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 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 ioq(ask=True): pipeline = [(('object', 'model'), ('model', ), ('world', )), (('world', ), ('view', 'camera'), ('camera', 'eye')), (('camera', 'eye'), ('projection', ), ('canonical view volume', 'clip')), (('canonical view volume', 'clip'), ('perspective division', ), ('2d', )), (('2d', ), ('viewport', ), ('screen', ))] stage = rv.choose_random_from(pipeline) space_syn = rv.choose_random_from(("space", "coordinates")) qp = ( rv.choose_random_from(stage[0]), rv.choose_random_from(stage[1]), rv.choose_random_from(stage[2]), ) qidx = rv.choose_random_from(range(len(qp))) q = 'The %s transformation transforms %s %s into %s %s.\n' % ( qp[1], qp[0], space_syn, qp[2], space_syn) q = q.replace(qp[qidx], rv.blank()) # hacky: fix phrasing for some terms that don't fit templates q = q.replace("The perspective division transformation", "Perspective division") q = q.replace("canonical view volume %s" % space_syn, "the canonical view volume") a = stage[qidx] categories = [y for x in pipeline for y in x[qidx]] if ask: ua = rv.expect_categorical(q, categories) rv.check_answer(a, ua, q, "input/output", part_of_str_answer_is_in_choices) else: return q, a, (categories)
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 samplingq(ask=True): ir = np.random.randint(2**4, 2**7, 2) q1 = "Given a texture of size (%d, %d) and an image of size (%d, %d), how many texels must cover each pixel?" % ( ir[0], ir[0], ir[1], ir[1]) a1 = ir[0] / ir[1] q2 = "Is this a problem of magnification (mag) or minification (min)?" if ir[0] < ir[1]: a2 = "mag" else: a2 = "min" rv.writeModule(dict(zip("ir, a1, a2".split(','), (ir, a1, a2)))) if ask: ua1 = rv.expect_float(q1) rv.check_answer(a1, ua1, q1, "texel:pixel") ua2 = rv.expect_categorical(q2, ('mag', 'min')) rv.check_answer(a2, ua2, q2, "magnification") else: return rv.combine((q1, q2), False), rv.combine((a1, a2), False)