# # gik.cad # # GIK # # Neil Gershenfeld # 8/1/07 # # # define shapes and transformation # # circle(x0, y0, r) # cylinder(x0, y0, z0, z1, r) # cone(x0, y0, z0, z1, r0) # sphere(x0, y0, z0, r) # torus(x0, y0, z0, r0, r1) # rectangle(x0, x1, y0, y1) # cube(x0, x1, y0, y1, z0, z1) # right_triangle(x0, y0, h) # triangle(x0, y0, x1, y1, x2, y2) (points in clockwise order) # pyramid(x0, x1, y0, y1, z0, z1) # function(Z_of_XY) # functions(upper_Z_of_XY,lower_Z_of_XY) # add(part1, part2) # subtract(part1, part2) # intersect(part1, part2) # move(part,dx,dy) # translate(part,dx,dy,dz) # rotate(part, angle) # rotate_x(part, angle) # rotate_y(part, angle) # rotate_z(part, angle) # rotate_90(part) # rotate_180(part) # rotate_270(part) # reflect_x(part) # reflect_y(part) # reflect_z(part) # reflect_xy(part) # reflect_xz(part) # reflect_yz(part) # scale_x(part, x0, sx) # scale_y(part, y0, sy) # scale_z(part, z0, sz) # scale_xy(part, x0, y0, sxy) # scale_xyz(part, x0, y0, z0, sxyz) # coscale_x_y(part, x0, y0, y1, angle0, angle1, amplitude, offset) # coscale_x_z(part, x0, z0, z1, angle0, angle1, amplitude, offset) # coscale_xy_z(part, x0, y0, z0, z1, angle0, angle1, amplitude, offset) # taper_x_y(part, x0, y0, y1, s0, s1) # taper_x_z(part, x0, z0, z1, s0, s1) # taper_xy_z(part, x0, y0, z0, z1, s0, s1) # shear_x_y(part, y0, y1, dx0, dx1) # shear_x_z(part, z0, z1, dx0, dx1) # (more to come) def circle(x0, y0, r): part = "(((X-x0)**2 + (Y-y0)**2) <= r**2)" part = replace(part,'x0',str(x0)) part = replace(part,'y0',str(y0)) part = replace(part,'r',str(r)) return part def cylinder(x0, y0, z0, z1, r): part = "(((X-x0)**2 + (Y-y0)**2 <= r**2) & (Z >= z0) & (Z <= z1))" part = replace(part,'x0',str(x0)) part = replace(part,'y0',str(y0)) part = replace(part,'z0',str(z0)) part = replace(part,'z1',str(z1)) part = replace(part,'r',str(r)) return part def cone(x0, y0, z0, z1, r0): part = cylinder(x0, y0, z0, z1, r0) part = taper_xy_z(part, x0, y0, z0, z1, 1.0, 0.0) return part def sphere(x0, y0, z0, r): part = "(((X-x0)**2 + (Y-y0)**2 + (Z-z0)**2) <= r**2)" part = replace(part,'x0',str(x0)) part = replace(part,'y0',str(y0)) part = replace(part,'z0',str(z0)) part = replace(part,'r',str(r)) return part def torus(x0, y0, z0, r0, r1): part = "(((r0 - sqrt((X-x0)**2 + (Y-y0)**2))**2 + (Z-z0)**2) <= r1**2)" part = replace(part,'x0',str(x0)) part = replace(part,'y0',str(y0)) part = replace(part,'z0',str(z0)) part = replace(part,'r0',str(r0)) part = replace(part,'r1',str(r1)) return part def rectangle(x0, x1, y0, y1): part = "((X >= x0) & (X <= x1) & (Y >= y0) & (Y <= y1))" part = replace(part,'x0',str(x0)) part = replace(part,'x1',str(x1)) part = replace(part,'y0',str(y0)) part = replace(part,'y1',str(y1)) return part def cube(x0, x1, y0, y1, z0, z1): part = "((X >= x0) & (X <= x1) & (Y >= y0) & (Y <= y1) & (Z >= z0) & (Z <= z1))" part = replace(part,'x0',str(x0)) part = replace(part,'x1',str(x1)) part = replace(part,'y0',str(y0)) part = replace(part,'y1',str(y1)) part = replace(part,'z0',str(z0)) part = replace(part,'z1',str(z1)) return part def right_triangle(x0, y0, l): part = "((X > x0) & (X < x0 + l - (Y-y0)) & (Y > y0))" part = replace(part,'x0',str(x0)) part = replace(part,'y0',str(y0)) part = replace(part,'l',str(l)) return part def triangle(x0, y0, x1, y1, x2, y2): # points in clockwise order part = "((((y1-y0)*(X-x0)-(x1-x0)*(Y-y0)) >= 0) & (((y2-y1)*(X-x1)-(x2-x1)*(Y-y1)) >= 0) & (((y0-y2)*(X-x2)-(x0-x2)*(Y-y2)) >= 0))" part = replace(part,'x0',str(x0)) part = replace(part,'y0',str(y0)) part = replace(part,'x1',str(x1)) part = replace(part,'y1',str(y1)) part = replace(part,'x2',str(x2)) part = replace(part,'y2',str(y2)) return part def pyramid(x0, x1, y0, y1, z0, z1): part = cube(x0, x1, y0, y1, z0, z1) part = taper_xy_z(part, (x0+x1)/2., (y0+y1)/2., z0, z1, 1.0, 0.0) return part def function(Z_of_XY): part = '(Z <= '+Z_of_XY+')' return part def functions(upper_Z_of_XY,lower_Z_of_XY): part = '(Z <= '+upper_Z_of_XY+') & (Z >= '+lower_Z_of_XY+')' return part def add(part1, part2): part = "part1 | part2" part = replace(part,'part1',part1) part = replace(part,'part2',part2) return part def subtract(part1, part2): part = "(part1) & ~(part2)" part = replace(part,'part1',part1) part = replace(part,'part2',part2) return part def intersect(part1, part2): part = "(part1) & (part2)" part = replace(part,'part1',part1) part = replace(part,'part2',part2) return part def move(part,dx,dy): part = replace(part,'X','(X-'+str(dx)+')') part = replace(part,'Y','(Y-'+str(dy)+')') return part def translate(part,dx,dy,dz): part = replace(part,'X','(X-'+str(dx)+')') part = replace(part,'Y','(Y-'+str(dy)+')') part = replace(part,'Z','(Z-'+str(dz)+')') return part def rotate(part, angle): angle = angle*pi/180 part = replace(part,'X','(cos(angle)*X+sin(angle)*y)') part = replace(part,'Y','(-sin(angle)*X+cos(angle)*y)') part = replace(part,'y','Y') part = replace(part,'angle',str(angle)) return part def rotate_x(part, angle): angle = angle*pi/180 part = replace(part,'Y','(cos(angle)*Y+sin(angle)*z)') part = replace(part,'Z','(-sin(angle)*Y+cos(angle)*z)') part = replace(part,'z','Z') part = replace(part,'angle',str(angle)) return part def rotate_y(part, angle): angle = angle*pi/180 part = replace(part,'X','(cos(angle)*X+sin(angle)*z)') part = replace(part,'Z','(-sin(angle)*X+cos(angle)*z)') part = replace(part,'z','Z') part = replace(part,'angle',str(angle)) return part def rotate_z(part, angle): angle = angle*pi/180 part = replace(part,'X','(cos(angle)*X+sin(angle)*y)') part = replace(part,'Y','(-sin(angle)*X+cos(angle)*y)') part = replace(part,'y','Y') part = replace(part,'angle',str(angle)) return part def rotate_90(part): part = reflect_xy(part) part = reflect_y(part) return part def rotate_180(part): part = reflect_xy(part) part = reflect_y(part) part = reflect_xy(part) part = reflect_y(part) return part def