def generate_octahedra():
view = create_lookat(eye=[-15, -60, 120], target=[0, 0, 0], up=[0, 1, 0])
projection = create_perspective(fovy=15, aspect=1, near=10, far=200)
camera = svg3d.Camera(view, projection)
verts, faces = icosahedron()
verts, faces = np.float32(verts), np.uint32(faces)
faces = 15 * verts[faces]
centroids = []
for face in faces:
centroid = np.float32([0, 0, 0])
for vert in face:
centroid += vert
centroid /= len(face)
centroids.append(centroid)
centroids = np.float32([centroids])
point_style = dict(fill="black", fill_opacity="0.75", stroke="none")
poly_style = dict(
fill="#f0f0f0",
fill_opacity="0.75",
stroke="black",
stroke_linejoin="round",
stroke_width="0.01",
)
left_viewport = svg3d.Viewport.from_string("-1.0 -0.5 1.0 1.0")
right_viewport = svg3d.Viewport.from_string("0.0 -0.5 1.0 1.0")
back_shader = lambda face_index, winding: None if winding >= 0 else poly_style
front_shader = lambda face_index, winding: None if winding < 0 else poly_style
two_pass_scene = svg3d.Scene([])
two_pass_scene.add_mesh(svg3d.Mesh(faces, back_shader))
two_pass_scene.add_mesh(svg3d.Mesh(faces, front_shader))
two_pass_scene.add_mesh(
svg3d.Mesh(centroids, style=point_style, circle_radius=0.005)
)
one_pass_scene = svg3d.Scene([])
one_pass_scene.add_mesh(svg3d.Mesh(faces, style=poly_style))
one_pass_scene.add_mesh(
svg3d.Mesh(centroids, style=point_style, circle_radius=0.005)
)
view0 = svg3d.View(camera, one_pass_scene, left_viewport)
view1 = svg3d.View(camera, two_pass_scene, right_viewport)
svg3d.Engine([view0, view1]).render(
"octahedra.svg", (512, 256), "-1.0 -0.5 2.0 1.0"
)
def capsule():
verts, indices = octasphere(ndivisions=3,
radius=4,
width=18,
height=0,
depth=0)
view_matrix = create_lookat(eye=[25, 20, 60],
target=[0, 0, 0],
up=[0, 1, 0])
faces = verts[indices]
ones = np.ones(faces.shape[:2] + (1, ))
eyespace_faces = np.dstack([faces, ones])
eyespace_faces = np.dot(eyespace_faces, view_matrix)[:, :, :3]
L = pyrr.vector.normalize(np.float32([20, 20, 50]))
E = np.float32([0, 0, 1])
H = pyrr.vector.normalize(L + E)
def frontface_shader(face_index, winding):
if winding < 0:
return None
face = eyespace_faces[face_index]
p0, p1, p2 = face[0], face[1], face[2]
N = pyrr.vector3.cross(p1 - p0, p2 - p0)
l2 = pyrr.vector3.squared_length(N)
if l2 > 0:
N = N / np.sqrt(l2)
df = max(0, np.dot(N, L))
sf = pow(max(0, np.dot(N, H)), SHININESS)
color = df * DIFFUSE + sf * SPECULAR
color = np.power(color, 1.0 / 2.2)
return dict(fill=rgb(*color), stroke="black", stroke_width="0.001")
return svg3d.Mesh(faces, frontface_shader)
def create_surface_plot():
divs = 25
X, Y = np.meshgrid(np.linspace(-2, 2, divs), np.linspace(-2, 2, divs))
Z = 2 * X * np.exp(-X * X - Y * Y)
verts = np.reshape(np.dstack([X, Y, Z]), [divs * divs, 3])
i, j = np.mgrid[0 : divs * 2, 0 : divs * 2]
coords = np.uint32(np.dstack([i / 2, j / 2]))
coords = coords[1 : divs * 2 - 1, 1 : divs * 2 - 1]
indices = coords[:, :, 0] * divs + coords[:, :, 1]
nw = indices[0::2][:, 0::2]
ne = indices[0::2][:, 1::2]
sw = indices[1::2][:, 0::2]
se = indices[1::2][:, 1::2]
