Tracing Analytic Ray Curves for Light and Sound Propagation in Non-Linear Media

The physical world consists of spatially varying media, such as the atmosphere and the ocean, in which light and sound propagates along non-linear trajectories. This presents a challenge to existing ray-tracing based methods, which are widely adopted to simulate propagation due to their efficiency and flexibility, but assume linear rays. We present a novel algorithm that traces analytic ray curves computed from local media gradients, and utilizes the closed-form solutions of both the intersections of the ray curves with planar surfaces, and the travel distance. By constructing an adaptive unstructured mesh, our algorithm is able to model general media profiles that vary in three dimensions with complex boundaries consisting of terrains and other scene objects such as buildings. Our analytic ray curve tracer with the adaptive mesh improves the efficiency considerably over prior methods. We highlight the algorithm's application on simulation of visual and sound propagation in outdoor scenes

MFA-DVR: Direct Volume Rendering of MFA Models

3D volume rendering is widely used to reveal insightful intrinsic patterns of volumetric datasets across many domains. However, the complex structures and varying scales of volumetric data can make efficiently generating high-quality volume rendering results a challenging task. Multivariate functional approximation (MFA) is a new data model that addresses some of the critical challenges: high-order evaluation of both value and derivative anywhere in the spatial domain, compact representation for large-scale volumetric data, and uniform representation of both structured and unstructured data. In this paper, we present MFA-DVR, the first direct volume rendering pipeline utilizing the MFA model, for both structured and unstructured volumetric datasets. We demonstrate improved rendering quality using MFA-DVR on both synthetic and real datasets through a comparative study. We show that MFA-DVR not only generates more faithful volume rendering than using local filters but also performs faster on high-order interpolations on structured and unstructured datasets. MFA-DVR is implemented in the existing volume rendering pipeline of the Visualization Toolkit (VTK) to be accessible by the scientific visualization community

Gradient Calculation Methods on Arbitrary Polyhedral Unstructured Meshes for Cell-Centered CFD Solvers

A survey of gradient reconstruction methods for cell-centered data on unstructured meshes is conducted within the scope of accuracy assessment. Formal order of accuracy, as well as error magnitudes for each of the studied methods, are evaluated on a complex mesh of various cell types through consecutive local scaling of an analytical test function. The tests highlighted several gradient operator choices that can consistently achieve 1st order accuracy regardless of cell type and shape. The tests further offered error comparisons for given cell types, leading to the observation that the "ideal" gradient operator choice is not universal. Practical implications of the results are explored via CFD solutions of a 2D inviscid standing vortex, portraying the discretization error properties. A relatively naive, yet largely unexplored, approach of local curvilinear stencil transformation exhibited surprisingly favorable propertie

