vAPE4D

Real-time rendering for time-variying volumes (4D = 3D Space + Time) written in WebGPU and Rust.

The renderer runs in your brower or embeded in a Jupyter Notebook (e.g. inside vscode)

How it works

TLDR: We map the values in the volume to RGBA color with a user defined transfer function (colormap) and use standard volume rendering.

Rendering Technique

The rendering techniques used for volume rendering rely heavily on methods described in the book Real-Time Volume Graphics.

A user defined transfer function \(f\) is used that maps a value \(\hat{v_i}\in[0,1]\) to RGBA color:

\(c_i := f_\textrm{RGB}(\hat{v_i})\quad a_i := f_\textrm{A}(\hat{v_i})\)

For each pixel we march along a ray with step size \(\delta\). At each step the volume is sampled to retrive a value \(v_i\). The value \(v_i\) is normalized using the user provided \(v_\textrm{min}\) and \(v_\textrm{max}\) (defaults to minimum and maximum of volume):

\(\hat{v_i} = \min(\max(\frac{v_i -v_\textrm{min}}{v_\textrm{max}-v_\textrm{min}}\),0),1)

To calculate the final pixel color the \(N\) samples along a ray are accumulated using alpha blending:

\(C_p = \sum_{i=0}^{N} \hat{a_i} C_i \prod_{j=0}^{i-1}(1-\hat{a_j})\)

The step size \(\delta\) and a distance scaling factor \(s\) are user controlled and the opacity (alpha) must be corrected accordingly:

\(\hat{a_i} = 1-a_i^{\delta s}\)

Step size \(\delta\): A smaller step size gives more detailed / accurate results but results in worse performance.

Distance Scaling: Since the "original" sampling rate is not known the user has to specify it. A larger value makes the whole volume appear more opaque/dense.

Getting Started

Installation

pip install vape4d

Usage

Viewer (jupyter notebook)

from vape4d import viewer
import numpy as np
from matplotlib import pyplot as plt

viewer(
    #[T,C,D,W,H]
    np.random.rand(1,1,32,32,32),
    plt.get_cmap("viridis"),   
)

Render Image

import numpy as np
from vape4d import diverging_alpha, render
import matplotlib.pyplot as plt

colormap = diverging_alpha(plt.get_cmap("magma"))
img = render(
        # [T,D,H,W]
        np.random.rand(2,32,32,32).astype(np.float32),
        colormap,
        0.5, # timestep
        width=1024,
        height=1024,
    )

plt.imshow(img)
plt.axis("off")

plt.savefig("test.png", bbox_inches="tight", pad_inches=0)
plt.show()