Direct quad-dominant meshing of point cloud via global parameterization

In this paper, we present a new algorithm for quad-dominant meshing of unorganized point clouds based on periodic global parameterization. Our meshing method is guided by principal directions so as to preserve the intrinsic geometric properties. We use local Delaunay triangulation to smooth the initial principal directions and adapt the global parameterization to point clouds. By optimizing the fairness measure we can find the two scalar functions whose gradients best align with the guided principal directions. To handle the redundant vertices in the iso-lines due to overlapped triangles, an approach is specially designed to clean the iso-lines. Our approach is fully automatic and applicable to a surface of arbitrary genus. We also show an application of our method in curve skeleton extraction from incomplete point cloud data.     

AD-Frustum: adaptive frustum tracing for interactive sound propagation

We present an interactive algorithm to compute sound propagation paths for transmission, specular reflection and edge diffraction in complex scenes. Our formulation uses an adaptive frustum representation that is automatically sub-divided to accurately compute intersections with the scene primitives. We describe a simple and fast algorithm to approximate the visible surface for each frustum and generate new frusta based on specular reflection and edge diffraction. Our approach is applicable to all triangulated models and we demonstrate its performance on architectural and outdoor models with tens or hundreds of thousands of triangles and moving objects. In practice, our algorithm can perform geometric sound propagation in complex scenes at 4-20 frames per second on a multi-core PC.     

Glint Rendering based on a Multiple‐Scattering Patch BRDF

Rendering materials such as metallic paints, scratched metals and rough plastics requires glint integrators that can capture all micro‐specular highlights falling into a pixel footprint, faithfully replicating surface appearance. Specular normal maps can be used to represent a wide range of arbitrary micro‐structures. The use of normal maps comes with important drawbacks though: the appearance is dark overall due to back‐facing normals and importance sampling is suboptimal, especially when the micro‐surface is very rough. We propose a new glint integrator relying on a multiple‐scattering patch‐based BRDF addressing these issues. To do so, our method uses a modified version of microfacet‐based normal mapping [SHHD17] designed for glint rendering, leveraging symmetric microfacets. To model multiple‐scattering, we re‐introduce the lost energy caused by a perfectly specular, single‐scattering formulation instead of using expensive random walks. This reflectance model is the basis of our patch‐based BRDF, enabling robust sampling and artifact‐free rendering with a natural appearance. Additional calculation costs amount to about 40% in the worst cases compared to previous methods [YHMR16, CCM18].     

Implicit Surface-Based Geometric Fusion

This paper introduces a general purpose algorithm for reliable integration of sets of surface measurements into a single 3D model. The new algorithm constructs a single continuous implicit surface representation which is the zero-set of a scalar field function. An explicit object model is obtained using any implicit surface polygonization algorithm. Object models are reconstructed from both multiple view conventional 2.5D range images and hand-held sensor range data. To our knowledge this is the first geometric fusion algorithm capable of reconstructing 3D object models from noisy hand-held sensor range data.This approach has several important advantages over existing techniques. The implicit surface representation allows reconstruction of unknown objects of arbitrary topology and geometry. A continuous implicit surface representation enables reliable reconstruction of complex geometry. Correct integration of overlapping surface measurements in the presence of noise is achieved using geometric constraints based on measurement uncertainty. The use of measurement uncertainty ensures that the algorithm is robust to significant levels of measurement noise. Previous implicit surface-based approaches use discrete representations resulting in unreliable reconstruction for regions of high curvature or thin surface sections. Direct representation of the implicit surface boundary ensures correct reconstruction of arbitrary topology object surfaces. Fusion of overlapping measurements is performed using operations in 3D space only. This avoids the local 2D projection required for many previous methods which results in limitations on the object surface geometry that is reliably reconstructed. All previous geometric fusion algorithms developed for conventional range sensor data are based on the 2.5D image structure preventing their use for hand-held sensor data. Performance evaluation of the new integration algorithm against existing techniques demonstrates improved reconstruction of complex geometry.     

Fuzzy Contour Trees: Alignment and Joint Layout of Multiple Contour Trees

We describe a novel technique for the simultaneous visualization of multiple scalar fields, e.g. representing the members of an ensemble, based on their contour trees. Using tree alignments, a graph-theoretic concept similar to edit distance mappings, we identify commonalities across multiple contour trees and leverage these to obtain a layout that can represent all trees simultaneously in an easy-to-interpret, minimally-cluttered manner. We describe a heuristic algorithm to compute tree alignments for a given similarity metric, and give an algorithm to compute a joint layout of the resulting aligned contour trees. We apply our approach to the visualization of scalar field ensembles, discuss basic visualization and interaction possibilities, and demonstrate results on several analytic and real-world examples.     

