Fast cosine transform for FCC lattices

Voxel representation and processing is an important issue in a broad spectrum of applications. E.g., 3D imaging in biomedical engineering applications, video game development and volumetric displays are often based on data representation by voxels. By replacing the standard sampling lattice with a face-centered lattice one can obtain the same sampling density with less sampling points and reduce aliasing error, as well. We introduce an analog of the discrete cosine transform for the facecentered lattice relying on multivariate Chebyshev polynomials. A fast algorithm for this transform is deduced based on algebraic signal processing theory and the rich geometry of the special unitary Lie group of degree four.Comment: Presented at 13th APCA International Conference on Automatic Control and Soft Computing (CONTROLO 2018); 9 figure

Validating Stereoscopic Volume Rendering

The evaluation of stereoscopic displays for surface-based renderings is well established in terms of accurate depth perception and tasks that require an understanding of the spatial layout of the scene. In comparison direct volume rendering (DVR) that typically produces images with a high number of low opacity, overlapping features is only beginning to be critically studied on stereoscopic displays. The properties of the specific images and the choice of parameters for DVR algorithms make assessing the effectiveness of stereoscopic displays for DVR particularly challenging and as a result existing literature is sparse with inconclusive results. In this thesis stereoscopic volume rendering is analysed for tasks that require depth perception including: stereo-acuity tasks, spatial search tasks and observer preference ratings. The evaluations focus on aspects of the DVR rendering pipeline and assess how the parameters of volume resolution, reconstruction filter and transfer function may alter task performance and the perceived quality of the produced images. The results of the evaluations suggest that the transfer function and choice of recon- struction filter can have an effect on the performance on tasks with stereoscopic displays when all other parameters are kept consistent. Further, these were found to affect the sensitivity and bias response of the participants. The studies also show that properties of the reconstruction filters such as post-aliasing and smoothing do not correlate well with either task performance or quality ratings. Included in the contributions are guidelines and recommendations on the choice of pa- rameters for increased task performance and quality scores as well as image based methods of analysing stereoscopic DVR images

Solution of the inverse scattering problem by T-matrix completion. II. Simulations

This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory and here we present simulations for inverse scattering of scalar waves. The underlying mathematical model is the scalar wave equation and the object function that is reconstructed is the medium susceptibility. The simulations are relevant to ultrasound tomographic imaging and seismic tomography. It is shown that DCTMC is a viable method for solving strongly nonlinear inverse problems with large data sets. It provides not only the overall shape of the object but the quantitative contrast, which can correspond, for instance, to the variable speed of sound in the imaged medium.Comment: This is Part II of a paper series. Part I contains theory and is available at arXiv:1401.3319 [math-ph]. Accepted in this form to Phys. Rev.

Many-Light Real-Time Global Illumination using Sparse Voxel Octree

Global illumination (GI) rendering simulates the propagation of light through a 3D volume and its interaction with surfaces, dramatically increasing the fidelity of computer generated images. While off-line GI algorithms such as ray tracing and radiosity can generate physically accurate images, their rendering speeds are too slow for real-time applications. The many-light method is one of many novel emerging real-time global illumination algorithms. However, it requires many shadow maps to be generated for Virtual Point Light (VPL) visibility tests, which reduces its efficiency. Prior solutions restrict either the number or accuracy of shadow map updates, which may lower the accuracy of indirect illumination or prevent the rendering of fully dynamic scenes. In this thesis, we propose a hybrid real-time GI algorithm that utilizes an efficient Sparse Voxel Octree (SVO) ray marching algorithm for visibility tests instead of the shadow map generation step of the many-light algorithm. Our technique achieves high rendering fidelity at about 50 FPS, is highly scalable and can support thousands of VPLs generated on the fly. A survey of current real-time GI techniques as well as details of our implementation using OpenGL and Shader Model 5 are also presented

The investigation of a method to generate conformal lattice structures for additive manufacturing

