Set-based queries for multiscale shape-material modeling

TL;DR

A set-based query is developed that retains the compatibility and usability of the point-based query while leveraging locality between multiple point-based queries to provide a significant speedup and further decrease the memory consumption for common applications, including visualization and slicing for manufacturing planning.

Abstract

Multiscale structures are becoming increasingly prevalent in the field of mechanical design. The variety of fine-scale structures and their respective representations results in an interoperability challenge. To address this, a query-based API was recently proposed which allows different representations to be combined across the scales for multiscale structures modeling. The query-based approach is fully parallelizable and has a low memory footprint; however, this architecture requires repeated evaluation of the fine-scale structures locally for each individual query. While this overhead is manageable for simpler fine-scale structures such as parametric lattice structures, it is problematic for structures requiring non-trivial computations, such as Voronoi foam structures. In this paper, we develop a set-based query that retains the compatibility and usability of the point-based query while leveraging locality between multiple point-based queries to provide a significant speedup and further decrease the memory consumption for common applications, including visualization and slicing for manufacturing planning. We first define the general set-based query that consolidates multiple point-based queries at arbitrary locations. We then implement specialized preprocessing methods for different types of fine-scale structures which are otherwise inefficient with the point-based query. Finally, we apply the set-based query to downstream applications such as ray-casting and slicing, increasing their performance by an order of magnitude. The overall improvements result in the generation and rendering of complex fine-scale structures such as Voronoi foams at interactive frame rates on the CPU.

Figures (9)

• Figure 1: A classification of different types of fine scale structures based on the two parameters that affect what can be exploited to achieve a speedup using our approach. Functional representations appear twice, because the repetition of these depends on the particular functions chosen.
• Figure 2: Examples of parametric lattice structures. Left: Unit cells which form up a parametric lattice. Right: A coarse-scale femur with a parametric lattice substructure.
• Figure 3: An Example of triply periodic minimal surface structures formed with functional representation.
• Figure 4: Examples of the Voronoi foam structures.
• Figure 5: An illustration of the multiscale shape-material modeling API. Top: A three-scale structure with parametric lattices visualized at the second and third scales. Bottom: A two-scale cantilever beam with functionally graded Voronoi foam structures on the fine scale following the effective material property field on the coarse scale.