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import numpy as np
from manim import *
from isosurfaces import plot_isosurface
metaball_pts = [np.array([0, 1.6, 0]), np.array([0, -1.6, 0])]
def fn(p):
# metaballs
# return sum(1 / np.linalg.norm(p - q) for q in metaball_pts) - 1
# cone with singularity at origin
return p[0] ** 2 + p[1] ** 2 - p[2] ** 2
pmin = np.array([-4, -4, -4])
pmax = np.array([4, 4, 4])
simplices, faces = plot_isosurface(fn, pmin, pmax, 2, 64)
faces = list(faces)
class Isosurface(Surface):
def __init__(self, faces, **kwargs):
# Need the right resolution to trick the surface into rendering all of the faces
# Each face is a triangle (list of three points)
num_points = len(faces) * 3
super().__init__(uv_func=None, resolution=(num_points, 1), **kwargs)
s_points = [p for face in faces for p in face]
# du_points and dv_points are used to compute vertex normals
du_points = [p for face in faces for p in face[1:] + face[:1]]
dv_points = [p for face in faces for p in face[2:] + face[:2]]
# The three lists have equal length and are stored consecutively
self.set_points(s_points + du_points + dv_points)
# manim -pql isosurface_demo.py --renderer=opengl --enable_gui --fullscreen
class DemoScene(ThreeDScene):
def construct(self):
self.add(ThreeDAxes())
self.set_camera_orientation(phi=75 * DEGREES, theta=30 * DEGREES)
self.add(Isosurface(faces))
# sgroup = VGroup()
# for s in simplices[:16]:
# [a, b, c, d] = map(lambda p: p.pos, s)
# sgroup.add(
# Line(a, b), Line(b, c), Line(c, d), Line(d, a), Line(a, c), Line(b, d)
# )
# self.add(sgroup)
self.wait(20)
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