def __init__(self, origin, normal, resolutionX, resolutionY, pixelSizeInWorldCoords): Plane.__init__(self, origin, normal) self.resolutionX = resolutionX self.resolutionY = resolutionY self.pixelSizeInWorldCoords = pixelSizeInWorldCoords self.width = resolutionX * pixelSizeInWorldCoords self.height = resolutionY * pixelSizeInWorldCoords
def test_from_normal_and_point():
corners1 = [
Point(0.0, 0.0, 0.0),
Point(1.0, 0.0, 0.0),
Point(1.0, 1.0, 0.0),
Point(0.0, 1.0, 0.0)
]
center1 = Point(0.5, 0.5, 0.0)
polygon1 = Polygon(corners1, center1)
plane1 = Plane.from_normal_and_point(polygon1.plane().normal(), center1)
assert polygon1.plane(
) == plane1 # tests the reduced normal form coefficients.
corners2 = [
Point(0.0, 0.0, 0.0),
Point(0.0, 1.0, 0.0),
Point(0.0, 1.0, 1.0),
Point(0.0, 0.0, 1.0)
]
center2 = Point(0.0, 0.5, 0.5)
polygon2 = Polygon(corners2, center2)
plane2 = Plane.from_normal_and_point(polygon2.plane().normal(), center2)
assert polygon2.plane() == plane2
corners4 = [
Point(1.0, 0.0, 0.0),
Point(1.0, 1.0, 0.0),
Point(1.0, 1.0, 1.0),
Point(1.0, 0.0, 1.0)
]
center4 = Point(1.0, 0.5, 0.5)
polygon4 = Polygon(corners4, center4)
plane4 = Plane.from_normal_and_point(polygon4.plane().normal(), center4)
assert polygon4.plane() == plane4
def test_on_interior_side(a, b, c, d):
plane = Plane.from_normal(Vector(1.0, 0.0, 0.0))
assert b.on_interior_side_of(plane) == +1 # Interior side
assert c.on_interior_side_of(plane) == 0 # In plane
assert d.on_interior_side_of(plane) == -1 # Exterior side
points = [ Point(0.0, 0.0, -1.0), Point(0.0, 1.0, -1.0), Point(0.0, 1.0, 0.0), Point(0.0, 0.0, 0.0) ]
plane = Plane.from_points(points)
assert b.on_interior_side_of(plane) == +1 # Interior side
assert c.on_interior_side_of(plane) == 0 # In plane
assert d.on_interior_side_of(plane) == -1 # Exterior side
def test_intersection():
plane = Plane(0.0, 0.0, 1.0, -0.9)
a = Point(0.5, 0.5, -0.9)
b = Point(0.0, 0.0, 0.0)
assert plane.intersection(a, b) == Point(-0.5, -0.5, 0.9)
points = [Point(0.5, 0.0, 0.0), Point(0.5, 1.0, 0.0), Point(0.5, 1.0, 1.0), Point(0.5, 0.1, 1.0)]
polygon = Polygon(points, Point(0.5, 0.5, 0.5))
source = Point(0.5, 0.5, 0.5)
mirror = source.mirror_with(Plane.from_normal_and_point(Vector(1.0, 0.0, 0.0), Point(1.0, 0.5, 0.5)))
intersection = polygon.plane().intersection(mirror, Point(1.0, 0.0, 0.0))
assert intersection == Point(0.5, -0.5, -0.5)
def __init__(self):
self.objects = [Plane(Point3D(0, -.5, 0),
Vector3D(0, 1, 0),
color=Color(1, 1, 1)),
Sphere(Point3D(0, 0, -1.0), 0.1,
color=Color(1.0, 0, 0))]
self.lights = [UniformPointLight(Point3D(-.5, 0, -1),
Color(100, 100, 100))]
def test_on_interior_side(a, b, c, d):
plane = Plane.from_normal(Vector(1.0, 0.0, 0.0))
assert b.on_interior_side_of(plane) == +1 # Interior side
assert c.on_interior_side_of(plane) == 0 # In plane
assert d.on_interior_side_of(plane) == -1 # Exterior side
points = [
Point(0.0, 0.0, -1.0),
Point(0.0, 1.0, -1.0),
Point(0.0, 1.0, 0.0),
Point(0.0, 0.0, 0.0)
]
plane = Plane.from_points(points)
assert b.on_interior_side_of(plane) == +1 # Interior side
assert c.on_interior_side_of(plane) == 0 # In plane
assert d.on_interior_side_of(plane) == -1 # Exterior side
def make_conic(R, K, z_offset, material=None, reverse_normal=False):
"""
See https://en.wikipedia.org/wiki/Conic_constant
r^2 - 2Rz + (K+1)z^2 = 0
Be careful about the sign convention for radius of curvature. We follow the convention
in https://en.wikipedia.org/wiki/Conic_constant but this is opposite the convention in
https://en.wikipedia.org/wiki/Lens#Lensmaker's_equation .
