def test_cc_int():
"""Generates two random circles, computes the intersection,
and verifies that the number of intersections and the
positions of the intersections are correct.
Returns True or False"""
# gen two random circles p1,r2 and p2, r2
p1 = vector.randvec(2, 0.0, 10.0, 1.0)
r1 = random.uniform(0, 10.0)
p2 = vector.randvec(2, 0.0, 10.0, 1.0)
r2 = random.uniform(0, 10.0)
# 33% change that r2=abs(r1-|p1-p2|)
if random.random() < 0.33:
r2 = abs(r1 - vector.norm(p1 - p2))
# do interesection
diag_print(
"problem:" + str(p1) + "," + str(r1) + "," + str(p2) + "," + str(r2),
"test_cc_int")
sols = cc_int(p1, r1, p2, r2)
diag_print("solutions:" + str(map(str, sols)), "test_cc_int")
# test number of intersections
if len(sols) == 0:
if not tol_gt(vector.norm(p2 - p1), r1 + r2) and not tol_lt(
vector.norm(p2 - p1), abs(r1 - r2)) and not tol_eq(
vector.norm(p1 - p2), 0):
diag_print("number of solutions 0 is wrong", "test_cc_int")
return False
elif len(sols) == 1:
if not tol_eq(vector.norm(p2 - p1), r1 + r2) and not tol_eq(
vector.norm(p2 - p1), abs(r1 - r2)):
diag_print("number of solutions 1 is wrong", "test_cc_int")
return False
elif len(sols) == 2:
if not tol_lt(vector.norm(p2 - p1), r1 + r2) and not tol_gt(
vector.norm(p2 - p1), abs(r1 - r2)):
diag_prin("number of solutions 2 is wrong")
return False
else:
diag_print("number of solutions > 2 is wrong", "test_cc_int")
return False
# test intersection coords
for p3 in sols:
if not tol_eq(vector.norm(p3 - p1), r1):
diag_print("solution not on circle 1", "test_cc_int")
return False
if not tol_eq(vector.norm(p3 - p2), r2):
diag_print("solution not on circle 2", "test_cc_int")
return False
diag_print("OK", "test_cc_int")
return True
def test_cc_int():
"""Generates two random circles, computes the intersection,
and verifies that the number of intersections and the
positions of the intersections are correct.
Returns True or False"""
# gen two random circles p1,r2 and p2, r2
p1 = vector.randvec(2, 0.0, 10.0,1.0)
r1 = random.uniform(0, 10.0)
p2 = vector.randvec(2, 0.0, 10.0,1.0)
r2 = random.uniform(0, 10.0)
# 33% change that r2=abs(r1-|p1-p2|)
if random.random() < 0.33:
r2 = abs(r1-vector.norm(p1-p2))
# do interesection
diag_print("problem:"+str(p1)+","+str(r1)+","+str(p2)+","+str(r2),"test_cc_int")
sols = cc_int(p1, r1, p2, r2)
diag_print("solutions:"+str(map(str, sols)),"test_cc_int")
# test number of intersections
if len(sols) == 0:
if not tol_gt(vector.norm(p2-p1),r1 + r2) and not tol_lt(vector.norm(p2-p1),abs(r1 - r2)) and not tol_eq(vector.norm(p1-p2),0):
diag_print("number of solutions 0 is wrong","test_cc_int")
return False
elif len(sols) == 1:
if not tol_eq(vector.norm(p2-p1),r1 + r2) and not tol_eq(vector.norm(p2-p1),abs(r1-r2)):
diag_print("number of solutions 1 is wrong","test_cc_int")
return False
elif len(sols) == 2:
if not tol_lt(vector.norm(p2-p1),r1 + r2) and not tol_gt(vector.norm(p2-p1),abs(r1 - r2)):
diag_prin("number of solutions 2 is wrong")
return False
else:
diag_print("number of solutions > 2 is wrong","test_cc_int")
return False
# test intersection coords
for p3 in sols:
if not tol_eq(vector.norm(p3-p1), r1):
diag_print("solution not on circle 1","test_cc_int")
return False
if not tol_eq(vector.norm(p3-p2), r2):
diag_print("solution not on circle 2","test_cc_int")
return False
diag_print("OK","test_cc_int")
return True
def test_perp_3d():
for i in range(10):
u = normalised(vector.randvec(3))
v, w = perp_3d(u)
print u, vector.norm(u)
print v, vector.norm(v)
print w, vector.norm(w)
print tol_eq(vector.dot(u, v), 0.0)
print tol_eq(vector.dot(v, w), 0.0)
print tol_eq(vector.dot(w, u), 0.0)
def test_perp_3d():
for i in range(10):
u = normalised(vector.randvec(3))
v,w = perp_3d(u)
print u, vector.norm(u)
print v, vector.norm(v)
print w, vector.norm(w)
print tol_eq(vector.dot(u,v),0.0)
print tol_eq(vector.dot(v,w),0.0)
print tol_eq(vector.dot(w,u),0.0)
def test_rr_int():
"""test random ray-ray intersection. returns True iff succesful"""