rotate_270(part): part = reflect_xy(part) part = reflect_y(part) part = reflect_xy(part) part = reflect_y(part) part = reflect_xy(part) part = reflect_y(part) return part def reflect_x(part): part = replace(part,'X','-X') return part def reflect_y(part): part = replace(part,'Y','-Y') return part def reflect_z(part): part = replace(part,'Z','-Z') return part def reflect_xy(part): part = replace(part,'X','temp') part = replace(part,'Y','X') part = replace(part,'temp','Y') return part def reflect_xz(part): part = replace(part,'X','temp') part = replace(part,'Z','X') part = replace(part,'temp','Z') return part def reflect_yz(part): part = replace(part,'Y','temp') part = replace(part,'Z','Y') part = replace(part,'temp','Z') return part def scale_x(part, x0, sx): part = replace(part,'X','(x0 + (X-x0)/sx)') part = replace(part,'x0',str(x0)) part = replace(part,'sx',str(sx)) return part def scale_y(part, y0, sy): part = replace(part,'Y','(y0 + (Y-y0)/sy)') part = replace(part,'y0',str(y0)) part = replace(part,'sy',str(sy)) return part def scale_z(part, z0, sz): part = replace(part,'Z','(z0 + (Z-z0)/sz)') part = replace(part,'z0',str(z0)) part = replace(part,'sz',str(sz)) return part def scale_xy(part, x0, y0, sxy): part = replace(part,'X','(x0 + (X-x0)/sxy)') part = replace(part,'Y','(y0 + (Y-y0)/sxy)') part = replace(part,'x0',str(x0)) part = replace(part,'y0',str(y0)) part = replace(part,'sxy',str(sxy)) return part def scale_xyz(part, x0, y0, z0, sxyz): part = replace(part,'X','(x0 + (X-x0)/sxyz)') part = replace(part,'Y','(y0 + (Y-y0)/sxyz)') part = replace(part,'Z','(z0 + (Z-z0)/sxyz)') part = replace(part,'x0',str(x0)) part = replace(part,'y0',str(y0)) part = replace(part,'z0',str(z0)) part = replace(part,'sxyz',str(sxyz)) return part def coscale_x_y(part, x0, y0, y1, angle0, angle1, amplitude, offset): phase0 = pi*angle0/180. phase1 = pi*angle1/180. part = replace(part,'X','(x0 + (X-x0)/(offset + amplitude*cos(phase0 + (phase1-phase0)*(Y-y0)/(y1-y0))))') part = replace(part,'x0',str(x0)) part = replace(part,'y0',str(y0)) part = replace(part,'y1',str(y1)) part = replace(part,'phase0',str(phase0)) part = replace(part,'phase1',str(phase1)) part = replace(part,'amplitude',str(amplitude)) part = replace(part,'offset',str(offset)) return part def coscale_x_z(part, x0, z0, z1, angle0, angle1, amplitude, offset): phase0 = pi*angle0/180. phase1 = pi*angle1/180. part = replace(part,'X','(x0 + (X-x0)/(offset + amplitude*cos(phase0 + (phase1-phase0)*(Z-z0)/(z1-z0))))') part = replace(part,'x0',str(x0)) part = replace(part,'z0',str(z0)) part = replace(part,'z1',str(z1)) part = replace(part,'phase0',str(phase0)) part = replace(part,'phase1',str(phase1)) part = replace(part,'amplitude',str(amplitude)) part = replace(part,'offset',str(offset)) return part def coscale_xy_z(part, x0, y0, z0, z1, angle0, angle1, amplitude, offset): phase0 = pi*angle0/180. phase1 = pi*angle1/180. part = replace(part,'X','(x0 + (X-x0)/(offset + amplitude*cos(phase0 + (phase1-phase0)*(Z-z0)/(z1-z0))))') part = replace(part,'Y','(y0 + (Y-y0)/(offset + amplitude*cos(phase0 + (phase1-phase0)*(Z-z0)/(z1-z0))))') part = replace(part,'x0',str(x0)) part = replace(part,'y0',str(y0)) part = replace(part,'z0',str(z0)) part = replace(part,'z1',str(z1)) part = replace(part,'phase0',str(phase0)) part = replace(part,'phase1',str(phase1)) part = replace(part,'amplitude',str(amplitude)) part = replace(part,'offset',str(offset)) return part def taper_x_y(part, x0, y0, y1, s0, s1): part = replace(part,'X','(x0 + (X-x0)*(y1-y0)/(s1*(Y-y0) + s0*(y1-Y)))') part = replace(part,'x0',str(x0)) part = replace(part,'y0',str(y0)) part = replace(part,'y1',str(y1)) part = replace(part,'s0',str(s0)) part = replace(part,'s1',str(s1)) return part def taper_x_z(part, x0, z0, z1, s0, s1): part = replace(part,'X','(x0 + (X-x0)*(z1-z0)/(s1*(Z-z0) + s0*(z1-Z)))') part = replace(part,'x0',str(x0)) part = replace(part,'z0',str(z0)) part = replace(part,'z1',str(z1)) part = replace(part,'s0',str(s0)) part = replace(part,'s1',str(s1)) return part def taper_xy_z(part, x0, y0, z0, z1, s0, s1): part = replace(part,'X','(x0 + (X-x0)*(z1-z0)/(s1*(Z-z0) + s0*(z1-Z)))') part = replace(part,'Y','(y0 + (Y-y0)*(z1-z0)/(s1*(Z-z0) + s0*(z1-Z)))') part = replace(part,'x0',str(x0)) part = replace(part,'y0',str(y0)) part = replace(part,'z0',str(z0)) part = replace(part,'z1',str(z1)) part = replace(part,'s0',str(s0)) part = replace(part,'s1',str(s1)) return part def shear_x_y(part, y0, y1, dx0, dx1): part = replace(part,'X','(X - dx0 - (dx1-dx0)*(Y-y0)/(y1-y0))') part = replace(part,'y0',str(y0)) part = replace(part,'y1',str(y1)) part = replace(part,'dx0',str(dx0)) part = replace(part,'dx1',str(dx1)) return part def shear_x_z(part, z0, z1, dx0, dx1): part = replace(part,'X','(X - dx0 - (dx1-dx0)*(Z-z0)/(z1-z0))') part = replace(part,'z0',str(z0)) part = replace(part,'z1',str(z1)) part = replace(part,'dx0',str(dx0)) part = replace(part,'dx1',str(dx1)) return part def coshear_x_z(part, z0, z1, angle0, angle1, amplitude, offset): phase0 = pi*angle0/180. phase1 = pi*angle1/180. part = replace(part,'X','(X - offset - amplitude*cos(phase0 + (phase1-phase0)*(Z-z0)/(z1-z0)))') part = replace(part,'z0',str(z0)) part = replace(part,'z1',str(z1)) part = replace(part,'phase0',str(phase0)) part = replace(part,'phase1',str(phase1)) part = replace(part,'amplitude',str(amplitude)) part = replace(part,'offset',str(offset)) return part # # define part # w = 0.14 # slot width l = 0.3 # slot length c = 0.03 # champher length s = .1 # part space xstart = .5 # xmin ystart = -.5 # ymax slot = rectangle(0,l/2,-w/2,w/2) slot = add(slot,right_triangle(0,w/2,c)) slot = add(slot,reflect_y(right_triangle(0,w/2,c))) double_slot = rectangle(0,l+w/2,-w/2,w/2) double_slot = add(double_slot,right_triangle(0,w/2,c)) double_slot = add(double_slot,reflect_y(right_triangle(0,w/2,c))) square_gik = rectangle(-l-w/2,l+w/2,-l-w/2,l+w/2) square_gik = subtract(square_gik,translate(slot,-l-w/2,0,0)) square_gik = subtract(square_gik,translate(reflect_x(slot),l+w/2,0,0)) square_gik = subtract(square_gik,translate(reflect_xy(slot),0,-l-w/2,0)) square_gik = subtract(square_gik,translate(reflect_xy(reflect_x(slot)),0,l+w/2,0)) dxy = 2*l+w+s x0 = xstart y0 = ystart square_giks = translate(square_gik,x0+.5*dxy,y0-.5*dxy,0) square_giks = add(square_giks,translate(square_gik,x0+1.5*dxy,y0-.5*dxy,0)) square_giks = add(square_giks,translate(square_gik,x0+.5*dxy,y0-1.5*dxy,0)) square_giks = add(square_giks,translate(square_gik,x0+1.5*dxy,y0-1.5*dxy,0)) square_giks = add(square_giks,translate(square_gik,x0+.5*dxy,y0-2.5*dxy,0)) square_giks = add(square_giks,translate(square_gik,x0+1.5*dxy,y0-2.5*dxy,0)) square_giks = add(square_giks,translate(square_gik,x0+.5*dxy,y0-3.5*dxy,0)) square_giks = add(square_giks,translate(square_gik,x0+1.5*dxy,y0-3.5*dxy,0)) gik = square_giks pi_gik = rectangle(-l-w/2,l+w/2,-l-w/2,l+w/2) pi_gik = subtract(pi_gik,translate(slot,-l-w/2,0,0)) pi_gik = subtract(pi_gik,translate(reflect_x(slot),l+w/2,0,0)) pi_gik = subtract(pi_gik,translate(reflect_xy(double_slot),0,-l-w/2,0)) x0 = x0 + 2.5*dxy pi_giks = translate(pi_gik,x0,y0-.5*dxy,0) pi_giks = add(pi_giks,translate(pi_gik,x0,y0-1.5*dxy,0)) pi_giks = add(pi_giks,translate(pi_gik,x0,y0-2.5*dxy,0)) pi_giks = add(pi_giks,translate(pi_gik,x0,y0-3.5*dxy,0)) gik = add(gik,pi_giks) tee_gik = rectangle(-l-w/2,l+w/2,-l-w/2,3*w/2) tee_gik = subtract(tee_gik,translate(slot,-l-w/2,0,0)) tee_gik = subtract(tee_gik,translate(reflect_x(slot),l+w/2,0,0)) tee_gik = subtract(tee_gik,translate(reflect_xy(slot),0,-l-w/2,0)) x0 = x0 + dxy dy0 = 3*w/2+s/2 dy = l+2*w+s tee_giks = translate(tee_gik,x0,y0-dy0,0) tee_giks = add(tee_giks,translate(tee_gik,x0,y0-dy0-dy,0)) tee_giks = add(tee_giks,translate(tee_gik,x0,y0-dy0-2*dy,0)) tee_giks = add(tee_giks,translate(tee_gik,x0,y0-dy0-3*dy,0)) tee_giks = add(tee_giks,translate(tee_gik,x0,y0-dy0-4*dy,0)) gik = add(gik,tee_giks) corner_gik = rectangle(-l-w/2,3*w/2,-l-w/2,3*w/2) corner_gik = subtract(corner_gik,translate(slot,-l-w/2,0,0)) corner_gik = subtract(corner_gik,translate(reflect_xy(slot),0,-l-w/2,0)) x0 = x0 + dxy dx0 = l+2*w+s corner_giks = translate(corner_gik,x0,y0-dy0,0) corner_giks = add(corner_giks,translate(corner_gik,x0,y0-dy0-dy,0)) corner_giks = add(corner_giks,translate(corner_gik,x0,y0-dy0-2*dy,0)) corner_giks = add(corner_giks,translate(corner_gik,x0,y0-dy0-3*dy,0)) corner_giks = add(corner_giks,translate(corner_gik,x0,y0-dy0-4*dy,0)) corner_giks = add(corner_giks,translate(corner_gik,x0+dx0,y0-dy0,0)) corner_giks = add(corner_giks,translate(corner_gik,x0+dx0,y0-dy0-dy,0)) corner_giks = add(corner_giks,translate(corner_gik,x0+dx0,y0-dy0-2*dy,0)) corner_giks = add(corner_giks,translate(corner_gik,x0+dx0,y0-dy0-3*dy,0)) corner_giks = add(corner_giks,translate(corner_gik,x0+dx0,y0-dy0-4*dy,0)) gik = add(gik,corner_giks) connector_gik = rectangle(-l,l,-3*w/2,3*w/2) connector_gik = subtract(connector_gik,translate(slot,-l,0,0)) connector_gik = subtract(connector_gik,translate(reflect_x(slot),l,0,0)) x0 = x0 + 2*dx0 - w/2 dx = 2*l+s dy0 = 3*w/2 + s/2 dy = 3*w+s connector_giks = translate(connector_gik,x0,y0-dy0,0) connector_giks = add(connector_giks,translate(connector_gik,x0,y0-dy0-dy,0)) connector_giks = add(connector_giks,translate(connector_gik,x0,y0-dy0-2*dy,0)) connector_giks = add(connector_giks,translate(connector_gik,x0,y0-dy0-3*dy,0)) connector_giks = add(connector_giks,translate(connector_gik,x0,y0-dy0-4*dy,0)) connector_giks = add(connector_giks,translate(connector_gik,x0,y0-dy0-5*dy,0)) gik = add(gik,connector_giks) r = l + w/(2*sqrt(3)) round_gik = circle(0,0,r) round_gik = subtract(round_gik,translate(slot,-r,0,0)) round_gik = subtract(rotate(round_gik,120),translate(slot,-r,0,0)) round_gik = subtract(rotate(round_gik,120),translate(slot,-r,0,0)) x0 = x0 + l + r + s d = sqrt(3)*r h = sqrt(3)*d triangle_gik = triangle(-d,-r,0,h-r,d,-r) triangle_gik = subtract(triangle_gik,translate(reflect_xy(slot),0,-r,0)) triangle_gik = subtract(rotate(triangle_gik,120),translate(reflect_xy(slot),0,-r,0)) triangle_gik = subtract(rotate(triangle_gik,120),translate(reflect_xy(slot),0,-r,0)) inverted_triangle_gik = translate(reflect_y(triangle_gik),0,h-2*r,0) x0 = x0 + r/2 + d + s dx = d + s dy0 = -h + r dy = h + s triangle_giks = translate(triangle_gik,x0,y0+dy0,0) triangle_giks = add(triangle_giks,translate(inverted_triangle_gik,x0,y0+dy0-dy,0)) triangle_giks = add(triangle_giks,translate(triangle_gik,x0,y0+dy0-2*dy,0)) triangle_giks = add(triangle_giks,translate(inverted_triangle_gik,x0+dx,y0+dy0,0)) triangle_giks = add(triangle_giks,translate(triangle_gik,x0+dx,y0+dy0-dy,0)) triangle_giks = add(triangle_giks,translate(inverted_triangle_gik,x0+dx,y0+dy0-2*dy,0)) gik = add(gik,triangle_giks) x0 = x0 - r/2 - d - s dy0 = -h/2 round_giks = translate(round_gik,x0,y0+dy0,0) round_giks = add(round_giks,translate(round_gik,x0,y0+dy0-dy,0)) round_giks = add(round_giks,translate(round_gik,x0,y0+dy0-2*dy,0)) x0 = x0 + r/2 + d + s x0 = x0 + dx x0 = x0 + r/2 + d + s round_giks = add(round_giks,translate(round_gik,x0,y0+dy0,0)) round_giks = add(round_giks,translate(round_gik,x0,y0+dy0-dy,0)) round_giks = add(round_giks,translate(round_gik,x0,y0+dy0-2*dy,0)) gik = add(gik,round_giks) # # define limits and parameters # cad.xmin = xstart - s # min x to render cad.xmax = x0 + r + s # max x to render cad.ymin = ystart - 4*dxy - s # min y to render cad.ymax = ystart + s # max y to render dpi = 50 # low resolution for previewing #dpi = 100 # high resolution for machining nxy = int(dpi*(cad.xmax-cad.xmin)) cad.nx = nxy # x points to render cad.ny = nxy # y points to render cad.inches_per_unit = 1.0 # use inch units cad.view('xy') # show xy view # # assign part to cad.function # cad.function = gik