Args:
R: radius of curvature; use R > 0 for concave "up" (direction of positive z-axis) while R < 0
is concave "down"
K: conic constant; should be < -1 for hyperboloids, -1 for paraboloids, > -1 for ellipses
(including 0 for spheres). The relationship with eccentricity e is K = -e^2 (when
K <= 0).
z_offset: z-coordinate where the surface intersects z-axis
material: mostly self explanatory; None means reflector
reverse_normal: If true, surface points in direction of negative z-axis rather than
positive z-axis
"""
M = np.diag([1, 1, (K + 1), 0])
M[2, 3] = -R
M[3, 2] = M[2, 3]
# For either sign of R, we want the convention that gradient points up at origin.
# That gradient is (0,0,-R).
# When R < 0, we already have that.
# For R > 0, we need to negate M to get that.
if R > 0:
M *= -1
if reverse_normal:
M *= -1
quad = Quadric(M)
geometry = quad.untransform(translation3f(0, 0, -z_offset))
if R > 0:
# We want to keep the top sheet.
# TODO: Let clip_z be halfway between the two foci.
clip_z = z_offset - 1e-6
clip = Plane(make_bound_vector(point(0, 0, clip_z), vector(0, 0, -1)))
else:
clip_z = z_offset + 1e-6
clip = Plane(make_bound_vector(point(0, 0, clip_z), vector(0, 0, 1)))
return SubElement(geometry, clip, material=material)
def test_pickle():
a = Plane(0.0, 0.0, 1.0, -0.9)
with tempfile.TemporaryDirectory() as tmpdirname:
with open('obj.pickle', mode='w+b') as f:
pickle.dump(a, f)
with open('obj.pickle', mode='r+b') as f:
a2 = pickle.load(f)
assert a2 == a
def test_from_normal_and_point():
corners1 = [ Point(0.0, 0.0, 0.0), Point(1.0, 0.0, 0.0), Point(1.0, 1.0, 0.0), Point(0.0, 1.0, 0.0) ]
center1 = Point(0.5, 0.5, 0.0)
polygon1 = Polygon(corners1, center1)
plane1 = Plane.from_normal_and_point(polygon1.plane().normal(), center1)
assert polygon1.plane() == plane1 # tests the reduced normal form coefficients.