# generate tree points A,B,C an two rays AC, BC.
# then calculate the intersection of the two rays
# and check that it equals C
p_a = vector.randvec(2, 0.0, 10.0, 1.0)
p_b = vector.randvec(2, 0.0, 10.0, 1.0)
p_c = vector.randvec(2, 0.0, 10.0, 1.0)
# print p_a, p_b, p_c
if tol_eq(vector.norm(p_c - p_a), 0) or tol_eq(vector.norm(p_c - p_b), 0):
return True # ignore this case
v_ac = (p_c - p_a) / vector.norm(p_c - p_a)
v_bc = (p_c - p_b) / vector.norm(p_c - p_b)
s = rr_int(p_a, v_ac, p_b, v_bc)
if tol_eq(math.fabs(vector.dot(v_ac, v_bc)), 1.0):
return len(s) == 0
else:
if len(s) > 0:
p_s = s[0]
return tol_eq(p_s[0], p_c[0]) and tol_eq(p_s[1], p_c[1])
else:
return False
def test_rr_int():
"""test random ray-ray intersection. returns True iff succesful"""
# generate tree points A,B,C an two rays AC, BC.
# then calculate the intersection of the two rays
# and check that it equals C
p_a = vector.randvec(2, 0.0, 10.0,1.0)
p_b = vector.randvec(2, 0.0, 10.0,1.0)
p_c = vector.randvec(2, 0.0, 10.0,1.0)
# print p_a, p_b, p_c
if tol_eq(vector.norm(p_c - p_a),0) or tol_eq(vector.norm(p_c - p_b),0):
return True # ignore this case
v_ac = (p_c - p_a) / vector.norm(p_c - p_a)
v_bc = (p_c - p_b) / vector.norm(p_c - p_b)
s = rr_int(p_a, v_ac, p_b, v_bc)
if tol_eq(math.fabs(vector.dot(v_ac, v_bc)),1.0):
return len(s) == 0
else:
if len(s) > 0:
p_s = s[0]
return tol_eq(p_s[0],p_c[0]) and tol_eq(p_s[1],p_c[1])
else:
return False
def test_sss_int():
p1 = vector.randvec(3, 0.0, 10.0, 1.0)
p2 = vector.randvec(3, 0.0, 10.0, 1.0)
p3 = vector.randvec(3, 0.0, 10.0, 1.0)
p4 = vector.randvec(3, 0.0, 10.0, 1.0)
#p1 = vector.vector([0.0,0.0,0.0])
#p2 = vector.vector([1.0,0.0,0.0])
#p3 = vector.vector([0.0,1.0,0.0])
#p4 = vector.vector([1.0,1.0,1.0])
d14 = vector.norm(p4 - p1)
d24 = vector.norm(p4 - p2)
d34 = vector.norm(p4 - p3)
sols = sss_int(p1, d14, p2, d24, p3, d34)
sat = True
for sol in sols:
# print sol
d1s = vector.norm(sol - p1)
d2s = vector.norm(sol - p2)
d3s = vector.norm(sol - p3)
sat = sat and tol_eq(d1s, d14)
sat = sat and tol_eq(d2s, d24)
sat = sat and tol_eq(d3s, d34)
# print sat
return sat
def test_sss_int():
p1 = vector.randvec(3, 0.0, 10.0,1.0)
p2 = vector.randvec(3, 0.0, 10.0,1.0)
p3 = vector.randvec(3, 0.0, 10.0,1.0)
p4 = vector.randvec(3, 0.0, 10.0,1.0)
#p1 = vector.vector([0.0,0.0,0.0])
#p2 = vector.vector([1.0,0.0,0.0])
#p3 = vector.vector([0.0,1.0,0.0])
#p4 = vector.vector([1.0,1.0,1.0])
d14 = vector.norm(p4-p1)
d24 = vector.norm(p4-p2)
d34 = vector.norm(p4-p3)
sols = sss_int(p1,d14,p2,d24,p3,d34)
sat = True
for sol in sols:
# print sol
d1s = vector.norm(sol-p1)
d2s = vector.norm(sol-p2)
d3s = vector.norm(sol-p3)
sat = sat and tol_eq(d1s,d14)
sat = sat and tol_eq(d2s,d24)
sat = sat and tol_eq(d3s,d34)
# print sat
return sat
def test_cl_int():
"""Generates random circle and line, computes the intersection,
and verifies that the number of intersections and the
positions of the intersections are correct.
