def __init__(self, width=1.5, thickness=0.3):
tangent = v3.vector(0, 0, 1)
up = v3.vector(0, width, 0)
right = v3.cross(up, tangent)
right = thickness / width * right
self.arcs = [
right + up, +up, -right + up, -right - up, -up, right - up
]
self.normals = calc_cyclic_normals(self.arcs, tangent)
def test_vector_make(): v = v3.vector() assert v3.is_similar_vector(v3.vector(), v3.vector(0, 0, 0)) v = v3.random_vector() w = v3.vector(v) assert v3.is_similar_vector(v, w) u = v3.vector(*v) assert v3.is_similar_vector(v, u) w = v u = v3.random_vector() v3.set_vector(w, *u) assert v3.is_similar_vector(w, v)
def test_vector_make():
v = v3.vector()
assert v3.is_similar_vector(v3.vector(), v3.vector(0, 0, 0))
v = v3.random_vector()
w = v3.vector(v)
assert v3.is_similar_vector(v, w)
u = v3.vector(*v)
assert v3.is_similar_vector(v, u)
w = v
u = v3.random_vector()
v3.set_vector(w, *u)
assert v3.is_similar_vector(w, v)
def __init__(self, n_arc=10, radius=1.0):
self.n_arc = n_arc
tangent = v3.vector(0, 0, 1)
rotator = v3.vector(0, radius, 0)
self.arcs = []
angle = v3.radians(360 / n_arc)
rotation = v3.rotation(tangent, angle)
self.arcs.append(v3.vector(rotator))
for i_segment in range(n_arc - 1):
rotator = v3.transform(rotation, rotator)
self.arcs.append(rotator)
self.normals = calc_cyclic_normals(self.arcs, tangent)
def test_orthogonality(): x = v3.vector(v3.random_mag(), 0, 0) y = v3.vector(0, v3.random_mag(), 0) z = v3.vector(0, 0, v3.random_mag()) ry_x = v3.transform(v3.rotation(y, v3.radians(90)), x) assert v3.is_similar_vector(v3.norm(ry_x), -v3.norm(z)) assert v3.is_similar_mag(v3.mag(ry_x), v3.mag(x)) ry_z = v3.transform(v3.rotation(y, v3.radians(90)), z) assert v3.is_similar_vector(v3.norm(ry_z), v3.norm(x)) cross_x_y = v3.cross(x, y) assert v3.is_similar_vector(v3.norm(cross_x_y), v3.norm(z)) cross_y_x = v3.cross(y, x) assert v3.is_similar_vector(v3.norm(cross_y_x), -v3.norm(z))
def test_orthogonality():
x = v3.vector(v3.random_mag(), 0, 0)
y = v3.vector(0, v3.random_mag(), 0)
z = v3.vector(0, 0, v3.random_mag())
ry_x = v3.transform(v3.rotation(y, v3.radians(90)), x)
assert v3.is_similar_vector(v3.norm(ry_x), -v3.norm(z))
assert v3.is_similar_mag(v3.mag(ry_x), v3.mag(x))
ry_z = v3.transform(v3.rotation(y, v3.radians(90)), z)
assert v3.is_similar_vector(v3.norm(ry_z), v3.norm(x))
cross_x_y = v3.cross(x, y)
assert v3.is_similar_vector(v3.norm(cross_x_y), v3.norm(z))
cross_y_x = v3.cross(y, x)
assert v3.is_similar_vector(v3.norm(cross_y_x), -v3.norm(z))
def __init__(self, n_stack=5, n_arc=5, scale=1.0):
self.arcs = []
self.stacks = []
self.indices = []
self.points = []
vert_angle = math.pi / (n_stack - 1)
arc_angle = math.pi * 2.0 / n_arc
for i_stack in range(n_stack):
radius = math.sin(i_stack * vert_angle)
z = -scale * math.cos(i_stack * vert_angle)
for i_arc in range(n_arc):
x = scale * radius * math.cos(i_arc * arc_angle)
y = scale * radius * math.sin(i_arc * arc_angle)
self.points.append(v3.vector(x, y, z))
for i_stack in range(n_stack - 1):
for i_arc in range(n_arc):
j_arc = (i_arc + 1) % n_arc
self.indices.extend([
(i_stack) * n_arc + i_arc,
(i_stack + 1) * n_arc + i_arc,
(i_stack + 1) * n_arc + j_arc,
(i_stack + 1) * n_arc + j_arc,
(i_stack) * n_arc + j_arc,
(i_stack) * n_arc + i_arc,
])
self.n_vertex = n_stack * n_arc
def __init__(self, n_arc, radius=1.0):
self.points = []
self.normals = []
self.indices = []
arc_angle = math.pi * 2.0 / n_arc
for z in [0.0, 1.0]:
for j in range(n_arc):
x = radius * math.cos(j * arc_angle)
y = radius * math.sin(j * arc_angle)
self.normals.append(v3.vector(x, y, 0.0))
self.points.append(v3.vector(x, y, z))
for i_arc in range(n_arc):
j_arc = (i_arc + 1) % n_arc
self.indices.extend([
j_arc, i_arc, n_arc + i_arc, j_arc, n_arc + i_arc,
n_arc + j_arc
])
self.n_vertex = 2 * n_arc
def test_matrix_combination():
n = 4
x = v3.random_vector()
y1 = v3.vector(x)
matrix = v3.identity()
for i in range(4):
r_matrix = v3.random_matrix()
y1 = v3.transform(r_matrix, y1)
matrix = v3.combine(r_matrix, matrix)
y2 = v3.transform(matrix, x)
assert v3.is_similar_vector(y1, y2)
def test_matrix_combination():
n = 4
x = v3.random_vector()
y1 = v3.vector(x)
matrix = v3.identity()
for i in range(4):
r_matrix = v3.random_matrix()
y1 = v3.transform(r_matrix, y1)
matrix = v3.combine(r_matrix, matrix)
y2 = v3.transform(matrix, x)
assert v3.is_similar_vector(y1, y2)
def __init__(self, length, width, thickness):
self.vertices = [
v3.vector(thickness, 0, length),
v3.vector(thickness, -width, -length),
v3.vector(thickness, width, -length),
v3.vector(-thickness, 0, length),
v3.vector(-thickness, -width, -length),
v3.vector(-thickness, width, -length),
]
self.indices = [1, 0, 2, 3, 4, 5]
n_arc = 3
for i in range(n_arc):
j = (i + 1) % n_arc
self.indices.extend([i + n_arc, i, j, j + n_arc, i + n_arc, j])
def test_translation(): x = v3.vector(v3.random_mag(), 0, 0) y = v3.vector(0, v3.random_mag(), 0) x_and_y = v3.transform(v3.translation(y), x) assert v3.is_similar_vector(x_and_y, x+y)
def test_translation():
x = v3.vector(v3.random_mag(), 0, 0)
y = v3.vector(0, v3.random_mag(), 0)
x_and_y = v3.transform(v3.translation(y), x)
assert v3.is_similar_vector(x_and_y, x + y)
