Volume Rendering

Volume rendering projects a three-dimensional scalar field directly to the screen without first extracting surfaces, revealing internal structure.

Direct rendering of 3D fields

Volume rendering treats a scalar field defined on a 3D grid as a semi-transparent medium. Rather than reducing the data to surfaces, it integrates light along rays through the volume, so the viewer sees interior structure such as density gradients, hot cores, or nested layers. It is the natural technique for continuous fields like plasma density, temperature, or neutron flux.

The emission-absorption model

Kronos motion — three machines

The standard model assigns each point an emitted color and an absorption coefficient. Along a viewing ray the accumulated intensity is the integral of emission weighted by the transmittance from the eye to that point. Discretized, this becomes front-to-back or back-to-front compositing over sample points.

python

import numpy as np
# front-to-back compositing along one ray
def composite(colors, alphas):
    C = np.zeros(3); T = 1.0
    for c, a in zip(colors, alphas):
        C += T * a * c
        T *= (1.0 - a)
        if T < 1e-3: break
    return C, 1.0 - T

Transfer functions

A transfer function maps scalar value (and sometimes gradient magnitude) to color and opacity. It is the single most consequential choice: it decides which values become visible and which fade away. Designing it well is an iterative, data-aware task, covered in Transfer Functions.

Sampling and quality

Step size along the ray trades speed for accuracy; too coarse yields wood-grain artifacts.
Pre-integrated transfer functions reduce sampling error at feature boundaries.
Gradient-based shading adds surface-like cues to soft regions.

Kronos use

Volume rendering of simulated neutron flux and plasma density lets engineers inspect where energy and particles concentrate inside a device, without committing to a single isosurface threshold.