You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
With virtual reality, digital painting on 2D canvases is now being extended to 3D spaces. Tilt Brush and Oculus Quill are widely accepted among artists as tools that pave the way to a new form of art - 3D emmersive painting. Current 3D painting systems are only a start, emitting textured triangular geometries. In this paper, we advance this new art of 3D painting to 3D volumetric painting that enables an artist to draw a huge scene with full control of spatial color fields. Inspired by the fact that 2D paintings often use vast space to paint background and small but detailed space for foreground, we claim that supporting a large canvas in varying detail is essential for 3D painting. In order to help artists focus and audiences to navigate the large canvas space, we provide small artist-defined areas, called rooms, that serve as beacons for artist-suggested scales, spaces, locations for intended appreciation view of the painting. Artists and audiences can easily transport themselves between different rooms. Technically, our canvas is represented as an array of deep octrees of depth 24 or higher, built on CPU for volume painting and on GPU for volume rendering using accurate ray casting. In CPU side, we design an efficient iterative algorithm to refine or coarsen octree, as a result of volumetric painting strokes, at highly interactive rates, and update the corresponding GPU textures. Then we use GPU-based ray casting algorithms to render the volumetric painting result. We explore precision issues stemming from ray-casting the octree of high depth, and provide a new analysis and verification. From our experimental results as well as the positive feedback from the participating artists, we strongly believe that our new 3D volume painting system can open up a new possibility for VR-driven digital art medium to professional artists as well as to novice users.

Cited Abstract(s):
[1]: We have developed a novel hierarchical data structure for the efficient representation of sparse, time-varying volumetric data discretized on a 3D grid. Our “VDB”, so named because it is a Volumetric, Dynamic grid that shares several characteristics with Bptrees, exploits spatial coherency of time-varying data to separately and compactly encode data values and grid topology. VDB models a virtually infinite 3D index space that allows for cache-coherent and fast data access into sparse volumes of high resolution. It imposes no topology restrictions on the sparsity of the volumetric data, and it supports fast (average O(1)) random access patterns when the data are inserted, retrieved, or deleted. This is in contrast to most existing sparse volumetric data structures, which assume either static or manifold topology and require specific data access patterns to compensate for slow random access. Since the VDB data structure is fundamentally hierarchical, it also facilitates adaptive grid sampling, and the inherent acceleration structure leads to fast algorithms that are well-suited for simulations. As such, VDB has proven useful for several applications that call for large, sparse, animated volumes, for example, level set dynamics and cloud modeling. In this article, we showcase some of these algorithms and compare VDB with existing, state-of-the-art data structures.
To our best knowledge, octrees as deep as 24 were not used for ray casting. The deepest trees we found was @math used in [1] , which is equivalent to the octree depth of 12 (our canvas is equivalent to @math ), and the ray angle drift error has not been identified as a challenge. We propose a solution and thoroughly analyze the numerical precision associated with ray drift during ray traversal using a very deep tree.