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 barycentricq(ask=True):
triangle = gf.triangle()
if rv.coinflip(.5):
p = gf.pointProbablyInPolygon(triangle)
else:
p = gf.pointNotInPolygon(triangle)
bary = gf.getBarycentricCoordinates(triangle, p)
q1 = "What are the barycentric coordinates of point P=%s with respect to triangle T with vertices\n %s?" % (numpy.array_str(p), '\n '.join(' '.join("%.2f" % v for v in vx) for vx in triangle))
a1 = bary
q2 = "Is point P inside or outside T?"
a2 = (bary >= 0).all() and (bary <= 1).all()
colors = numpy.array([rv.color() for _ in range(3)])
q3 = "If vertex 0 has color %s, and vertex 1 has color %s, and vertex 2 has color %s, what is P's color?" % tuple(numpy.array_str(c) for c in colors)
a3 = sum(b*c for b,c in zip(bary, colors))
rv.writeModule(dict(zip(('triangle','p','bary','colors','a1','a2','a3'), (triangle, p, bary, colors, a1, a2, a3))))
if ask:
ua1 = rv.expect_vector(q1)
rv.check_answer(a1, ua1, q1, "barycentric coordinates", rv.vector_check)
ua2 = rv.expect_boolish(q2, {'inside':True, 'outside':False} )
rv.check_answer(a2, ua2, q2, "barycentric inside", rv.bool_check)
if a2:
ua3 = rv.expect_vector(q3)
rv.check_answer(a3, ua3, q3, "barycentric mixing", rv.vector_check)
else:
return rv.combine((q1, q2, q3)), rv.combine((a1, a2, a3)), ()
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 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 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 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 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 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 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 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 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 totalq(ask=True): (cr, normal, cl, ld, ed, ca) = (rv.color(), rv.direction(), rv.color(), rv.direction(), rv.direction(), rv.color()) q = "Point p has a surface color of %s and a surface normal of %s. Given a light of color %s and direction %s, a view direction %s, and an ambient color %s, what will be p's final color, with a Phong exponent of 2?" % tuple(numpy.array_str(s) for s in (cr, normal, cl, ld, ed, ca)) a = diffuseColor(cl, cr, ld, normal) + specularColor(cl, ld, normal, ed, 2) + ca * cr if ask: ua = rv.expect_vector(q) rv.check_answer(a, ua, q, "total") 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 diffuseq(ask=True): cl = rv.color() cr = rv.color() ld = rv.direction() normal = rv.direction() 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 polygonq(ask=True): p, n = gf.plane() vertices = gf.polygon(p, n) if rv.coinflip(0.5): px = gf.pointProbablyInPolygon(vertices) else: px = gf.pointNotInPolygon(vertices) e, d = gf.rayToPoint(px) q = "Ray R has starting point e=%s and direction d=%s.\n Polygon P has vertices \n%s." % (numpy.array_str(e), numpy.array_str(d), '\n'.join(numpy.array_str(v) for v in vertices)) print(q) q1 = "What is the normal to P?" a1 = gf.getNormal(vertices) q2 = "What is the t intersection point of R and P?" a2 = gf.rayPlane(e, d, v=vertices) q3 = "What is the (x, y, z) intersection point on R at t?" a3 = gf.pointOnRay(e, d, a2) q4 = "Is the intersection point inside the polygon?" a4 = gf.pointInPolygon(a3, vertices) q5 = "Is the intersection point in front of the viewpoint e?" a5 = a2 > 0 if ask: ua1 = rv.expect_vector(q1) rv.check_answer(a1, ua1, q1, "normal", rv.vector_check) ua2 = rv.expect_float(q2) rv.check_answer(a2, ua2, q2, "ray-plane", rv.float_check) ua3 = rv.expect_vector(q3) rv.check_answer(a3, ua3, q3, "point on ray", rv.vector_check) ua4 = rv.expect_yesno(q4) rv.check_answer(a4, ua4, q4, "point in polygon", rv.bool_check) ua5 = rv.expect_yesno(q5) rv.check_answer(a5, ua5, q5, "ray distance", rv.bool_check) else: return rv.combine((q, q1, q2, q3, q4, q5)), rv.combine((a1, a2, a3, a4,a5), False), ()
def mipmapq(ask=True):
ir = np.random.randint(2**4, 2**7)
q = "Suppose a texture is applied to an area of size %d x %d." % (ir, ir)
q1 = "What two levels of detail (powers of two) should be used for trilinear interpolation?"
q2 = "How should each one be weighted?"