Fermion confinement induced by geometry

We consider a five-dimensional model in which fermions are confined in a hypersurface due to an interaction with a purely geometric field. Inspired by the Rubakov-Shaposhnikov field-theoretical model, in which massless fermions can be localized in a domain wall through the interaction of a scalar field, we show that particle confinement may also take place if we endow the five-dimensional bulk with a Weyl integrable geometric structure, or if we assume the existence of a torsion field acting in the bulk. In this picture, the kind of interaction considered in the Rubakov-Shaposhnikov model is replaced by an interaction of fermions with a geometric field, namely a Weyl scalar field or a torsion field. We show that in both cases the confinement is independent of the energy and mass of the fermionic particle. We generalize these results to the case in which the bulk is an arbitrary n-dimensional curved space.     

Advection‐Based Function Matching on Surfaces

A tangent vector field on a surface is the generator of a smooth family of maps from the surface to itself, known as the flow. Given a scalar function on the surface, it can be transported, or advected, by composing it with a vector field's flow. Such transport is exhibited by many physical phenomena, e.g., in fluid dynamics. In this paper, we are interested in the inverse problem: given source and target functions, compute a vector field whose flow advects the source to the target. We propose a method for addressing this problem, by minimizing an energy given by the advection constraint together with a regularizing term for the vector field. Our approach is inspired by a similar method in computational anatomy, known as LDDMM, yet leverages the recent framework of functional vector fields for discretizing the advection and the flow as operators on scalar functions. The latter allows us to efficiently generalize LDDMM to curved surfaces, without explicitly computing the flow lines of the vector field we are optimizing for. We show two approaches for the solution: using linear advection with multiple vector fields, and using non‐linear advection with a single vector field. We additionally derive an approximated gradient of the corresponding energy, which is based on a novel vector field transport operator. Finally, we demonstrate applications of our machinery to intrinsic symmetry analysis, function interpolation and map improvement.     

Gaussian Product Sampling for Rendering Layered Materials

To increase diversity and realism, surface bidirectional scattering distribution functions (BSDFs) are often modelled as consisting of multiple layers, but accurately evaluating layered BSDFs while accounting for all light transport paths is a challenging problem. Recently, Guo et al. [GHZ18] proposed an accurate and general position-free Monte Carlo method, but this method introduces variance that leads to longer render time compared to non-stochastic layered models. We improve the previous work by presenting two new sampling strategies, pair-product sampling and multiple-product sampling. Our new methods better take advantage of the layered structure and reduce variance compared to the conventional approach of sequentially sampling one BSDF at a time. Our pair-product sampling strategy importance samples the product of two BSDFs from a pair of adjacent layers. We further generalize this to multiple-product sampling, which importance samples the product of a chain of three or more BSDFs. In order to compute these products, we developed a new approximate Gaussian representation of individual layer BSDFs. This representation incorporates spatially varying material properties as parameters so that our techniques can support an arbitrary number of textured layers. Compared to previous Monte Carlo layering approaches, our results demonstrate substantial variance reduction in rendering isotropic layered surfaces.     

Real-time rendering of deformable heterogeneous translucent objects using multiresolution splatting

In this paper, we present a novel real-time rendering algorithm for heterogenous translucent objects with deformable geometry. The proposed method starts by rendering the surface geometry in two separate geometry buffers—the irradiance buffer and the splatting buffer—with corresponding mipmaps from the lighting and viewing directions, respectively. Irradiance samples are selected from the irradiance buffer according to geometric and material properties using a novel and fast selection algorithm. Next, we gather the irradiance per visible surface point by splatting the irradiance samples to the splatting buffer. To compute the appearance of long-distance low-frequency subsurface scattering, as well as short-range detailed scattering, a fast novel multiresolution GPU algorithm is developed that computes everything on the fly and which does not require any precomputations. We illustrate the effectiveness of our method on several deformable geometries with measured heterogeneous translucent materials.     

Efficient skeleton-guided displaced subdivision surfaces

Displacement mapping is a computer graphics technique that uses scalar offsets along normals on a base surface to represent and render a model with highly geometric details. The technique natively compresses the model and saves memory I/O. A subdivision surface is the ideal base surface, due to its good geometric properties, such as arbitrary topology, global smoothness, and multi-resolution via hardware tessellation, among others. Two of the main challenges in displacement mapping representation are constructing the base surface faithfully and generating displacement maps efficiently. In this paper, we propose an efficient skeleton-guided displaced subdivision surfaces method. The construction of the base mesh is guided by a sketched skeleton. To make the shape of the base surface fit the input model well, we develop an efficient progressive GPU-based subdivision fitting method. Finally, a GPU-based raycasting method is proposed to sample the input model and generate the displacement maps. The experimental results demonstrate that the proposed method can efficiently generate a high-quality displacement mapping representation. Compared with the traditional displaced subdivision surface method, the proposed method is more suitable for the modern rendering pipeline and has higher efficiency.     

