def vsumq():
x = rv.vector3()
y = rv.vector3()
a = x + y
q = "%s + %s" % (numpy.array_str(x), numpy.array_str(y))
ua = rv.expect_vector(q)
rv.check_answer(a, ua, q, "sum")
def cross_productq():
x = rv.vector3()
y = rv.vector3()
a = numpy.cross(x, y)
q = "%s x %s" % (numpy.array_str(x), numpy.array_str(y))
ua = rv.expect_vector(q)
rv.check_answer(a, ua, q, "cross_product")
def dot_productq():
x = rv.vector3()
y = rv.vector3()
a = x.dot(y)
q = "%s dot %s\n" % (numpy.array_str(x), numpy.array_str(y))
ua = rv.expect_float(q)
rv.check_answer(a, ua, q, "dot product")
def angleq():
x = rv.vector3()
y = rv.vector3()
a = numpy.arccos(gf.normalize(x).dot(gf.normalize(y)))
q = "What is the angle between the following two vectors (in radians)?\n %s, %s\n" % (
numpy.array_str(x), numpy.array_str(y))
ua = rv.expect_float(q)
rv.check_answer(a, ua, q, "angle")
def point_to_pointq():
x = rv.vector3()
y = rv.vector3()
a = y - x
q = "What is the vector from %s to %s?\n" % (numpy.array_str(x),
numpy.array_str(y))
ua = rv.expect_vector(q)
rv.check_answer(a, ua, q, "point to point")
def cross_productq(ask=True):
x = rv.vector3()
y = rv.vector3()
a = numpy.cross(x, y)
q = "%s x %s" % (numpy.array_str(x), numpy.array_str(y))
if ask:
ua = rv.expect_vector(q)
rv.check_answer(a, ua, q, "cross_product")
else:
return q, a, ()
def dot_productq(ask=True):
x = rv.vector3()
y = rv.vector3()
a = x.dot(y)
q = "%s dot %s\n" % (numpy.array_str(x), numpy.array_str(y))
if ask:
ua = rv.expect_float(q)
rv.check_answer(a, ua, q, "dot product")
else:
return q, a, ()
def vsumq(ask=True):
x = rv.vector3()
y = rv.vector3()
a = x + y
q = "%s + %s" % (numpy.array_str(x), numpy.array_str(y))
if ask:
ua = rv.expect_vector(q)
rv.check_answer(a, ua, q, "sum")
else:
return q, a, ()
def ldirq(ask=True): ppos = rv.vector3() lpos = rv.vector3() q = "Given a point location of %s and a light location of %s, what is the light direction? (Remember to normalize.)" % (numpy.array_str(ppos), numpy.array_str(lpos)) a = gf.normalize(lpos - ppos) if ask: ua = rv.expect_vector(q) rv.check_answer(a, ua, q, "light direction") else: return q, a, ()
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 point_to_pointq(ask=True):
x = rv.vector3()
y = rv.vector3()
a = y - x
q = "What is the vector from %s to %s?\n" % (numpy.array_str(x),
numpy.array_str(y))
if ask:
ua = rv.expect_vector(q)
rv.check_answer(a, ua, q, "point to point")
else:
return q, a, ()
def lineq(ask=True):
p0 = rv.vector3()
p1 = rv.vector3()
q = "What are the A, B, and C components of the line passing through %s and %s, where Ax + By + C = 0" % (numpy.array_str(p0), numpy.array_str(p1))
a = gf.lineEq(p0, p1)[:-1]
rv.writeModule(dict(zip(('p0','p1','a'), (p0, p1,a))))
if ask:
ua = rv.expect_vector(q)
rv.check_answer(a, ua, q, "line equation", rv.vector_check)
else:
return q, rv.combine(a), ()
def directionq():
x = rv.vector3()
y = rv.vector3()
a = 'a'
if (x.dot(y) < 0):
a = 'b'
elif x.dot(y) == 0:
a = 'c'
q = "What is the relationship between the following two vectors?\n %s, %s\n a) They point in the same direction\n b) they point in opposite directions\n c) they are perpendicular\n" % (
numpy.array_str(x), numpy.array_str(y))
ua = rv.expect_categorical(q, ('a', 'b', 'c'))
rv.check_answer(a, ua, q, "direction")
def diffuseq(ask=True):
cl = rv.color()
cr = rv.color()
ld = gf.normalize(rv.vector3())
normal = gf.normalize(rv.vector3())
q = "Point p has a surface color of %s and a surface normal of %s. Given a light of color %s and direction %s, what will be the diffuse component of p's final color?" % (
rv.tostring(cr), rv.tostring(normal), rv.tostring(cl), rv.tostring(ld))
a = cl * cr * max((0, ld.dot(normal)))
if ask:
ua = rv.expect_vector(q)
rv.check_answer(a, ua, q, "diffuse")
else:
return q, a
def rayq(ask=True):
# camera frame
x = gf.normalize(rv.vector3())
y = gf.normalize(rv.vector3())
z = gf.normalize(rv.vector3())
e = rv.vector3()
# view volume
l, r, b, t = numpy.random.randint(-5, 5, 4)
l, r = rv.strict_order(l, r)
b, t = rv.strict_order(b, t)
# u, v, coordinates
i, j = numpy.random.randint(0, 5, 2)
nx, ny = numpy.random.randint(250, 750, 2)
u = l + (r-l)*(i+0.5)/nx
v = b + (t-b)*(j+0.5)/ny
# ray
if rv.coinflip(0.5):
vt = 'orthographic'
d = -z
o = e + u*x + v*y
ip = None
else:
vt = 'perspective'
ip = numpy.random.randint(0, 5)
o = e
d = -ip*z + u*x + v*y
q = """What are the origin and direction of a ray cast from the viewpoint to pixel (%d, %d) in a %d x %d image with the following parameters?