d = np.log2(ir)
a1 = 2**np.floor(d), 2**np.ceil(d)
dd = (ir - a1[0]) / (a1[1] - a1[0])
a2 = 1 - dd, dd
rv.writeModule(
dict(zip(("ir", "d", "dd", "a1", "a2"), (ir, d, dd, a1, a2))))
if ask:
print(q)
ua1 = rv.expect_vector(q1, 2)
rv.check_answer(a1, ua1, q1, "level of detail")
ua2 = rv.expect_vector(q2, 2)
rv.check_answer(a2, ua2, q2, "trilinear interpolation")
else:
return rv.combine((q, q1, q2)), rv.combine((a1, a2), False)
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 nearestq(ask=True):
u, v = np.round(np.random.random(2), 2)
rs, rt = np.random.randint(16, 2048, 2)
q = "Given (u, v) coordinates of (%.2f, %.2f) and a texture of size (%d, %d), what texel will be chosen by nearest neighbor sampling?" % (
u, v, rs, rt)
a = np.round(u * rs), np.round(v * rt)
rv.writeModule(dict(zip("u,v,rs,rt,a".split(','), (u, v, rs, rt, a))))
if ask:
ua = rv.expect_vector(q, 2)
rv.check_answer(a, ua, q, "nearest neighbor")
else:
return q, a
def triangleq(ask=True):
p, n = gf.plane()
vertices = gf.polygon(p, n, 3)
if rv.coinflip(0.5):
px = gf.pointProbablyInPolygon(vertices)
else:
px = gf.pointNotInPolygon(vertices)
e, d = gf.rayToPoint(px)
q = "Triangle T has vertices p0=%s, p1=%s, p2=%s. Ray R has starting point e=%s and direction d=%s." % tuple(numpy.array_str(s) for s in tuple(vertices) + (e, d))
q1 = "What are the beta and gamma barycentric coordinates and the t distance along the ray of the intersection between R and the plane defined by T?"
# answer calculations
e1 = vertices[1]-vertices[0]
e2 = vertices[2]-vertices[0]
x = numpy.cross(d, e2)
m = e1.dot(x) # determinant of original matrix
s = e - vertices[0] # solution
beta = s.dot(x)/m # |-d s p2-p0| = -(-d x (p2-p0)) dot s
r = numpy.cross(s, e1)
gamma = d.dot(r)/m
t = e2.dot(r)/m
a1 = (beta, gamma, t)
q2 = "Is the intersection point inside the triangle?"
a2 = beta >= 0 and beta <= 1 and gamma >= 0 and gamma <= 1
q3 = "Is the intersection point in front of the viewpoint e?"
a3 = t > 0
rv.writeModule(dict(zip(('p','n','vertices','e','d','e1','e2','x','m','s','beta','r','gamma','t', 'px'), (p, n, vertices, e, d, e1, e2, x, m, s, beta, r, gamma, t, px))))
if ask:
print(q)
ua = rv.expect_vector(q1)
rv.check_answer(numpy.array(a1), ua, q1, "triangle intersection", rv.vector_check)
ua = rv.expect_boolish(q2, {'y':True, 'n':False} )
rv.check_answer(a2, ua, q2, "triangle inside", rv.bool_check)
ua = rv.expect_boolish(q3, {'y':True, 'n':False} )
rv.check_answer(a3, ua, q3, "ray distance", rv.bool_check)
else:
finalq = rv.combine((q, q1, q2, q3), True)
finala = rv.combine((a1, a2, a3))
return finalq, finala, ()
def specularq(ask=True): cl = rv.color() ld = rv.direction() cr = rv.color() normal = rv.direction() r = gf.reflect(ld, normal) e = rv.direction() 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 linearq(ask=True):
smin, smax, tmin, tmax = rv.vector(4)
smin, smax = rv.strict_order(smin, smax)
tmin, tmax = rv.strict_order(tmin, tmax)
s = np.random.randint(smin, smax + 1)
t = np.random.randint(tmin, tmax + 1)
u = (s - smin) / (smax - smin)
v = (t - tmin) / (tmax - tmin)
q = "Given a 2D image texture with coordinates ranging from 0 to 1, and a rectangular surface with x ranging from %d to %d and y ranging from %d to %d, what are the (u, v) texture coordinates of surface point (%d, %d) by simple linear interpolation?" % (
smin, smax, tmin, tmax, s, t)
a = (u, v)
if ask:
ua = rv.expect_vector(q, 2)
rv.check_answer(a, ua, q, 'linear interpolation')
else:
return q, a
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")
