Development of numerical methods for overset grids with applications for the integrated Space Shuttle vehicle

Algorithms and computer code developments were performed for the overset grid approach to solving computational fluid dynamics problems. The techniques developed are applicable to compressible Navier-Stokes flow for any general complex configurations. The computer codes developed were tested on different complex configurations with the Space Shuttle launch vehicle configuration as the primary test bed. General, efficient and user-friendly codes were produced for grid generation, flow solution and force and moment computation

Automatic Generation of Near-Body Structured Grids

Numerical grid generation has been a bottleneck in the computational fluid dynamics process for a long time when using the structured overset grids. Many current structured overset grid generation schemes like the hyperbolic grid generation method require significant user interaction to generate good computational grids robustly. Other grid generation schemes like the elliptic grid generation method take a significant amount of time for grid calculation, which is not desirable for computational fluid dynamics. Herein a new grid generation method is presented that combines the hyperbolic grid generation scheme with the elliptic grid generation scheme that uses Poisson’s equation. The new scheme builds upon the strengths of the different techniques by first applying hyperbolic grid generation, which is very fast but sometimes fails in strong concavities, and then using elliptic grid generation to locally fix the problems where hyperbolic grid generation results are not acceptable for computational fluid dynamics calculation. The new technique is demonstrated in various examples that are known to cause problems for either hyperbolic or elliptic grid generation when applied alone. The computational speed of the combined scheme grid generation is also exanimated by comparing the results with hyperbolic and elliptic grid generation. The combined grid generation scheme is further implemented in Engineering Sketch Pad to get useful near-body structure grids based on the geometry of the model. Attributes in Engineering Sketch Pad are used to define the places where the surface and volume grids should be generated, while the tessellations are used to locate and project grid generation results and therefore boost grid generation speed. Three cases are tested to illustrate the implementation of the combined grid generation scheme in Engineering Sketch Pad

Surface Shape Perception in Volumetric Stereo Displays

In complex volume visualization applications, understanding the displayed objects and their spatial relationships is challenging for several reasons. One of the most important obstacles is that these objects can be translucent and can overlap spatially, making it difficult to understand their spatial structures. However, in many applications, for example medical visualization, it is crucial to have an accurate understanding of the spatial relationships among objects. The addition of visual cues has the potential to help human perception in these visualization tasks. Descriptive line elements, in particular, have been found to be effective in conveying shape information in surface-based graphics as they sparsely cover a geometrical surface, consistently following the geometry. We present two approaches to apply such line elements to a volume rendering process and to verify their effectiveness in volume-based graphics. This thesis reviews our progress to date in this area and discusses its effects and limitations. Specifically, it examines the volume renderer implementation that formed the foundation of this research, the design of the pilot study conducted to investigate the effectiveness of this technique, the results obtained. It further discusses improvements designed to address the issues revealed by the statistical analysis. The improved approach is able to handle visualization targets with general shapes, thus making it more appropriate to real visualization applications involving complex objects

Surface Modeling and Analysis Using Range Images: Smoothing, Registration, Integration, and Segmentation

This dissertation presents a framework for 3D reconstruction and scene analysis, using a set of range images. The motivation for developing this framework came from the needs to reconstruct the surfaces of small mechanical parts in reverse engineering tasks, build a virtual environment of indoor and outdoor scenes, and understand 3D images. The input of the framework is a set of range images of an object or a scene captured by range scanners. The output is a triangulated surface that can be segmented into meaningful parts. A textured surface can be reconstructed if color images are provided. The framework consists of surface smoothing, registration, integration, and segmentation. Surface smoothing eliminates the noise present in raw measurements from range scanners. This research proposes area-decreasing flow that is theoretically identical to the mean curvature flow. Using area-decreasing flow, there is no need to estimate the curvature value and an optimal step size of the flow can be obtained. Crease edges and sharp corners are preserved by an adaptive scheme. Surface registration aligns measurements from different viewpoints in a common coordinate system. This research proposes a new surface representation scheme named point fingerprint. Surfaces are registered by finding corresponding point pairs in an overlapping region based on fingerprint comparison. Surface integration merges registered surface patches into a whole surface. This research employs an implicit surface-based integration technique. The proposed algorithm can generate watertight models by space carving or filling the holes based on volumetric interpolation. Textures from different views are integrated inside a volumetric grid. Surface segmentation is useful to decompose CAD models in reverse engineering tasks and help object recognition in a 3D scene. This research proposes a watershed-based surface mesh segmentation approach. The new algorithm accurately segments the plateaus by geodesic erosion using fast marching method. The performance of the framework is presented using both synthetic and real world data from different range scanners. The dissertation concludes by summarizing the development of the framework and then suggests future research topics

