We developed a new data structure for the efficient representation of spatial data, called SCom DAG — Similarity Compressed Directed Acyclic Graph. It subdivides space with an octree and utilizes local data similarities and topology for compact encoding. Our method exploits the fact that many surface and volume areas are similar to each other up to a transformation. We store spatial transformations on the edges of the graph and data transformations on terminal links pointing to data blocks. Compression is achieved mainly by reducing the number of graph nodes and data blocks while maintaining the same number of paths in the graph. Spatial transformations are compact due to the use of hyper-octahedral groups that are relatively small even in 4D space. SCom DAG works with data of different dimensionality, such as 2D textures, 3D meshes and 4D time-varying volumetric data. Thus, it is well suited for volumetric data visualization and rendering large scenes. The proposed algorithm performs lossy compression, creating a compact representation of various data with controlled quality, which is especially valuable for low-end devices and convenient browser use. It provides a balance of compression and quality comparable to state-of-the-art technologies in various domains, such as compact texture and geometry representation, volumetric data, radiance fields, and precomputed 4D volume animations. At the same time, our data structure enables fast sampling and real-time ray tracing, and its hierarchical nature allows for rendering with a continuous level of detail.

Abstract With the wider availability of full‐color 3D printers, color‐accurate 3D‐print preparation has received increased attention. A key challenge lies in the inherent translucency of commonly used print materials that blurs out details of the color texture. Previous work tries to compensate for these scattering effects through strategic assignment of colored primary materials to printer voxels. To date, the highest‐quality approach uses iterative optimization that relies on computationally expensive Monte Carlo light transport simulation to predict the surface appearance from subsurface scattering within a given print material distribution; that optimization, however, takes in the order of days on a single machine. In our work, we dramatically speed up the process by replacing the light transport simulation with a data‐driven approach. Leveraging a deep neural network to predict the scattering within a highly heterogeneous medium, our method performs around two orders of magnitude faster than Monte Carlo rendering while yielding optimization results of similar quality level. The network is based on an established method from atmospheric cloud rendering, adapted to our domain and extended by a physically motivated weight sharing scheme that substantially reduces the network size. We analyze its performance in an end‐to‐end print preparation pipeline and compare quality and runtime to alternative approaches, and demonstrate its generalization to unseen geometry and material values. This for the first time enables full heterogenous material optimization for 3D‐print preparation within time frames in the order of the actual printing time.

Abstract The paper describes the colour approximation problem and the method of dynamic palette construction is suggested for its solution. The method uses the graphic display palette based on the computed true colour of the individual picture. Some aspects of human colour perception are considered. Two metrics in colour space are introduced to estimate closeness of the suggested colour approximation. The method was applied to visualize 3D scenes generated by ray tracing.