corners2 = [ Point(0.0, 0.0, 0.0), Point(0.0, 1.0, 0.0), Point(0.0, 1.0, 1.0), Point(0.0, 0.0, 1.0) ]
center2 = Point(0.0, 0.5, 0.5)
polygon2 = Polygon(corners2, center2)
plane2 = Plane.from_normal_and_point(polygon2.plane().normal(), center2)
assert polygon2.plane() == plane2
corners4 = [ Point(1.0, 0.0, 0.0), Point(1.0, 1.0, 0.0), Point(1.0, 1.0, 1.0), Point(1.0, 0.0, 1.0) ]
center4 = Point(1.0, 0.5, 0.5)
polygon4 = Polygon(corners4, center4)
plane4 = Plane.from_normal_and_point(polygon4.plane().normal(), center4)
assert polygon4.plane() == plane4
def __init__(self, start, p2, end, color=(0, 1, 0, .3), num_points=50):
plane = Plane(start, p2, end)
pr1 = plane.project(start)
pr2 = plane.project(p2)
pr3 = plane.project(end)
circle = Circle(pr1, pr2, pr3)
radian_len = circle.chord_angle(pr1.distance(pr3))
increment = radian_len / num_points
diff = pr1 - circle.center
offset = np.arctan(diff.y / diff.x)
# the range of arcsin is from -90 to 90 so (or radians but that's harder to type)
if diff.x < 0:
offset += np.pi / 2
else:
offset -= np.pi / 2
points3d = []
for p in range(num_points):
radian = increment * p - offset
point = circle.center + Vector(
np.sin(radian) * circle.radius,
np.cos(radian) * circle.radius)
points3d.append(plane.unproject(point))
points3d.append(end)
super(Arc, self).__init__(pos=np.array(points3d),
color=color,
width=2,
antialias=True,
mode='line_strip')
def test_intersection():
plane = Plane(0.0, 0.0, 1.0, -0.9)
a = Point(0.5, 0.5, -0.9)
b = Point(0.0, 0.0, 0.0)
assert plane.intersection(a, b) == Point(-0.5, -0.5, 0.9)
points = [
Point(0.5, 0.0, 0.0),
Point(0.5, 1.0, 0.0),
Point(0.5, 1.0, 1.0),
Point(0.5, 0.1, 1.0)
]
polygon = Polygon(points, Point(0.5, 0.5, 0.5))
source = Point(0.5, 0.5, 0.5)
mirror = source.mirror_with(
Plane.from_normal_and_point(Vector(1.0, 0.0, 0.0),
Point(1.0, 0.5, 0.5)))
intersection = polygon.plane().intersection(mirror, Point(1.0, 0.0, 0.0))
assert intersection == Point(0.5, -0.5, -0.5)
from geometry import create_cube, clip, Plane
from unfolding import unfold
import svg
cube = create_cube()
plane1 = Plane(0,0,1, 1/3)
plane2 = Plane(0,0,1,-1/3)
ph12 = clip(cube,plane2)
ph1 = clip(ph12,plane1)
ph2 = clip(ph12,-plane1)
ph3 = clip(cube,-plane2)
svg.write_unfolded_faces('test2a.svg', unfold(ph1))
svg.write_unfolded_faces('test2b.svg', unfold(ph2))
svg.write_unfolded_faces('test2c.svg', unfold(ph3))
if out != b'0\r\n':
print(out)
if out == b'':
raise TimeoutError('Arduino serial not respond')
def __del__(self):
self._pos = [0, 0, 0]
self._serial.close()
if __name__ == "__main__":
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from geometry import Ray, Plane, Intersection, Reflection
plt.ion()
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.set_xlim(-100, 100)
ax.set_ylim(-90, 90)
ax.set_zlim(0, 600)
p1, p2 = Plane(ax=ax), Plane(ax=ax)
p1.z, p2.z = 200, 400
p1.phi, p2.phi = 0, 0
c = Chanosat_Driver(ax=ax)
r1 = Reflection(c, p1)
a = Intersection(c, p1)
#!/usr/bin/python
from geometry import Plane, Sphere, Triangle, Cube
from scene import Screen, Scene
from tracer import SimpleRayTracer, SimpleShadowRayTracer, ShadingShadowRayTracer, RecursiveRayTracer, PathTracer
from material import Material, Color
from window import Window
if __name__ == "__main__":
p1 = Plane([0, 5, 0], [0, -1, 0], Material(Color(255, 0, 0), 1, 0, 0.1))
p2 = Plane([0, -5, 0], [0, 1, 0], Material(Color(0, 255, 0), 1, 0, 0.1))
p3 = Plane([5, 0, 0], [-1, 0, 0], Material(Color(0, 0, 255), 1, 0, 0.1))
p4 = Plane([-5, 0, 0], [1, 0, 0], Material(Color(255, 255, 0), 1, 0, 0.1))
p5 = Plane([0, 0, 5], [0, 0, -1], Material(Color(255, 0, 255), 1, 0, 0.1))
p6 = Plane([0, 0, -5], [0, 0, 1], Material(Color(0, 255, 255), 1, 0, 0.1))
s1 = Sphere([0, 3, 2], 2,
Material(Color(100, 100, 100),
1,
0,
0.1,
refractive=False,