l=%d, r=%d, b=%d, t=%d
view type = %s
camera origin = %s
camera u axis = %s
camera v axis = %s
camera w axis = %s
""" % (i, j, nx, ny, l, r, b, t, vt, numpy.array_str(e), numpy.array_str(x), numpy.array_str(y), numpy.array_str(z))
if v == 'perspective':
q = q + "image plane at distance %d in front of viewpoint\n" % ip
rv.writeModule(dict(zip(('i', 'j', 'nx', 'ny', 'l', 'r', 'b', 't', 'vt', 'e', 'x', 'y', 'z', 'ip', 'u', 'v', 'o', 'd'), (i, j, nx, ny, l, r, b, t, vt, e, x, y, z, ip, u, v, o, d))))
if ask:
print(q)
ua = rv.expect_vector("origin:")
rv.check_answer(o, ua, q, "ray casting: origin", rv.vector_check)
ua = rv.expect_vector("direction:")
rv.check_answer(d, ua, q, "ray casting: direction", rv.vector_check)
else:
return q, rv.combine((o, d)), ()
def normalizeq(ask=True):
x = rv.vector3()
a = gf.normalize(x)
q = "normalize %s" % numpy.array_str(x)
if ask:
ua = rv.expect_vector(q)
rv.check_answer(a, ua, q, "normalize")
else:
return q, a, ()
def magnitudeq(ask=True):
x = rv.vector3()
a = gf.magnitude(x)
q = "||%s||\n" % numpy.array_str(x)
if ask:
ua = rv.expect_float(q)
rv.check_answer(a, ua, q, "magnitude")
else:
return q, a, ()
def normalq(ask=True): vertices = [rv.vector3() for _ in range(3)] q = "What is the normal to a triangle defined by vertices %s, %s, and %s (listed in the order of positive rotation)?" % tuple(numpy.array_str(p) for p in vertices) a = gf.getNormal(vertices) if ask: ua = rv.expect_vector(q) rv.check_answer(a, ua, q, "normal") else: return q, a, ()
def specularq(ask=True):
cl = rv.color()
ld = gf.normalize(rv.vector3())
cr = rv.color()
normal = gf.normalize(rv.vector3())
r = gf.reflect(ld, normal)
e = gf.normalize(rv.vector3())
p = 2
q = "Point p has a surface color of %s and a surface normal of %s. Given a light of color %s and direction %s, and a view direction %s, what will be the specular component of p's final color, with a Phong exponent of %d?" % (
numpy.array_str(cr), numpy.array_str(normal), numpy.array_str(cl),
numpy.array_str(ld), numpy.array_str(e), p)
a = cl * max((r.dot(e), 0))**p
if ask:
ua = rv.expect_vector(q)
rv.check_answer(a, ua, q, "specular")
else:
return q, a
def pointOnPlane(p, n):
# find point whose vector to p is perpendicular to n
# take another random vector and take the cross product of that and n
# now we have a vector perpendicular to n
# add that to p to get another point on the plane.
v = rv.vector3()
v2 = numpy.cross(v, n)
p2 = p + v2
if not (p - p2).dot(n) < 0.000001:
print("ERROR")
return (v, v2, p2)
return p2
def perspectiveq(ask=True):
p = rv.vector3()
p = numpy.append(p, 1)
n = rv.vector3()[0]
if n == 0:
n = 1
q = "Project point %s onto the plane n=%d. " % (numpy.array_str(p), n)
q1 = "What will px, py, pw be after the perspective transformation is applied? (before the scaling and translation of the orthographic transformation) "
q2 = "What will px, py be after perspective division?"
a1 = numpy.array((p[0] * n, p[1] * n, p[2]))
a2 = numpy.array((a1[0] / a1[2], a1[1] / a1[2]))
if ask:
print(q)
ua1 = rv.expect_vector(q1)
rv.check_answer(a1, ua1, q1, "perspective.a")
ua2 = rv.expect_vector(q2, 2)
rv.check_answer(a2, ua2, q2, "perspective.b")
else:
finalq = r"%s\\a) %s\\b) %s" % (q, q1, q2)
finala = r"a) %s \\ b) %s" % (a1, a2)
return finalq, finala, ()
def triangle():
return [rv.vector3() for _ in range(3)]
def ray():
return rv.vector3(), normalize(rv.vector3())
def rayToPoint(p):
d = numpy.random.random() * rv.vector3()
e = p + d
return e, -normalize(d)
def magnitudeq():
x = rv.vector3()
a = gf.magnitude(x)
q = "||%s||\n" % numpy.array_str(x)
ua = rv.expect_float(q)
rv.check_answer(a, ua, q, "magnitude")
def normalizeq():
x = rv.vector3()
a = gf.normalize(x)
q = "normalize %s" % numpy.array_str(x)
ua = rv.expect_vector(q)
rv.check_answer(a, ua, q, "normalize")
def plane():
return rv.vector3(), normalize(rv.vector3())
