def arc12_pt3(xyz1, xyz2, xyz3):
'''
Three points should be on same circle.
'''
vec1 = x1, y1, z1 = xyz1
vec2 = x2, y2, z2 = xyz2
vec3 = x3, y3, z3 = xyz3
unit_nvec = normal_vector(vec1, vec2, normalize=True)
cp1 = np.dot(unit_nvec, np.cross(vec1, vec3))
cp2 = np.dot(unit_nvec, np.cross(vec2, vec3))
if feq(cp1,0):
if feq(cp2,0):
raise ValueError("cp1 and cp2 are both zero")
elif flt(cp2,0):
return 'pt1'
elif fgt(cp2,0):
return 'out'
elif flt(cp1,0):
return 'out'
elif fgt(cp1,0):
if feq(cp2,0):
return 'pt2'
elif flt(cp2,0):
return 'between'
elif fgt(cp2,0):
return 'out'
def xyz2xyp(X, Y, Z, R=1):
assert feq(sqrt(X*X + Y*Y + Z*Z),R), 'The (x,y,z) (%s,%s,%s) is not on the sphere.'%(X,Y,Z)
a = R/sqrt(3)
at1, at2 = a*tan(-pi/4), a*tan(pi/4)
xyp_dict = dict()
if fgt(X,0):
x, y = a*(Y/X), a*(Z/X)
if flge(at1,x,at2) and flge(at1,y,at2):
xyp_dict[1] = (x,y)
elif flt(X,0):
x, y = a*(Y/X), -a*(Z/X)
if flge(at1,x,at2) and flge(at1,y,at2):
xyp_dict[3] = (x,y)
if fgt(Y,0):
x, y = -a*(X/Y), a*(Z/Y)
if flge(at1,x,at2) and flge(at1,y,at2):
xyp_dict[2] = (x,y)
elif flt(Y,0):
x, y = -a*(X/Y), -a*(Z/Y)
if flge(at1,x,at2) and flge(at1,y,at2):
xyp_dict[4] = (x,y)
if flt(Z,0):
x, y = -a*(Y/Z), -a*(X/Z)
if flge(at1,x,at2) and flge(at1,y,at2):
xyp_dict[5] = (x,y)
elif fgt(Z,0):
x, y = a*(Y/Z), -a*(X/Z)
if flge(at1,x,at2) and flge(at1,y,at2):
xyp_dict[6] = (x,y)
return xyp_dict
def plane12_pt3(xyz1, xyz2, xyz3):
'''
plane generated by xyz1 and xyz2
left if xyz3 is in normal vector direction
'''
plane = plane_origin(xyz1, xyz2)
#nvec = normal_vector(xyz1, xyz2)
#print np.dot(plane,nvec) # > 0
val = np.dot(plane, xyz3)
if feq(val,0):
return 'straight'
elif flt(val,0):
return 'right'
elif fgt(val,0):
return 'left'