BVH와 토러스 패치를 이용한 곡면 교차곡선 연산

학위논문(박사) -- 서울대학교대학원 : 공과대학 컴퓨터공학부, 2021.8. 김명수.두 변수를 가지는 B-스플라인 자유곡면의 곡면간 교차곡선과 자가 교차곡선, 그리고 오프셋 곡면의 자가 교차곡선을 구하는 효율적이고 안정적인 알고리즘을 개발하는 새로운 접근 방법을 제시한다. 새로운 방법은 최하단 노드에 최대 접촉 토러스를 가지는 복합 바운딩 볼륨 구조에 기반을 두고 있다. 이 바운딩 볼륨 구조는 곡면간 교차나 자가 교차가 발생할 가능성이 있는 작은 곡면 조각 쌍들의 기하학적 검색을 가속화한다. 최대 접촉 토러스는 자기가 근사한 C2-연속 자유곡면과 2차 접촉을 가지므로 주어진 곡면에서 다양한 기하 연산의 정밀도를 향상시키는데 필수적인 역할을 한다. 효율적인 곡면간 교차곡선 계산을 지원하기 위해, 미리 만들어진, 최하단 노드에 최대 접촉 토러스가 있으며 구형구면 트리를 가지는 복합 이항 바운딩 볼륨 구조를 설계하였다. 최대 접촉 토러스는 거의 모든 곳에서 접선교차가 발생하는, 자명하지 않은 곡면간 교차곡선 계산 문제에서도 효율적이고 안정적인 결과를 제공한다. 곡면의 자가 교차 곡선을 구하는 문제는 주로 마이터 점 때문에 곡면간 교차곡선을 계산하는 것 보다 훨씬 더 어렵다. 자가 교차 곡면은 마이터 점 부근에서 법선 방향이 급격히 변하며, 마이터 점은 자가 교차 곡선의 끝점에 위치한다. 따라서 마이터 점은 자가 교차 곡면의 기하 연산 안정성에 큰 문제를 일으킨다. 마이터 점을 안정적으로 감지하여 자가 교차 곡선의 계산을 용이하게 하기 위해, 자유곡면을 위한 복합 바운딩 볼륨 구조에 적용할 수 있는 삼항 트리 구조를 제시한다. 특히, 두 변수를 가지는 곡면의 매개변수영역에서 마이터 점을 충분히 작은 사각형으로 감싸는 특별한 표현 방법을 제시한다. 접선교차와 마이터 점을 가지는, 아주 자명하지 않은 자유곡면 예제를 사용하여 새 방법이 효과적임을 입증한다. 모든 실험 예제에서, 기하요소들의 정확도는 하우스도르프 거리의 상한보다 낮음을 측정하였다.We present a new approach to the development of efficient and stable algorithms for intersecting freeform surfaces, including the surface-surface-intersection and the surface self-intersection of bivariate rational B-spline surfaces. Our new approach is based on a hybrid Bounding Volume Hierarchy(BVH) that stores osculating toroidal patches in the leaf nodes. The BVH structure accelerates the geometric search for the potential pairs of local surface patches that may intersect or self-intersect. Osculating toroidal patches have second-order contact with C2-continuous freeform surfaces that they approximate, which plays an essential role in improving the precision of various geometric operations on the given surfaces. To support efficient computation of the surface-surface-intersection curve, we design a hybrid binary BVH that is basically a pre-built Rectangle-Swept Sphere(RSS) tree enhanced with osculating toroidal patches in their leaf nodes. Osculating toroidal patches provide efficient and robust solutions to the problem even in the non-trivial cases of handling two freeform surfaces intersecting almost tangentially everywhere. The surface self-intersection problem is considerably more difficult than computing the intersection of two different surfaces, mainly due to the existence of miter points. A self-intersecting surface changes its normal direction dramatically around miter points, located at the open endpoints of the self-intersection curve. This undesirable behavior causes serious problems in the stability of geometric algorithms on self-intersecting surfaces. To facilitate surface self-intersection computation with a stable detection of miter points, we propose a ternary tree structure for the hybrid BVH of freeform surfaces. In particular, we propose a special representation of miter points using sufficiently small quadrangles in the parameter domain of bivariate surfaces and expand ideas to offset surfaces. We demonstrate the effectiveness of the proposed new approach using some highly non-trivial examples of freeform surfaces with tangential intersections and miter points. In all the test examples, the closeness of geometric entities is measured under the Hausdorff distance upper bound.Chapter 1 Introduction 1 1.1 Background 1 1.2 Surface-Surface-Intersection 5 1.3 Surface Self-Intersection 8 1.4 Main Contribution 12 1.5 Thesis Organization 14 Chapter 2 Preliminaries 15 2.1 Differential geometry of surfaces 15 2.2 Bezier curves and surfaces 17 2.3 Surface approximation 19 2.4 Torus 21 2.5 Summary 24 Chapter 3 Previous Work 25 3.1 Surface-Surface-Intersection 25 3.2 Surface Self-Intersection 29 3.3 Summary 32 Chapter 4 Bounding Volume Hierarchy for Surface Intersections 33 4.1 Binary Structure 33 4.1.1 Hierarchy of Bilinear Surfaces 34 4.1.2 Hierarchy of Planar Quadrangles 37 4.1.3 Construction of Leaf Nodes with Osculating Toroidal Patches 41 4.2 Ternary Structure 44 4.2.1 Miter Points 47 4.2.2 Leaf Nodes 50 4.2.3 Internal Nodes 51 4.3 Summary 56 Chapter 5 Surface-Surface-Intersection 57 5.1 BVH Traversal 58 5.2 Construction of SSI Curve Segments 59 5.2.1 Merging SSI Curve Segments with G1-Biarcs 60 5.2.2 Measuring the SSI Approximation Error Using G1-Biarcs 63 5.3 Tangential Intersection 64 5.4 Summary 65 Chapter 6 Surface Self-Intersection 67 6.1 Preprocessing 68 6.2 BVH Traversal 69 6.3 Construction of Intersection Curve Segments 70 6.4 Summary 72 Chapter 7 Trimming Offset Surfaces with Self-Intersection Curves 74 7.1 Offset Surface and Ternary Hybrid BVH 75 7.2 Preprocessing 77 7.3 Merging Intersection Curve Segments 81 7.4 Summary 84 Chapter 8 Experimental Results 85 8.1 Surface-Surface-Intersection 85 8.2 Surface Self-Intersection 97 8.2.1 Regular Surfaces 97 8.2.2 Offset Surfaces 100 Chapter 9 Conclusion 106 Bibliography 108 초록 120박