비정렬격자에서 정확하고 효율적인 구배 계산을 위한 최소제곱법 스위칭 함수 설계

학위논문 (석사)-- 서울대학교 대학원 : 공과대학 기계항공공학부, 2019. 2. 김종암.본 연구는 최소제곱법 방법간의 스위칭 함수의 설계를 통해 비정렬 격자에서 정확하고 효율적인 구배 계산 제안한다. 다양한 예제들을 분석한 결과, 비정렬 격자에서 가장 널리 사용되는 구배 계산방법 중 하나인 그린-가우스 정리를 이용한 구배 계산방법이 본질적으로 inconsistent하며, 또한 최소 제곱법을 활용하는 구배 계산방법이 점성경계층 및 일반 격자에서 그린-가우스 정리를 사용하는 방법보다 더 정확함을 보였다. 앞선 분석을 바탕으로 상대적으로 효율적인 좁은 스텐실을 사용하는 가중 최소제곱법 방법과 상대적으로 정확한 넓은 스텐실을 사용하는 가중 최소제곱법 사이의 스위칭을 추구하였다. 한편 최소제곱법 행렬의 조건수가 구배 오차와 상관관계를 보이며, 오직 격자의 정보만으로도 계산이 가능하므로 이를 스위칭 기준으로 삼았다. 일반적인 격자에 적용하기 위해서 조건수를 분석한 결과, 삼각함수를 이용하여 조건수를 스텐실 개수와 스텐실 벡터간의 각도의 함수로 표현하였다. 그리고 넓은 스텐실을 사용하는 최소제곱법 방법의 평균 조건수가 적합한 스위칭 기준 값임을 확인하였다. 2차원 및 3차원 간단한 문제들에 대하여 스위칭 메커니즘을 보였다. 마지막으로 SWLSQ의 우수함을 보이기 위해 2차원 익형, 3차원 윙바디 및전투기 형상에 대해 3가지 최소제곱법 방법들의 구배 정확도와 계산 비용을 비교하였다.The present work proposes accurate and efficient gradient estimation on unstructured grid by designing a switching function between two Least-Square methods. Through various test cases, it is shown that gradient by Green-Gauss theorem, one of the most widely preferred gradient estimation on unstructured grid, is inherently inconsistent, and gradient by Least-Square methods show higher gradient accuracy on viscous boundary layer and general grid compared to Green-Gauss approach. Regarding the observation, switching between two Least-Square methods, relatively efficient compact weighted Least-Square method and accurate extended weighted Least-Square method, is pursued. Since condition number of the Least-Square matrix can be calculated from the geometric information of the given grid, and shows correlation with the gradient error, it is chosen as the switching criterion. To implement on general grid, the condition number is analyzed and formulated as the function of number of stencils and angle between stencil vectors using trigonometric relations. Then, it is confirmed that average condition number of extended weighted Least-Square method is suitable switching criterion value. The switching mechanism is demonstrated through two and three-dimensional simple cases. Finally, comparison of gradient accuracy and computational cost of three Least -Square methods are addressed on two-dimensional airfoil, three-dimensional wing-body and modern fighter configuration to show the excellence of SWLSQ.Chapter 1 Introduction 1 1.1 Background 1 1.2 Research Objective 2 Chapter 2 Numerical Methods 4 2.1 Governing Equations 4 2.2 Gradient Estimation Methods on Unstructured Grid. 7 2.2.1 Least-Square Method 7 2.2.1.1 The Method of Normal Equations. 10 2.2.1.2 Weighting Function 12 2.2.1.3 QR Factorization 13 2.2.2 Green-Gauss Theorem 15 2.2.2.1 Simple Averaging 16 2.2.2.2 Node Averaging. 17 Chapter 3 Analysis on Preceding Approaches. 19 3.1 Numerical Test. 19 3.1.1 Grid Type 19 3.1.2 Test Function. 22 3.2 Observation 24 3.2.1 Quadrilateral grid with test functions.. 24 3.2.2 Results by Green-Gauss type methods 28 3.2.3 Results by Least-Square type methods. 29 Chapter 4 Least-Square Method Switching Function. 31 4.1 Motivation 31 4.2 Switching Criterion 32 4.2.1 Conventional Grid Quality Criterion. 32 4.2.2 Condition Number of Least-Square Matrix.. 34 4.2.3 Condition Number Calculation Method 38 4.2.3.1 Quadratic Formula. 38 4.2.3.2 Power Method 39 4.3 Switching Least-Square Method. 41 4.3.1 Behavior of Condition Number of CWLSQ and EWLSQ 41 4.3.2 Switching Procedure. 44 4.4 Simple Demonstration 46 4.4.1 Two-Dimensional Randomly Diagonalized Triangular Grid 46 4.4.2 Three-Dimensional Random tetrahedral Grid. 48 Chapter 5 Application.. 49 5.1 Two-Dimensional NACA0012 Airfoil 49 5.2 Three-Dimensional Wing-Body Configuration. 51 5.2.1 Test Function. 51 5.2.2 Flow Simulation 52 5.3 Three-Dimensional Modern Fighter 55 5.3.1 Test Function. 55 5.3.2 Flow Simulation 57 Chapter 6 Conclusion. 59 References. 61 국문초록. 64Maste

Unsupervised Training for 3D Morphable Model Regression

We present a method for training a regression network from image pixels to 3D morphable model coordinates using only unlabeled photographs. The training loss is based on features from a facial recognition network, computed on-the-fly by rendering the predicted faces with a differentiable renderer. To make training from features feasible and avoid network fooling effects, we introduce three objectives: a batch distribution loss that encourages the output distribution to match the distribution of the morphable model, a loopback loss that ensures the network can correctly reinterpret its own output, and a multi-view identity loss that compares the features of the predicted 3D face and the input photograph from multiple viewing angles. We train a regression network using these objectives, a set of unlabeled photographs, and the morphable model itself, and demonstrate state-of-the-art results.Comment: CVPR 2018 version with supplemental material (http://openaccess.thecvf.com/content_cvpr_2018/html/Genova_Unsupervised_Training_for_CVPR_2018_paper.html

Indoor Scene Reconstruction with Fine-Grained Details Using Hybrid Representation and Normal Prior Enhancement

The reconstruction of indoor scenes from multi-view RGB images is challenging due to the coexistence of flat and texture-less regions alongside delicate and fine-grained regions. Recent methods leverage neural radiance fields aided by predicted surface normal priors to recover the scene geometry. These methods excel in producing complete and smooth results for floor and wall areas. However, they struggle to capture complex surfaces with high-frequency structures due to the inadequate neural representation and the inaccurately predicted normal priors. To improve the capacity of the implicit representation, we propose a hybrid architecture to represent low-frequency and high-frequency regions separately. To enhance the normal priors, we introduce a simple yet effective image sharpening and denoising technique, coupled with a network that estimates the pixel-wise uncertainty of the predicted surface normal vectors. Identifying such uncertainty can prevent our model from being misled by unreliable surface normal supervisions that hinder the accurate reconstruction of intricate geometries. Experiments on the benchmark datasets show that our method significantly outperforms existing methods in terms of reconstruction quality