def intersect_sphere(sphere, ray):
# sphere a, ray a -> Maybe int
dirn = ry.get_dirn(ray)
pos = ry.get_pos(ray)
center = get_center(sphere)
to_center = vr.sub_vector(pos, center)
a = vr.dot_prod(dirn, dirn)
b = 2*vr.dot_prod(dirn, to_center)
c = vr.dot_prod(to_center, to_center) - get_radius(sphere) ** 2
det = b ** 2 - 4 * a * c
if det < 0:
return None
else:
t1 = (-b + math.sqrt(det)) / (2*a)
t2 = (-b - math.sqrt(det)) / (2*a)
return min([t1, t2])
def main():
# create 3 random vectors
v1 = [random.random(), random.random(), random.random()]
v2 = [random.random(), random.random(), random.random()]
v3 = [random.random(), random.random(), random.random()]
# Print out the 3 vectors
print("v1 = ", v1)
print("v2 = ", v2)
print("v3 = ", v3)
#Print magnitude of 3 vectors
print("v1 magnitude = ", vc.mod(v1))
print("v2 magnitude = ", vc.mod(v2))
print("v3 magnitude = ", vc.mod(v3))
#print addition, dot & cross products of v1 and v2
print("v1 + v2 =", vc.addv(v1, v2))
print("v1 . v2 =", vc.dot_prod(v1, v2))
print("v1 x v2 =", vc.crossprod(v1, v2))
#vector identities
#1
identity1part1 = vc.crossprod(v1, v2)
identity1part2 = vc.crossprod(vc.scale(v2, -1), v1)
if vc.same(identity1part1, identity1part2) == True:
print("Identity 1 is correct.")
#2
identity2part1 = vc.crossprod(v1, vc.addv(v2, v3))
identity2part2 = vc.addv(vc.crossprod(v1, v2), vc.crossprod(v1, v3))
if vc.same(identity2part1, identity2part2) == True:
print("Identity 2 is correct.")
#3
identity3part1 = vc.crossprod(v1, vc.crossprod(v2, v3))
identity3part2 = vc.subv((vc.scale(v2, vc.dot_prod(v1, v3))),
(vc.scale(v3, vc.dot_prod(v1, v2))))
if vc.same(identity3part1, identity3part2) == True:
print("Identity 3 is correct.")
def intersect_lights(scene, lights, pos, normal):
# scene, light, vector -> float
color = 1
for light in lights:
dirn = vr.normalize(vr.sub_vector(lt.get_pos(light), pos))
new_ray = ry.make_ray(pos, dirn)
t, n = intersect_scene(scene, new_ray)
if not t:
dot_or_0 = max([vr.dot_prod(dirn, normal), 0])
incr = dot_or_0 * lt.get_brightness(light)
color += incr
if color:
return min([8, color])
def mat_vec_prod(m, v):
"""Calculate the matrix-vector product."""
if m.shape[1] != v.shape[0]:
raise ValueError
l = [vector.dot_prod(m.rows[i], v) for i in range(m.shape[0])]
return vector.Vector(l)
v0 = [GF2.zero, GF2.zero, GF2.one, GF2.zero, GF2.zero, GF2.one, GF2.zero]
v_0010010 = match_vector_sums_to(p5_vectors, v0)
p5_v1 = [GF2.zero, GF2.one, GF2.zero, GF2.zero, GF2.zero, GF2.one, GF2.zero]
v_0100010 = match_vector_sums_to(p5_vectors, p5_v1)
## 6: (Problem 6) Solving Linear Equations over GF(2)
#You should be able to solve this without using a computer.
a = [GF2.one, GF2.one, GF2.zero, GF2.zero]
b = [GF2.one, GF2.zero, GF2.one, GF2.zero]
c = [GF2.one, GF2.one, GF2.one, GF2.one]
x_gf2 = [GF2.one, GF2.zero, GF2.zero, GF2.zero]
x_gf2_comp = vector.GF2_solve_dot_prod_sys(one, a, b, c)
## 7: (Problem 7) Formulating Equations using Dot-Product
#Please provide each answer as a list of numbers
v1 = [2, 3, -4, 1]
v2 = [1, -5, 2, 0]
v3 = [4, 1, -1, -1]
## 8: (Problem 8) Practice with Dot-Product
uv_a = vector.dot_prod([1, 0], [5, 4321])
uv_b = vector.dot_prod([0, 1], [12345, 6])
uv_c = vector.dot_prod([-1, 3], [5, 7])
uv_d = trunc(
vector.dot_prod(
[-(sqrt(2) / 2.0), sqrt(2) / 2.0],
[sqrt(2) / 2.0, -(sqrt(2) / 2.0)]
)
)
def test_dot_prod(self):
p = vector.dot_prod(self.v, self.v)
self.assertAlmostEqual(p, 8.75)
with self.assertRaises(ValueError):
vector.dot_prod(self.v, vector.Vector([1.0]))