Principal component and Voronoi skeleton alternatives for curve reconstruction from noisy point sets

Surface reconstruction from noisy point samples must take into consideration the stochastic nature of the sample -- In other words, geometric algorithms reconstructing the surface or curve should not insist in following in a literal way each sampled point -- Instead, they must interpret the sample as a “point cloud” and try to build the surface as passing through the best possible (in the statistical sense) geometric locus that represents the sample -- This work presents two new methods to find a Piecewise Linear approximation from a Nyquist-compliant stochastic sampling of a quasi-planar C1 curve C(u) : R → R3, whose velocity vector never vanishes -- One of the methods articulates in an entirely new way Principal Component Analysis (statistical) and Voronoi-Delaunay (deterministic) approaches -- It uses these two methods to calculate the best possible tape-shaped polygon covering the planarised point set, and then approximates the manifold by the medial axis of such a polygon -- The other method applies Principal Component Analysis to find a direct Piecewise Linear approximation of C(u) -- A complexity comparison of these two methods is presented along with a qualitative comparison with previously developed ones -- It turns out that the method solely based on Principal Component Analysis is simpler and more robust for non self-intersecting curves -- For self-intersecting curves the Voronoi-Delaunay based Medial Axis approach is more robust, at the price of higher computational complexity -- An application is presented in Integration of meshes originated in range images of an art piece -- Such an application reaches the point of complete reconstruction of a unified mes

Liquid simulation with mesh-based surface tracking

Animating detailed liquid surfaces has always been a challenge for computer graphics researchers and visual effects artists. Over the past few years, researchers in this field have focused on mesh-based surface tracking to synthesize extremely detailed liquid surfaces as efficiently as possible. This course provides a solid understanding of the steps required to create a fluid simulator with a mesh-based liquid surface. The course begins with an overview of several existing liquid-surface-tracking techniques and the pros and cons of each method. Then it explains how to embed a triangle mesh into a finite-difference-based fluid simulator and describes several methods for allowing the liquid surface to merge together or break apart. The final section showcases the benefits and further applications of a mesh-based liquid surface, highlighting state-of-the-art methods for tracking colors and textures, maintaining liquid volume, preserving small surface features, and simulating realistic surface-tension waves