Returns True or False"""
# 3 random points
p1 = vector.randvec(2, 0.0, 10.0, 1.0)
p2 = vector.randvec(2, 0.0, 10.0, 1.0)
p3 = vector.randvec(2, 0.0, 10.0, 1.0)
# prevent div by zero / no line direction
if tol_eq(vector.norm(p1 - p2), 0):
p2 = p1 + p3 * 0.1
# line (o,v): origin p1, direction p1-p2
o = p1
v = (p2 - p1) / vector.norm(p2 - p1)
# cirlce (c, r): centered in p3, radius p3-p2 + rx
c = p3
r0 = vector.norm(p3 - p2)
# cases rx = 0, rx > 0, rx < 0
case = random.choice([1, 2, 3])
if case == 1:
r = r0 #should have one intersection (unles r0 = 0)
elif case == 2:
r = random.random() * r0 # should have no ints (unless r0=0)
elif case == 3:
r = r0 + random.random() * r0 # should have 2 ints (unless r0=0)
# do interesection
diag_print(
"problem:" + str(c) + "," + str(r) + "," + str(o) + "," + str(v),
"test_cl_int")
sols = cl_int(c, r, o, v)
diag_print("solutions:" + str(map(str, sols)), "test_cl_int")
# distance from point on line closest to circle center
l = vector.dot(c - o, v) / vector.norm(v)
p = o + v * l / vector.norm(v)
d = vector.norm(p - c)
diag_print("distance center to line=" + str(d), "test_cl_int")
# test number of intersections
if len(sols) == 0:
if not tol_gt(d, r):
diag_print("wrong number of solutions: 0", "test_cl_int")
return False
elif len(sols) == 1:
if not tol_eq(d, r):
diag_print("wrong number of solutions: 1", "test_cl_int")
return False
elif len(sols) == 2:
if not tol_lt(d, r):
diag_print("wrong number of solutions: 2", "test_cl_int")
return False
else:
diag_print("wrong number of solutions: >2", "test_cl_int")
# test coordinates of intersection
for s in sols:
# s on line (o,v)
if not is_colinear(s, o, o + v):
diag_print("solution not on line", "test_cl_int")
return False
# s on circle c, r
if not tol_eq(vector.norm(s - c), r):
diag_print("solution not on circle", "test_cl_int")
return False
return True
def test_cl_int():
"""Generates random circle and line, computes the intersection,
and verifies that the number of intersections and the
positions of the intersections are correct.
Returns True or False"""
# 3 random points
p1 = vector.randvec(2, 0.0, 10.0,1.0)
p2 = vector.randvec(2, 0.0, 10.0,1.0)
p3 = vector.randvec(2, 0.0, 10.0,1.0)
# prevent div by zero / no line direction
if tol_eq(vector.norm(p1-p2),0):
p2 = p1 + p3 * 0.1
# line (o,v): origin p1, direction p1-p2
o = p1
v = (p2 - p1) / vector.norm(p2 - p1)
# cirlce (c, r): centered in p3, radius p3-p2 + rx
c = p3
r0 = vector.norm(p3-p2)
# cases rx = 0, rx > 0, rx < 0
case = random.choice([1,2,3])
if case==1:
r = r0 #should have one intersection (unles r0 = 0)
elif case==2:
r = random.random() * r0 # should have no ints (unless r0=0)
elif case==3:
r = r0 + random.random() * r0 # should have 2 ints (unless r0=0)
# do interesection
diag_print("problem:"+str(c)+","+str(r)+","+str(o)+","+str(v),"test_cl_int")
sols = cl_int(c,r,o,v)
diag_print("solutions:"+str(map(str, sols)),"test_cl_int")
# distance from point on line closest to circle center
l = vector.dot(c-o, v) / vector.norm(v)
p = o + v * l / vector.norm(v)
d = vector.norm(p-c)
diag_print("distance center to line="+str(d),"test_cl_int")
# test number of intersections
if len(sols) == 0:
if not tol_gt(d, r):
diag_print("wrong number of solutions: 0", "test_cl_int")
return False
elif len(sols) == 1:
if not tol_eq(d, r):
diag_print("wrong number of solutions: 1", "test_cl_int")
return False
elif len(sols) == 2:
if not tol_lt(d, r):
diag_print("wrong number of solutions: 2", "test_cl_int")
return False
else:
diag_print("wrong number of solutions: >2", "test_cl_int")
# test coordinates of intersection
for s in sols:
# s on line (o,v)
if not is_colinear(s, o, o+v):
diag_print("solution not on line", "test_cl_int")
return False
# s on circle c, r
if not tol_eq(vector.norm(s-c), r):
diag_print("solution not on circle", "test_cl_int")
return False
return True