def camera_help(ua, a):
if rv.lax_equal(a, ua):
return True
b = input(
"Incorrect. Enter 'b' to break down the problem into subproblems, or anything else to abandon this question.\n"
)
if b != 'b':
return False
q = "w is the normalized and negated gaze vector. Enter w."
ua = rv.expect_vector(q)
rv.check_answer(w, ua, q, "camera.w")
q = "u is the normalized cross product of the up vector and w. Enter u."
ua = rv.expect_vector(q)
rv.check_answer(u, ua, q, "camera.u")
q = "v is the normalized cross product of u and w. Enter v."
ua = rv.expect_vector(q)
rv.check_answer(v, ua, q, "camera.v")
f = [['ux', 'uy', 'uz', 'px'], ['vx', 'vy', 'vz', 'py'],
['wx', 'wy', 'wz', 'pz'], ['0', '0', '0', '1']]
print(numpy.array_str(numpy.matrix(f)))
print(rv.mxstr(f))
q = "The camera transformation matrix is composed of the three basis vectors and camera position in the following order:\n %s\n Enter the camera transformation matrix." % rv.mxstr(
f)
ua = rv.expect_matrix(q)
return rv.check_answer(a, ua, q, "camera.final")
def cameraq(ask=True):
eye = rv.vector3()
gaze = rv.vector3()
up = rv.vector3()
q = "Given a camera position of %s, a gaze vector of %s, and an up vector of %s, what is the resulting camera transformation matrix?" % (
numpy.array_str(eye), numpy.array_str(gaze), numpy.array_str(up))
# derive answer
w = -gf.normalize(gaze)
u = gf.normalize(numpy.cross(up, w))
v = gf.normalize(numpy.cross(w, u))
a = numpy.matrix([[u[0], u[1], u[2], eye[0]], [v[0], v[1], v[2], eye[1]],
[w[0], w[1], w[2], eye[2]], [0, 0, 0, 1]])
if ask:
ua = rv.expect_matrix(q)
# nested function for breaking down camera question
def camera_help(ua, a):
if rv.lax_equal(a, ua):
return True
b = input(
"Incorrect. Enter 'b' to break down the problem into subproblems, or anything else to abandon this question.\n"
)
if b != 'b':
return False
q = "w is the normalized and negated gaze vector. Enter w."
ua = rv.expect_vector(q)
rv.check_answer(w, ua, q, "camera.w")
q = "u is the normalized cross product of the up vector and w. Enter u."
ua = rv.expect_vector(q)
rv.check_answer(u, ua, q, "camera.u")
q = "v is the normalized cross product of u and w. Enter v."
ua = rv.expect_vector(q)
rv.check_answer(v, ua, q, "camera.v")
f = [['ux', 'uy', 'uz', 'px'], ['vx', 'vy', 'vz', 'py'],
['wx', 'wy', 'wz', 'pz'], ['0', '0', '0', '1']]
print(numpy.array_str(numpy.matrix(f)))
print(rv.mxstr(f))
q = "The camera transformation matrix is composed of the three basis vectors and camera position in the following order:\n %s\n Enter the camera transformation matrix." % rv.mxstr(
f)
ua = rv.expect_matrix(q)
return rv.check_answer(a, ua, q, "camera.final")
rv.check_answer(a, ua, q, "camera", camera_help)
else:
return q, a, (eye, gaze, up)
def rotationq(ask=True, twod=True):
r = numpy.round(numpy.random.random() + numpy.random.random(), 2)
if twod:
ax = 'z'
else:
ax = numpy.random.permutation(('x', 'y', 'z'))[0]
q = "Create a matrix to %s." % qtext(("rotation", r, ax))
a = rotation_matrix(r, ax)
if ask:
ua = rv.expect_matrix(q)
rv.check_answer(a, ua, q, "rotation")
else:
return q, a, (ax, r)
def translationq(ask=True, twod=False):
(x, y, z) = numpy.random.randint(-5, 5, 3)
if twod:
z = 0
q = "Create a matrix to %s." % qtext(("translation", {
'x': x,
'y': y,
'z': z
}))
a = translation_matrix(x, y, z)
if ask:
ua = rv.expect_matrix(q)
rv.check_answer(a, ua, q, "translation")
else:
return q, a, (x, y, z)
def pictureq(ask=True):
transformation = numpy.random.permutation(
((translationq, "translation"), (rotationq, "rotation"), (scaleq,
"scale")))[0]
(qt, a, params) = transformation[0](False, True)
q = "Create a matrix to transform the green triangle into the yellow triangle."
call(["Rscript", "Rcode/generate_figs.R", transformation[1]] +
[str(p) for p in params])
if ask:
with Image.open('tmp.png') as img:
img.show()
ua = rv.expect_matrix(q)
rv.check_answer(a, ua, q, "picture")
else:
return q, a, params
def comboq(ask=True):
transformations = numpy.random.permutation(
(translationq, rotationq, scaleq))[:numpy.random.randint(2, 4)]
transformations = [t(False) for t in transformations]
q = "Create a matrix to %s." % ", and then ".join([
qt.replace("Create a matrix to ", '')[:-1]
for (qt, a, params) in transformations
])
a = numpy.eye(4)
for q, m, p in reversed(transformations):
a = a * m
if ask:
ua = rv.expect_matrix(q)
rv.check_answer(a, ua, q, "combo")
else:
return q, a, transformations
def orthoq(ask=True):
(t, b, r, l, n, f) = rv.vector(6)
if t == b:
t = t + 1
if r == l:
r = r + 1
if n == f:
n = n + 1
a = orthomatrix(t, b, r, l, n, f)
q = "Create a matrix to transform a paralleliped defined by t=%d, b=%d, r=%d, l=%d, n=%d, and f=%d into the canonical view volume (an orthographic projection matrix)." % (
t, b, r, l, n, f)
if ask:
ua = rv.expect_matrix(q)
rv.check_answer(a, ua, q, "orthographic")
else:
return q, a, ()
def scaleq(ask=True, twod=False):
axes = ('x', 'y', 'z')
target_axes = numpy.random.permutation(
('x', 'y',
'z'))[:(numpy.random.randint(0, 3) +
1)] # randomly permute (x, y, z), then choose a random slice
if twod:
target_axes = [a for a in target_axes if a != 'z']
params = {
a: round(numpy.random.random() * 5, 2) if a in target_axes else 1
for a in axes
}
q = "Create a matrix to scale a point %s." % " and ".join([
"%.2f along the %s-axis" % (factor, axis)
for axis, factor in sorted(params.items()) if axis in target_axes
])
a = scale_matrix(params['x'], params['y'], params['z'])
if ask:
ua = rv.expect_matrix(q)
rv.check_answer(a, ua, q, "scale")
else:
return q, a, (params['x'], params['y'], params['z'])