indices = np.dstack([nw, ne, se, sw])
indices = np.reshape(indices, [(divs - 1) * (divs - 1), 4])
faces = verts[indices]
view = create_lookat(eye=[5, 20, 5], target=[0, 0, 0], up=[0, 0, 1])
projection = create_perspective(fovy=15, aspect=1, near=1, far=100)
camera = svg3d.Camera(view, projection)
style = dict(
fill="#f0f0f0",
fill_opacity="0.75",
stroke="black",
stroke_linejoin="round",
stroke_width="0.001",
)
rgb = apply_turbo_colormap(Z)
colors = np.reshape(rgb, [divs * divs, 3])
colors = colors[indices]
def shader(face_index, winding):
face_colors = colors[face_index]
rgb = ",".join([str(int(num * 255)) for num in face_colors[0]])
style["fill"] = f"rgb({rgb})"
return style
scene = svg3d.Scene([svg3d.Mesh(faces, shader)])
view = svg3d.View(camera, scene)
svg3d.Engine([view]).render("plot.svg")
def make_octaspheres(ndivisions: int,
radius: float,
width=0,
height=0,
depth=0):
verts, indices = octasphere(ndivisions, radius, width, height, depth)
faces = verts[indices]
left = translate_faces(faces, [-12, 0, 0])
right = translate_faces(rotate_faces(faces), [12, 0, 0])
faces = merge_faces(left, right)
ones = np.ones(faces.shape[:2] + (1, ))
eyespace_faces = np.dstack([faces, ones])
eyespace_faces = np.dot(eyespace_faces, view_matrix)[:, :, :3]
L = pyrr.vector.normalize(np.float32([20, 20, 50]))
E = np.float32([0, 0, 1])
H = pyrr.vector.normalize(L + E)
def frontface_shader(face_index, winding):
if winding < 0:
return None
face = eyespace_faces[face_index]
p0, p1, p2 = face[0], face[1], face[2]
N = pyrr.vector3.cross(p1 - p0, p2 - p0)
l2 = pyrr.vector3.squared_length(N)
if l2 > 0:
N = N / np.sqrt(l2)
df = max(0, np.dot(N, L))
sf = pow(max(0, np.dot(N, H)), SHININESS)
color = df * DIFFUSE + sf * SPECULAR
color = np.power(color, 1.0 / 2.2)
return dict(fill=rgb(*color), stroke="black", stroke_width="0.001")
print(
f"Generated octasphere: {ndivisions}, {radius}, {width}, {height}, {depth}"
)
return [svg3d.Mesh(faces, frontface_shader)]
def generate_overlapping_triangles():
X = 1
Y = 2
view = create_lookat(eye=[1.5, 1.5, 5], target=[1.5, 1.5, 0], up=[0, 1, 0])
projection = create_ortho(-X, X, -Y, Y, 0, 10)
pick = pyrr.matrix44.create_from_translation([1, 0, 0])
left_camera = svg3d.Camera(view, np.dot(projection, pick))
projection = create_ortho(-X, X, -Y, Y, 0, 10)
pick = pyrr.matrix44.create_from_translation([-1, 0, 0])
right_camera = svg3d.Camera(view, np.dot(pick, projection))
z0 = 0.00
z1 = 0.01
z2 = 0.02
z3 = -0.03
faces = np.float32(
[
[(0, 0, z0), (1, 0, z0), (0.5, 3, z0)],
[(0, 2, z1), (0, 3, z1), (3, 2.5, z1)],
[(2, 3, z2), (3, 3, z2), (2.5, 0, z2)],
[(3, 0, z3), (3, 1, z3), (0, 0.5, z3)],
]
)
poly_style = dict(
fill="#e0e0e0",
fill_opacity="0.75",
stroke="black",
stroke_linejoin="round",
stroke_width="0.01",
)
left_scene = svg3d.Scene([svg3d.Mesh(faces, style=poly_style)])
left_view = svg3d.View(
left_camera, left_scene, svg3d.Viewport.from_string("-.5 -.5 .5 1")
)
z3 = 0.03
faces = np.float32(
[
[(0, 0, z0), (1, 0, z0), (0.5, 3, z0)],
[(0, 2, z1), (0, 3, z1), (3, 2.5, z1)],
[(2, 3, z2), (3, 3, z2), (2.5, 0, z2)],