n=1.52))
s2 = Sphere([4, 2, 1], 0.5,
Material(Color(100, 100, 100),
1,
0,
0.1,
refractive=False,
n=1.52))
s3 = Sphere([-3, 2, 1], 1,
from geometry import Point3, create_cube, clip, Plane
from unfolding import unfold
import svg
import math
m = 5
cube = create_cube()
rest = cube
pieces = []
for i in range(m):
theta = math.pi/6 * (1-2*i/(m-1))
u = Point3(math.sin(theta),0,math.cos(theta))
plane = Plane(u.x,u.y,u.z, -2*u.x)
pieces.append(clip(rest, -plane))
rest = clip(rest, plane)
pieces.append(rest)
for i,piece in enumerate(pieces):
svg.write_unfolded_faces(f"test3-{i+1}.svg", unfold(piece))
from geometry import create_cube, clip, Plane
from unfolding import unfold
import svg
cube = create_cube()
cube.assert_integrity()
plane = Plane(1,1,0,0)
ph = clip(cube,plane)
ph.assert_integrity()
svg.write_unfolded_faces('test5.svg', unfold(ph))
def __init__(self, filename="scene.json"):
self.lights = []
self.objects = []
# read in the json
with open(filename, "r") as json_file:
scene = json.load(json_file)
for light in scene['scene']['lights']:
l = Light(origin=light['origin'],
radius=light['radius'],
brightness=light['brightness'],
color=light['color'])
self.lights.append(l)
self.objects.append(l)
for object in scene['scene']['objects']:
texture = None
scale = 1.0
if 'texture' in object:
texture = object['texture']
if 'scale' in object:
scale = object['scale']
if (object['shape'] == "Sphere"):
self.objects.append(
Sphere(origin=object['origin'],
radius=object['radius'],
diffuse=object['diffuse'],
reflection=object['reflection'],
shiny=object['shiny'],
k=object['k'],
refraction=object['refraction'],
index=object['index'],
color=object['color'],
texture=texture,
uv=object['uv']))
elif (object['shape'] == "Skybox"):
self.objects.append(
Skybox(origin=object['origin'],
radius=object['radius'],
diffuse=object['diffuse'],
reflection=object['reflection'],
shiny=object['shiny'],
k=object['k'],
refraction=object['refraction'],
index=object['index'],
color=object['color'],
texture=texture,
uv=object['uv']))
elif (object['shape'] == "Plane"):
self.objects.append(
Plane.Plane(origin=object['origin'],
normal=object['normal'],
diffuse=object['diffuse'],
reflection=object['reflection'],
refraction=object['refraction'],
index=object['index'],
shiny=object['shiny'],
k=object['k'],
color=object['color'],
texture=texture,
scale=scale))
elif (object['shape'] == "Triangle"):
self.objects.append(
Triangle.Triangle(v0=object['v0'],
v1=object['v1'],
v2=object['v2'],
diffuse=object['diffuse'],
reflection=object['reflection'],
refraction=object['refraction'],
index=object['index'],
shiny=object['shiny'],
k=object['k'],
color0=object['color0'],
color1=object['color1'],
color2=object['color2']))
camera = scene['scene']['camera']
self.camera = Camera(origin=camera['origin'],
target=camera['target'],
length=camera['length'],
aperture=camera['aperture'],
samples=camera['samples'])
self.ambient = np.array(scene['scene']['ambient'])
self.background = np.array(scene['scene']['background'])
from unfolding import unfold
import svg
import math
m = 5
cube = create_cube()
rest = cube
pieces = []
phi = math.pi / 4
cs_phi = math.cos(phi)
sn_phi = math.sin(phi)
for i in range(m):
theta = math.pi / 6 * (1 - 2 * i / (m - 1))
u = Point3(math.sin(theta), 0, math.cos(theta))
u.x, u.y = cs_phi * u.x, sn_phi * u.x
plane = Plane(u.x, u.y, u.z, -2 * (u.x + u.y))
pieces.append(clip(rest, -plane))
rest = clip(rest, plane)
pieces.append(rest)
for i, piece in enumerate(pieces):
svg.write_unfolded_faces(f"test4-{i+1}.svg", unfold(piece))
def __get_bragg_planes(zone_points):
"""Return the Bragg planes."""
for points in zone_points:
middle_points = map(lambda point: point * 0.5, points)
for middle_point in middle_points:
yield Plane(middle_point, Vector3D(tuple(middle_point)))