Pendulum - 3D Voxel Animation Learning Example

This guide walks you through how to generate a looping 3D voxel animation of a pendulum using SpatialStudio. The script creates a realistic pendulum with a metal bob that swings back and forth inside a cubic 3D space, then saves the animation to a .splv file.

What this script does

Creates a 3D scene of size 128×128×128
Spawns 1 pendulum with:
- A metallic spherical bob
- A thin suspension rod
- A fixed mounting point at the top
- Realistic physics-based swinging motion
Animates the pendulum swinging for 6 seconds at 30 FPS
Outputs the file pendulum.splv that you can play in your viewer

How it works (simplified)

Voxel volume Each frame is a 3D grid filled with RGBA values (SIZE × SIZE × SIZE × 4).
Physics simulation The pendulum follows realistic angular motion using sine and cosine functions to create natural swinging.
Pendulum bob A metallic sphere is drawn at the end of the pendulum arm with shading to simulate metal reflection.
Suspension rod A thin rod connects the fixed pivot point to the swinging bob, rotating with the pendulum motion.
Animation loop A normalized time variable t cycles from 0 → 2π, with the pendulum angle calculated using sine waves for smooth oscillation.
Encoding Frames are passed into splv.Encoder, which writes them into the .splv video file.

Try it yourself

Install requirements first:

pip install spatialstudio numpy tqdm

Then copy this script into pendulum.py and run:

python pendulum.py

Full Script

import numpy as np
from spatialstudio import splv
from tqdm import tqdm

# Scene setup
SIZE, FPS, SECONDS = 128, 30, 6
FRAMES = FPS * SECONDS
CENTER_X = CENTER_Y = CENTER_Z = SIZE // 2
OUT_PATH = "../outputs/pendulum.splv"

# Pendulum settings
PENDULUM_LENGTH = 45
BOB_RADIUS = 8
MAX_ANGLE = np.pi / 3  # 60 degrees max swing
ROD_THICKNESS = 2

def add_voxel(volume, x, y, z, color):
    if 0 <= x < SIZE and 0 <= y < SIZE and 0 <= z < SIZE:
        volume[x, y, z, :3] = color
        volume[x, y, z, 3] = 255

def generate_pendulum_bob(volume, cx, cy, cz, t):
    # Metallic silver color with variations
    base_color = (169, 169, 169)
    
    for dx in range(-BOB_RADIUS, BOB_RADIUS+1):
        for dy in range(-BOB_RADIUS, BOB_RADIUS+1):
            for dz in range(-BOB_RADIUS, BOB_RADIUS+1):
                distance = np.sqrt(dx*dx + dy*dy + dz*dz)
                if distance <= BOB_RADIUS:
                    # Create metallic shading effect
                    normal_factor = 1.0 - (distance / BOB_RADIUS)
                    brightness = 0.6 + 0.4 * normal_factor
                    
                    # Add subtle surface variation
                    surface_noise = np.sin(dx*0.5) * np.cos(dy*0.5) * np.sin(dz*0.5)
                    brightness += surface_noise * 0.1
                    
                    final_color = tuple(min(255, max(50, int(c * brightness))) for c in base_color)
                    add_voxel(volume, cx+dx, cy+dy, cz+dz, final_color)

def generate_pendulum_rod(volume, pivot_x, pivot_y, pivot_z, bob_x, bob_y, bob_z):
    # Dark metal rod color
    rod_color = (64, 64, 64)
    
    # Calculate direction vector
    dx = bob_x - pivot_x
    dy = bob_y - pivot_y
    dz = bob_z - pivot_z
    length = np.sqrt(dx*dx + dy*dy + dz*dz)
    
    if length == 0:
        return
    
    # Normalize direction
    dx, dy, dz = dx/length, dy/length, dz/length
    
    # Draw rod from pivot to bob
    steps = int(length)
    for i in range(steps):
        t = i / steps
        x = int(pivot_x + dx * i)
        y = int(pivot_y + dy * i)
        z = int(pivot_z + dz * i)
        
        # Add thickness to rod
        for offset_x in range(-ROD_THICKNESS//2, ROD_THICKNESS//2 + 1):
            for offset_z in range(-ROD_THICKNESS//2, ROD_THICKNESS//2 + 1):
                if offset_x*offset_x + offset_z*offset_z <= (ROD_THICKNESS//2)**2:
                    add_voxel(volume, x+offset_x, y, z+offset_z, rod_color)

def generate_pivot_point(volume, px, py, pz):
    # Dark metallic pivot point
    pivot_color = (32, 32, 32)
    
    for dx in range(-3, 4):
        for dy in range(-2, 3):
            for dz in range(-3, 4):
                if dx*dx + dy*dy + dz*dz <= 9:
                    add_voxel(volume, px+dx, py+dy, pz+dz, pivot_color)

def generate_pendulum_highlights(volume, cx, cy, cz):
    # Add bright highlights to simulate metallic reflection
    highlight_color = (220, 220, 255)
    
    for dx in range(-2, 3):
        for dy in range(-2, 3):
            for dz in range(-2, 3):
                if dx*dx + dy*dy + dz*dz <= 4:
                    add_voxel(volume, cx-3+dx, cy-2+dy, cz-1+dz, highlight_color)

def generate_scene(volume, t):
    # Pivot point at the top center
    pivot_x = CENTER_X
    pivot_y = CENTER_Y - 50  # High up in the scene
    pivot_z = CENTER_Z
    
    # Calculate pendulum angle (oscillating motion)
    angle = MAX_ANGLE * np.sin(t * 1.5)  # Adjust speed with multiplier
    
    # Calculate bob position based on angle
    bob_x = pivot_x + int(PENDULUM_LENGTH * np.sin(angle))
    bob_y = pivot_y + int(PENDULUM_LENGTH * np.cos(angle))
    bob_z = pivot_z
    
    # Generate all pendulum components
    generate_pivot_point(volume, pivot_x, pivot_y, pivot_z)
    generate_pendulum_rod(volume, pivot_x, pivot_y, pivot_z, bob_x, bob_y, bob_z)
    generate_pendulum_bob(volume, bob_x, bob_y, bob_z, t)
    generate_pendulum_highlights(volume, bob_x, bob_y, bob_z)

enc = splv.Encoder(SIZE, SIZE, SIZE, framerate=FPS, outputPath=OUT_PATH, motionVectors="off")

for frame in tqdm(range(FRAMES), desc="Generating pendulum"):
    volume = np.zeros((SIZE, SIZE, SIZE, 4), dtype=np.uint8)
    t = (frame / FRAMES) * 2*np.pi
    generate_scene(volume, t)
    enc.encode(splv.Frame(volume, lrAxis="x", udAxis="y", fbAxis="z"))

enc.finish()
print(f"Created {OUT_PATH}")

Next steps

Change MAX_ANGLE to make the pendulum swing wider or narrower.
Adjust PENDULUM_LENGTH for a longer or shorter pendulum.
Modify the speed by changing the multiplier in np.sin(t * 1.5).
Add multiple pendulums with different lengths and starting positions.
Experiment with different metallic colors for the bob.

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