Computation of gravity effects of two- and three-dimensional bodies with radial symmetry

A computer program in the form of a subroutine which computes the gravity effects of bodies with radial symmetry is described and presented. The program can be utilized in the situation of a circular disc, an infinite cylinder, a finite cylinder and for any arbitrary object which can be approximated into a set of circular discs about a common axis. The program has been applied to known situations and the results obtained are in excellent agreement with the previously known and reported ones.     

Computer programs for rapid computation of gravity effects of two-dimensional and three-dimensional bodies

A subroutine is presented which calculates the gravity effect of bodies of infinite strike length which have a polygonal cross section and uniform density. A second subroutine allows rapid calculation of end corrections, so approximating the effect of bodies of limited strike length. Modifications can be made which will allow the routines to be used for bodies asymmetrically positioned with respect to the line of observation.     

Reduction to the magnetic pole using a fast fourier series algorithm

An algorithm is developed for making magnetic field “reduction-to-the-pole” computations using two-dimensional Fourier series. A significant saving in computer time is achieved by using a “look-up table” to reduce the number of trigonometric functions to be evaluated. The algorithm is incorporated into an efficient FORTRAN program, RPØLE, for processing magnetic anomalies caused solely by induction in the earth's field.     

A geodetic approach to gravity data reduction for geophysics

The currently adopted approach to reduce observed gravity data for geophysical purposes includes several approximations. These were originally used to reduce computational effort, but have remained standard practice, even though the required computing power is now readily available. In contrast, more precise gravity reductions are routinely employed in physical geodesy. The difference between simple Bouguer gravity anomalies derived using the geophysical and geodetic approaches can reach several tens of μm sec⁻². The geodetic reductions include a more accurate calculation of normal gravity as a function of latitude, and a free air correction that accounts for the non-sphericity of the figure of the Earth. Also important, especially given the advent of Global Positioning System coordination of gravity surveys, is the need to ensure that the correct vertical and horizontal coordinate systems are used for the gravity reduction procedure. Errors associated with the use of non-geocentric horizontal coordinates and ellipsoidal heights are significant when compared with the accuracy of an individual gravity measurement. A generalised gravity reduction program and a coordinate transformation program are presented which can be employed to reduce geophysical data in a geodetic manner.     

The use of interactive computing in teaching geology and geophysics

In both geology and solid-earth geophysics first-degree courses we employ interactive computing to teach programming, statistics, and a variety of geological and geophysical procedures and concepts. BASIC is used on a system which offers teletype output or simple graphical display. As an example, details (procedure, annotated BASIC programs and graphical output) of a teaching package to determine the direction of magnetisation of a body are given. Graphical display is shown from packages to simulate (1) a trace fossil Chondrites, and (2) the development of flute mark profiles. The use of interactive computer packages, especially with graphical display, has greatly improved our teaching and the students' understanding of concepts and processes. Further teaching packages are now being written, for data analysis and reduction, and for geological modeling.     

基于对象模型技术的图形动画系统开发

通过面向对象分析方法，采用一种与编程语言无关的对象模型技术指导应用系统的开发。应用实例表明，这种模型适用于问题描述、需求分析、系统设计、对象设计直到系统实现的整个软件开发过程，从而有助于加快多媒体应用软件的开发进程。     

Walking On Broken Mesh: Defect‐Tolerant Geodesic Distances and Parameterizations

Efficient methods to compute intrinsic distances and geodesic paths have been presented for various types of surface representations, most importantly polygon meshes. These meshes are usually assumed to be well‐structured and manifold. In practice, however, they often contain defects like holes, gaps, degeneracies, non‐manifold configurations – or they might even be just a soup of polygons. The task of repairing these defects is computationally complex and in many cases exhibits various ambiguities demanding tedious manual efforts. We present a computational framework that enables the computation of meaningful approximate intrinsic distances and geodesic paths on raw meshes in a way which is tolerant to such defects. Holes and gaps are bridged up to a user‐specified tolerance threshold such that distances can be computed plausibly even across multiple connected components of inconsistent meshes. Further, we show ways to locally parameterize a surface based on geodesic distance fields, easily facilitating the application of textures and decals on raw meshes. We do all this without explicitly repairing the input, thereby avoiding the costly additional efforts. In order to enable broad applicability we provide details on two implementation variants, one optimized for performance, the other optimized for memory efficiency. Using the presented framework many applications can readily be extended to deal with imperfect meshes. Since we abstract from the input applicability is not even limited to meshes, other representations can be handled as well.     

Articulated Object Reconstruction and Markerless Motion Capture from Depth Video

We present an algorithm for acquiring the 3D surface geometry and motion of a dynamic piecewise‐rigid object using a single depth video camera. The algorithm identifies and tracks the rigid components in each frame, while accumulating the geometric information acquired over time, possibly from different viewpoints. The algorithm also reconstructs the dynamic skeleton of the object, thus can be used for markerless motion capture. The acquired model can then be animated to novel poses. We show the results of the algorithm applied to synthetic and real depth video.     

Geodesic-Controlled Developable Surfaces for Modeling Paper Bending

We present a novel and effective method for modeling a developable surface to simulate paper bending in interactive and animation applications. The method exploits the representation of a developable surface as the envelope of rectifying planes of a curve in 3D, which is therefore necessarily a geodesic on the surface. We manipulate the geodesic to provide intuitive shape control for modeling paper bending. Our method ensures a natural continuous isometric deformation from a piece of bent paper to its flat state without any stretching. Test examples show that the new scheme is fast, accurate, and easy to use, thus providing an effective approach to interactive paper bending. We also show how to handle non-convex piecewise smooth developable surfaces.     