Additive manufacturing (AM) allows a geometric complexity in products not seen in conventional manufacturing. This geometric freedom facilitates the design and fabrication of conformal hierarchical structures. Entire parts or regions of a part can be populated with lattice structure, designed to exhibit properties that differ from the solid material used in fabrication. Current computer aided design (CAD) software used to design products is not suitable for the generation of lattice structure models. Although conceptually simple, the memory requirements to store a virtual CAD model of a lattice structure are prohibitively high. Conventional CAD software defines geometry through boundary representation (B-rep); shapes are described by the connectivity of faces, edges and vertices. While useful for representing accurate models of complex shape, the sheer quantity of individual surfaces required to represent each of the relatively simple individual struts that comprise a lattice structure ensure that memory limitations are soon reached. Additionally, the conventional data flow from CAD to manufactured part is arduous, involving several conversions between file formats. As well as a lengthy process, each conversion risks the generation of geometric errors that must be fixed before manufacture. A method was developed to specifically generate large arrays of lattice structures, based on a general voxel modelling method identified in the literature review. The method is much less sensitive to geometric complexity than conventional methods and thus facilitates the design of considerably more complex structures. The ability to grade structure designs across regions of a part (termed functional grading ) was also investigated, as well as a method to retain connectivity between boundary struts of a conformal structure. In addition, the method streamlines the data flow from design to manufacture: earlier steps of the data conversion process are bypassed entirely. The effect of the modelling method on surface roughness of parts produced was investigated, as voxel models define boundaries with discrete, stepped blocks. It was concluded that the effect of this stepping on surface roughness was minimal. This thesis concludes with suggestions for further work to improve the efficiency, capability and usability of the conformal structure method developed in this work

IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures

Variable-density cellular structures can overcome connectivity and manufacturability issues of topologically optimized structures, particularly those represented as discrete density maps. However, the optimization of such cellular structures is challenging due to the multiscale design problem. Past work addressing this problem generally either only optimizes the volume fraction of single-type unit cells but ignoring the effects of unit cell geometry on properties, or considers the geometry-property relation but builds this relation via heuristics. In contrast, we propose a simple yet more principled way to accurately model the property to geometry mapping using a conditional deep generative model, named Inverse Homogenization Generative Adversarial Network (IH-GAN). It learns the conditional distribution of unit cell geometries given properties and can realize the one-to-many mapping from geometry to properties. We further reduce the complexity of IH-GAN by using the implicit function parameterization to represent unit cell geometries. Results show that our method can 1) generate various unit cells that satisfy given material properties with high accuracy (relative error <5%) and 2) improve the optimized structural performance over the conventional topology-optimized variable-density structure. Specifically, in the minimum compliance example, our IH-GAN generated structure achieves an 84.4% reduction in concentrated stress and an extra 7% reduction in displacement. In the target deformation examples, our IH-GAN generated structure reduces the target matching error by 24.2% and 44.4% for two test cases, respectively. We also demonstrated that the connectivity issue for multi-type unit cells can be solved by transition layer blending

Doctor of Philosophy

dissertationOne of the fundamental building blocks of many computational sciences is the construction and use of a discretized, geometric representation of a problem domain, often referred to as a mesh. Such a discretization enables an otherwise complex domain to be represented simply, and computation to be performed over that domain with a finite number of basis elements. As mesh generation techniques have become more sophisticated over the years, focus has largely shifted to quality mesh generation techniques that guarantee or empirically generate numerically well-behaved elements. In this dissertation, the two complementary meshing subproblems of vertex placement and element creation are analyzed, both separately and together. First, a dynamic particle system achieves adaptivity over domains by inferring feature size through a new information passing algorithm. Second, a new tetrahedral algorithm is constructed that carefully combines lattice-based stenciling and mesh warping to produce guaranteed quality meshes on multimaterial volumetric domains. Finally, the ideas of lattice cleaving and dynamic particle systems are merged into a unified framework for producing guaranteed quality, unstructured and adaptive meshing of multimaterial volumetric domains

A journey in a procedural volume Optimization and filtering of Perlin noise

National audiencePerlin noise is the most widely used tool in procedural texture synthesis. It is a simple and fast method to enhance the quantity of detail or to render natural materials with no use of storage resources. However, this technique is very sensitive to aliasing artifacts, especially when composed with shape and color functions. Moreover, it is computationally intensive and can become slow, especially when generating procedural volumes of density in real time. This study aims at analyzing Perlin noise properties in order to control the apparition of artifacts and optimize the computational cost. We present a method for computing a maximum and minimum frequency threshold per noise component, we propose an idea to handle the case of non linear transforms of the noise, and show an optimization method for volume generation