[(3, 0, z3), (3, 1, z3), (0, 0.5, z3)],
]
)
poly_style = dict(
fill="#e0e0e0",
fill_opacity="0.75",
stroke="black",
stroke_linejoin="round",
stroke_width="0.01",
)
right_scene = svg3d.Scene([svg3d.Mesh(faces, style=poly_style)])
right_view = svg3d.View(
right_camera, right_scene, svg3d.Viewport.from_string("0 -.5 .5 1")
)
svg3d.Engine([left_view, right_view]).render("overlapping_triangles.svg")
def create_complex_shapes():
projection = create_perspective(fovy=25, aspect=1, near=10, far=200)
view = create_lookat(eye=[25, 20, 60], target=[0, 0, 0], up=[0, 1, 0])
camera = svg3d.Camera(view, projection)
# Parametric Sphere
slices, stacks, radius = 64, 64, 12
faces = radius * parametric_surface(slices, stacks, sphere)
antialiasing = "auto" # use 'crispEdges' to fix cracks
def shader(face_index, winding):
slice = int(face_index / 64)
stack = int(face_index % 64)
if slice % 3 == 0 or stack % 3 == 0:
return dict(
fill="black",
fill_opacity="1.0",
stroke="none",
shape_rendering=antialiasing,
)
return dict(
fill="white",
fill_opacity="0.75",
stroke="none",
shape_rendering=antialiasing,
)
scene = svg3d.Scene([svg3d.Mesh(faces, shader)])
svg3d.Engine([svg3d.View(camera, scene)]).render("parametric_sphere.svg")
# Sphere Shell
verts, faces = icosahedron()
verts, faces = subdivide(verts, faces)
verts, faces = subdivide(verts, faces)
verts, faces = np.float32(verts), np.int32(faces)
faces = verts[faces]
def backface_shader(face_index, winding):
if winding >= 0:
return None
return dict(
fill="#7f7fff",
fill_opacity="1.0",
stroke="black",
stroke_linejoin="round",
stroke_width="0.001",
stroke_dasharray="0.01",
)
def frontface_shader(face_index, winding):
if winding < 0 or faces[face_index][0][2] > 0.9:
return None
return dict(
fill="#7fff7f",
fill_opacity="0.6",
stroke="black",
stroke_linejoin="round",
stroke_width="0.003",
)
scene = svg3d.Scene([])
scene.add_mesh(svg3d.Mesh(12.0 * faces, backface_shader))
scene.add_mesh(svg3d.Mesh(12.0 * faces, frontface_shader))
svg3d.Engine([svg3d.View(camera, scene)]).render("sphere_shell.svg")
# Sphere Lighting
ones = np.ones(faces.shape[:2] + (1,))
eyespace_faces = np.dstack([faces, ones])
eyespace_faces = np.dot(eyespace_faces, view)[:, :, :3]
shininess = 100
L = pyrr.vector.normalize(np.float32([20, 20, 50]))
E = np.float32([0, 0, 1])
H = pyrr.vector.normalize(L + E)
def frontface_shader(face_index, winding):
if winding < 0:
return None
face = eyespace_faces[face_index]
p0, p1, p2 = face[0], face[1], face[2]
N = pyrr.vector.normalize(pyrr.vector3.cross(p1 - p0, p2 - p0))
df = max(0, np.dot(N, L))
sf = pow(max(0, np.dot(N, H)), shininess)
color = df * np.float32([1, 1, 0]) + sf * np.float32([1, 1, 1])
color = np.power(color, 1.0 / 2.2)
return dict(
fill=rgb(*color), fill_opacity="1.0", stroke="black", stroke_width="0.001"
)
scene = svg3d.Scene([])
scene.add_mesh(svg3d.Mesh(12.0 * faces, frontface_shader))
svg3d.Engine([svg3d.View(camera, scene)]).render("sphere_lighting.svg")
# Mobius Tube
slices, stacks, radius = 48, 32, 7
faces = radius * parametric_surface(slices, stacks, mobius_tube)
