#

SAT_function = cutaway_bearing