/manimgl-best-practices

3D Surfaces - Reference Guide

Example file: examples/three_d_surfaces.py

User Query Scenarios

This example addresses queries like:

• "Create a 3D surface visualization"
• "Show a parametric surface"
• "Animate camera rotation around object"
• "Create a torus/sphere/cone"
• "Show saddle surface"

Scene Thinking Process (3b1b Style)

1. Core Concept

Parametric Surfaces: Define surfaces as functions (u,v) → (x,y,z). Camera movement reveals 3D structure.

2. Technical Implementation

Basic Parametric Surface

surface = ParametricSurface(
    lambda u, v: [u, v, np.sin(u) * np.cos(v)],
    u_range=(-3, 3),
    v_range=(-3, 3),
    resolution=(30, 30),
)
surface.set_color(BLUE)
surface.set_opacity(0.8)

Camera Setup and Movement

frame = self.frame
frame.reorient(-30, 70, 0)  # phi, theta, gamma
frame.set_height(10)

# Animate camera
self.play(frame.animate.reorient(30, 60, 0), run_time=3)

Sphere with Latitude/Longitude Lines

# Latitude lines
for phi in np.linspace(-PI/2 + 0.3, PI/2 - 0.3, 6):
    line = ParametricCurve(
        lambda t: radius * np.array([
            np.cos(t) * np.cos(phi),
            np.sin(t) * np.cos(phi),
            np.sin(phi)
        ]),
        t_range=(0, TAU),
    )

Torus Parameterization

R, r = 2, 0.7  # Major and minor radius
torus = ParametricSurface(
    lambda u, v: [
        (R + r * np.cos(v)) * np.cos(u),
        (R + r * np.cos(v)) * np.sin(u),
        r * np.sin(v)
    ],
    u_range=(0, TAU),
    v_range=(0, TAU),
)

3. Scene Variants

Key Patterns

Pattern: ThreeDAxes

axes = ThreeDAxes(
    x_range=(-3, 3, 1),
    y_range=(-3, 3, 1),
    z_range=(-2, 2, 1),
)

Pattern: Rotating Objects

self.play(
    Rotate(surface, TAU, axis=UP, run_time=6, rate_func=linear),
)

Pattern: Frame Reorientation

# reorient(phi, theta, gamma, center, height)
frame.reorient(-30, 70, 0)  # Just angles
frame.animate.reorient(60, 60, 0)  # Animated

Run Commands

manimgl three_d_surfaces.py ParametricSurface3D -w
manimgl three_d_surfaces.py SphereSurface -w
manimgl three_d_surfaces.py TorusSurface -w
manimgl three_d_surfaces.py SaddleSurface -w