ones = np.ones(faces.shape[:2] + (1,))
eyespace_faces = np.dstack([faces, ones])
eyespace_faces = np.dot(eyespace_faces, view)[:, :, :3]
shininess = 75
L = pyrr.vector.normalize(np.float32([10, -10, 50]))
E = np.float32([0, 0, 1])
H = pyrr.vector.normalize(L + E)
def frontface_shader(face_index, winding):
if winding < 0:
return None
face = eyespace_faces[face_index]
p0, p1, p2 = face[0], face[1], face[2]
N = pyrr.vector.normalize(pyrr.vector3.cross(p1 - p0, p2 - p0))
df = max(0, np.dot(N, L))
sf = pow(max(0, np.dot(N, H)), shininess)
color = df * np.float32([0, 0.8, 1]) + sf * np.float32([1, 1, 1])
color = np.power(color, 1.0 / 2.2)
return dict(
fill=rgb(*color),
fill_opacity="1.0",
stroke=rgb(*(color * 1.5)),
stroke_width="0.001",
)
scene = svg3d.Scene([])
scene.add_mesh(svg3d.Mesh(faces, frontface_shader))
svg3d.Engine([svg3d.View(camera, scene)]).render("mobius_tube.svg")
# Filmstrip
def shader(face_index, winding):
return dict(
fill="white",
fill_opacity="0.75",
stroke="black",
stroke_linejoin="round",
stroke_width="0.005",
)
thin = dict(
fill="white",
fill_opacity="0.75",
stroke="black",
stroke_linejoin="round",
stroke_width="0.001",
)
view = create_lookat(eye=[50, 40, 120], target=[0, 0, 0], up=[0, 1, 0])
projection = create_perspective(fovy=15, aspect=1, near=10, far=200)
camera = svg3d.Camera(view, projection)
viewport0 = svg3d.Viewport.from_string("-2.5 -0.5 1.0 1.0")
viewport1 = svg3d.Viewport.from_string("-1.5 -0.5 1.0 1.0")
viewport2 = svg3d.Viewport.from_string("-0.5 -0.5 1.0 1.0")
viewport3 = svg3d.Viewport.from_string(" 0.5 -0.5 1.0 1.0")
viewport4 = svg3d.Viewport.from_string(" 1.5 -0.5 1.0 1.0")
slices, stacks = 24, 32
sphere_faces = 15.0 * parametric_surface(slices, stacks, sphere)
slices, stacks = 32, 24
klein_faces = 3.0 * parametric_surface(slices, stacks, klein)
slices, stacks, radius = 48, 32, 7
mobius_faces = radius * parametric_surface(slices, stacks, mobius_tube)
# cube
view0 = svg3d.View(camera, svg3d.Scene([svg3d.Mesh(cube(), shader)]), viewport0)
# octahedron
view1 = svg3d.View(
camera, svg3d.Scene([svg3d.Mesh(12.0 * octahedron(), shader)]), viewport1
)
# sphere
view2 = svg3d.View(
camera, svg3d.Scene([svg3d.Mesh(sphere_faces, style=thin)]), viewport2
)
# klein
klein_view = create_lookat(eye=[50, 120, 50], target=[0, 0, 0], up=[0, 0, 1])
klein_projection = create_perspective(fovy=28, aspect=1, near=10, far=200)
klein_camera = svg3d.Camera(klein_view, klein_projection)
view3 = svg3d.View(
klein_camera, svg3d.Scene([svg3d.Mesh(klein_faces, style=thin)]), viewport3
)
# mobius
view4 = svg3d.View(
camera, svg3d.Scene([svg3d.Mesh(mobius_faces, frontface_shader)]), viewport4
)
drawing = svgwrite.Drawing(
"filmstrip.svg", (256 * 5, 256), viewBox="-2.5 -0.5 5.0 1.0"
)
svg3d.Engine([view0, view1, view2, view3, view4]).render_to_drawing(drawing)
drawing.save()
def create_simple_shapes():
view = create_lookat(eye=[50, 40, 120], target=[0, 0, 0], up=[0, 1, 0])
projection = create_perspective(fovy=15, aspect=1, near=10, far=200)
camera = svg3d.Camera(view, projection)