Conformal Flattening by Curvature Prescription and Metric Scaling

We present an efficient method to conformally parameterize 3D mesh data sets to the plane. The idea behind our method is to concentrate all the 3D curvature at a small number of select mesh vertices, called cone singularities, and then cut the mesh through those singular vertices to obtain disk topology. The singular vertices are chosen automatically. As opposed to most previous methods, our flattening process involves only the solution of linear systems of Poisson equations, thus is very efficient. Our method is shown to be faster than existing methods, yet generates parameterizations having comparable quasi‐conformal distortion.     

CHC++: Coherent Hierarchical Culling Revisited

We present a new algorithm for efficient occlusion culling using hardware occlusion queries. The algorithm significantly improves on previous techniques by making better use of temporal and spatial coherence of visibility. This is achieved by using adaptive visibility prediction and query batching. As a result of the new optimizations the number of issued occlusion queries and the number of rendering state changes are significantly reduced. We also propose a simple method for determining tighter bounding volumes for occlusion queries and a method which further reduces the pipeline stalls. The proposed method provides up to an order of magnitude speedup over the previous state of the art. The new technique is simple to implement, does not rely on hardware calibration and integrates well with modern game engines.     

基于OpenGL三维物体建模方法的研究与实现

使用OpenGL可以对读入的STL几何模型进行三维真实感渲染、视角变换、显示缩放、光照设置及鼠标拾取等。本文介绍了一种基于OpenGL的三维物体建模方法,分析了基于该方法设计相应软件的体系结构,并着重探讨了STL文件的载入及视角变换等关键技术。     

Modeling Complex Unfoliaged Trees from a Sparse Set of Images

We present a novel image‐based technique for modeling complex unfoliaged trees. Existing tree modeling tools either require capturing a large number of views for dense 3D reconstruction or rely on user inputs and botanic rules to synthesize natural‐looking tree geometry. In this paper, we focus on faithfully recovering real instead of realistically‐looking tree geometry from a sparse set of images. Our solution directly integrates 2D/3D tree topology as shape priors into the modeling process. For each input view, we first estimate a 2D skeleton graph from its matte image and then find a 2D skeleton tree from the graph by imposing tree topology. We develop a simple but effective technique for computing the optimal 3D skeleton tree most consistent with the 2D skeletons. For each edge in the 3D skeleton tree, we further apply volumetric reconstruction to recover its corresponding curved branch. Finally, we use piecewise cylinders to approximate each branch from the volumetric results. We demonstrate our framework on a variety of trees to illustrate the robustness and usefulness of our technique.     

A Statistical Model of Human Pose and Body Shape

Generation and animation of realistic humans is an essential part of many projects in today's media industry. Especially, the games and special effects industry heavily depend on realistic human animation. In this work a unified model that describes both, human pose and body shape is introduced which allows us to accurately model muscle deformations not only as a function of pose but also dependent on the physique of the subject. Coupled with the model's ability to generate arbitrary human body shapes, it severely simplifies the generation of highly realistic character animations. A learning based approach is trained on approximately 550 full body 3D laser scans taken of 114 subjects. Scan registration is performed using a non-rigid deformation technique. Then, a rotation invariant encoding of the acquired exemplars permits the computation of a statistical model that simultaneously encodes pose and body shape. Finally, morphing or generating meshes according to several constraints simultaneously can be achieved by training semantically meaningful regressors.     

Context-Aware Skeletal Shape Deformation

We describe a system for the animation of a skeleton-controlled articulated object that preserves the fine geometric details of the object skin and conforms to the characteristic shapes of the object specified through a set of examples. The system provides the animator with an intuitive user interface and produces compelling results even when presented with a very small set of examples. In addition it is able to generalize well by extrapolating far beyond the examples.     

Soft Articulated Characters with Fast Contact Handling

Fast contact handling of soft articulated characters is a computationally challenging problem, in part due to complex interplay between skeletal and surface deformation. We present a fast, novel algorithm based on a layered representation for articulated bodies that enables physically-plausible simulation of animated characters with a high-resolution deformable skin in real time. Our algorithm gracefully captures the dynamic skeleton-skin interplay through a novel formulation of elastic deformation in the pose space of the skinned surface. The algorithm also overcomes the computational challenges by robustly decoupling skeleton and skin computations using careful approximations of Schur complements, and efficiently performing collision queries by exploiting the layered representation. With this approach, we can simultaneously handle large contact areas, produce rich surface deformations, and capture the collision response of a character/s skeleton.     

High-Resolution Volumetric Computation of Offset Surfaces with Feature Preservation

We present a new algorithm for the efficient and reliable generation of offset surfaces for polygonal meshes. The algorithm is robust with respect to degenerate configurations and computes (self‐)intersection free offsets that do not miss small and thin components. The results are correct within a prescribed ε‐tolerance. This is achieved by using a volumetric approach where the offset surface is defined as the union of a set of spheres, cylinders, and prisms instead of surface‐based approaches that generally construct an offset surface by shifting the input mesh in normal direction. Since we are using the unsigned distance field, we can handle any type of topological inconsistencies including non‐manifold configurations and degenerate triangles. A simple but effective mesh operation allows us to detect and include sharp features (shocks) into the output mesh and to preserve them during post‐processing (decimation and smoothing). We discretize the distance function by an efficient multi‐level scheme on an adaptive octree data structure. The problem of limited voxel resolutions inherent to every volumetric approach is avoided by breaking the bounding volume into smaller tiles and processing them independently. This allows for almost arbitrarily high voxel resolutions on a commodity PC while keeping the output mesh complexity low. The quality and performance of our algorithm is demonstrated for a number of challenging examples.