Multiscale Heterogeneous Modeling with Surfacelets

Abstract

Computational design of structures and materials requires multiscale models to represent geometry and physical properties. In this paper, we propose a multiscale heterogeneous model, dual-Rep, to represent geometry and property distribution implicitly. A new basis function, called surfacelet, is proposed to capture boundary information more efficiently than traditional wavelets. Zoom operations are defined to support multiscale design. A method of materials model reconstruction from images is also developed.Even though multi-resolution geometry representations (e.g., subdivision and wavelets) have been developed, the geometric information is only at the same length scale; from this information, representations at different levels of detail (LOD) can be generated. The major difference between multiscale and multi-resolution modeling is that in a multi-resolution environment, the complete model information is available at the highest resolution, while in multiscale modeling, the highest resolution need not be generated, except when and where it may be needed. For instance, a multiscale model does not require the entire Boeing 787 airplane model to be available at the atomic scale if one component is required at this scale. Instead, in a multiscale environment, it is necessary to render the model at a specified scale when and where a specified region of a model can be rendered at a desired scale for a specific purpose, such as visualization, finite-element analysis, or manufacturing process planning [1].

Inverse Surfacelet Transform for Image Reconstruction With Constrained-Conjugate Gradient Methods

“…Transform. Recently, a surfacelet model [4] was proposed to construct the geometric boundary and internal material distribution of heterogeneous materials. As combinations of wavelets and implicit surfaces, surfacelets keep both the multi-resolution/multi-scale nature of wavelets and the advantage of implicit surfaces in constructing complex 3D geometry.…”

“…As a generalization of the Radon transform from 2D to 3D with the additional feature identification capability similar to the Hough transform, a surfacelet transform [4] converts 3D image pixels or voxels into surfacelet coefficients, which are the integrals of voxel values over some small surfaces corresponding to the external or internal singularities or boundaries of interest, followed by a 1D wavelet transform, as shown in Fig. 1.…”

Microstructure Feature Recognition for Materials Using Surfacelet-Based Methods for Computer-Aided Design-Material Integration

“…[13]. A surfacelet model can be generated by a combination of Radon-like surfacelet and wavelet transforms as introduced in Ref.…”

“…Other surfacelet forms can be defined for other geometric shapes [13]. Here, the shape parameter vector is p = (a, fi).…”

A Multi-Scale Materials Modeling Method With Seamless Zooming Capability Based on Surfacelets

“…The proposed materials specification scheme is based on a recently developed surfacelet transform [6 ]. A forward surfacelet transform enables the representation of material microstructures by effectively capturing microstructural features from material images.…”