thin_style = dict(
fill="white",
stroke="black",
stroke_linejoin="round",
fill_opacity="0.75",
stroke_width="0.002",
)
thick_style = dict(
fill="white",
stroke="black",
stroke_linejoin="round",
fill_opacity="0.75",
stroke_width="0.005",
)
left_viewport = svg3d.Viewport.from_string("-1.0 -0.5 1.0 1.0")
right_viewport = svg3d.Viewport.from_string("0.0 -0.5 1.0 1.0")
# Octahedron
style = dict(
fill="white",
fill_opacity="0.75",
stroke="black",
stroke_linejoin="round",
stroke_width="0.005",
)
mesh = svg3d.Mesh(15.0 * octahedron(), style=style)
view = svg3d.View(camera, svg3d.Scene([mesh]))
svg3d.Engine([view]).render("octahedron.svg")
# Sphere and Klein
def shader(face_index, winding):
return dict(
fill="white",
fill_opacity="0.75",
stroke="black",
stroke_linejoin="round",
stroke_width="0.002",
)
slices, stacks = 32, 32
faces = 15.0 * parametric_surface(slices, stacks, sphere)
sphere_view = svg3d.View(
camera, svg3d.Scene([svg3d.Mesh(faces, shader)]), left_viewport
)
klein_view = create_lookat(eye=[50, 120, 50], target=[0, 0, 0], up=[0, 0, 1])
klein_projection = create_perspective(fovy=28, aspect=1, near=10, far=200)
klein_camera = svg3d.Camera(klein_view, klein_projection)
faces = 3.0 * parametric_surface(slices, stacks, klein)
klein_view = svg3d.View(
klein_camera, svg3d.Scene([svg3d.Mesh(faces, shader)]), right_viewport
)
svg3d.Engine([sphere_view, klein_view]).render(
"sphere_and_klein.svg", (512, 256), "-1.0 -0.5 2.0 1.0"
)
def create_octahedron_pair(filename):
vp = svg3d.Viewport.from_aspect(2)
projection = create_perspective(fovy=25, aspect=2, near=10, far=200)
view = create_lookat(eye=[0, 20, 60], target=[0, 0, 0], up=[0, 1, 0])
camera = svg3d.Camera(view, projection)
scene = svg3d.Scene([])
faces = octahedron()
def backface_shader(face_index, winding):
if winding >= 0: return None
return dict(
fill="#7f7fff",
fill_opacity="1.0",
stroke="black",
stroke_linejoin="round",
stroke_width="0.002",
stroke_dasharray="0.01",
)
def frontface_shader(face_index, winding):
if winding < 0: return None
return dict(
fill="#7fff7f",
fill_opacity="0.4",
stroke="black",
stroke_linejoin="round",
stroke_width="0.003",
)
faces += np.array([-1.25, 0, 0])
scene.add_mesh(svg3d.Mesh(12.0 * faces, backface_shader))
scene.add_mesh(svg3d.Mesh(12.0 * faces, frontface_shader))
faces2 = hexahedron() * 0.8
def backface_shader2(face_index, winding):
if winding >= 0: return None
return dict(
fill="#7f7fff",
fill_opacity="1.0",
stroke="black",
stroke_linejoin="round",
stroke_width="0.002",
stroke_dasharray="0.01",
)
def frontface_shader2(face_index, winding):
if winding < 0: return None
return dict(
fill="#7fff7f",
fill_opacity="0.4",
stroke="black",
stroke_linejoin="round",
stroke_width="0.003",
)
q = quaternion.create_from_eulers([0, pi * 0.25, 0])
for f in faces2:
for v in f:
v[:] = quaternion.apply_to_vector(q, v)
faces2 += np.array([12.0, 0, 0])
scene.add_mesh(svg3d.Mesh(faces2, backface_shader2))
scene.add_mesh(svg3d.Mesh(faces2, frontface_shader2))
e = svg3d.Engine([svg3d.View(camera, scene, vp)])
e.render(filename, (1024, 512))