利用半点计算椭圆曲线双标量乘法算法

实现椭圆曲线密码体制最主要的运算是椭圆曲线点群上的标量乘法(或点乘)运算。一些基于椭圆曲线的密码协议比如ECDSA签名验证,就需要计算双标量乘法kP+lQ,其中P、Q为椭圆曲线点群上的任意两点。一个高效计算kP+lQ的方法就是同步计算两个标量乘法,而不是分别计算每个标量乘法再相加。通过对域F2m上的椭圆曲线双标量乘法算法进行研究,将半点公式应用于椭圆曲线的双标量乘法中,提出了一种新的同步计算双标量乘法算法,分析了效率,并与传统的基于倍点运算的双标量乘法算法进行了详细的比较,其效率更优。     

Multiple/arbitrary precision interval computations in C-XSC

As a new feature, C-XSC provides so-called wrapper classes to some external arbitrary precision real and interval packages. Operator and function name overloading is used to give the user easy access to the arithmetic operations and mathematical functions provided by the underlying Ansi C packages. We will discuss briefly so-called staggered precision arithmetics based on exact scalar products. Such an arithmetic is available in C-XSC e.g. for multiple precision complex intervals. We also discuss the usage of the arbitrary precision arithmetic packages MPFR and MPFI, which are now accessible conveniently from within C-XSC via class interfaces. As a typical application, we will present an arbitrary precision interval Newton method to find the root(s) of a continuously differentiable function in a prescribed domain. The user only has to supply the expression for the function in the usual mathematical notation. The derivative needed in the interval Newton operator is computed using automatic differentiation based on the arbitrary precision interval operations. To demonstrate the power of the package we compute an enclosure of the zero of a model problem with guaranteed accuracy of more than 10 million decimal digits.     

Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data

Scientific visualization has many effective methods for examining and exploring scalar and vector fields, but rather fewer for bivariate fields. We report the first general purpose approach for the interactive extraction of geometric separating surfaces in bivariate fields. This method is based on fiber surfaces: surfaces constructed from sets of fibers, the multivariate analogues of isolines. We show simple methods for fiber surface definition and extraction. In particular, we show a simple and efficient fiber surface extraction algorithm based on Marching Cubes. We also show how to construct fiber surfaces interactively with geometric primitives in the range of the function. We then extend this to build user interfaces that generate parameterized families of fiber surfaces with respect to arbitrary polygons. In the special case of isovalue‐gradient plots, fiber surfaces capture features geometrically for quantitative analysis that have previously only been analysed visually and qualitatively using multi‐dimensional transfer functions in volume rendering. We also demonstrate fiber surface extraction on a variety of bivariate data.     

Sparse GPU Voxelization of Yarn‐Level Cloth

Most popular methods in cloth rendering rely on volumetric data in order to model complex optical phenomena such as sub‐surface scattering. These approaches are able to produce very realistic illumination results, but their volumetric representations are costly to compute and render, forfeiting any interactive feedback. In this paper, we introduce a method based on the Graphics Processing Unit (GPU) for voxelization and visualization, suitable for both interactive and offline rendering. Recent features in the OpenGL model, like the ability to dynamically address arbitrary buffers and allocate bindless textures, are combined into our pipeline to interactively voxelize millions of polygons into a set of large three‐dimensional (3D) textures (>10⁹ elements), generating a volume with sub‐voxel accuracy, which is suitable even for high‐density woven cloth such as linen.     

Increasing the Spatial Resolution of BTF Measurement with Scheimpflug Imaging

We present an improved way of acquiring spatially varying surface reflectance represented by a bidirectional texture function (BTF). Planar BTF samples are measured as images at several inclination angles which puts constraints on the minimum depth of field of cameras used in the measurement instrument. For standard perspective imaging, we show that the size of a sample measured and the achievable spatial resolution are strongly interdependent and limited by diffraction at the lens' aperture. We provide a formula for this relationship. We overcome the issue of the required depth of field by using Scheimpflug imaging further enhanced by an anamorphic attachment. The proposed optics doubles the spatial resolution of images compared to standard perspective imaging optics. We built an instrument prototype with the proposed optics that is portable and allows for measurement on site. We show rendered images using the visual appearance measured by the instrument prototype.     

基于泊松标量场的任意亏格网格切割

网格切割在图形处理领域有着广泛的应用,为了更加有效和简单地得到同胚于圆盘的开网格,提出一种基于泊松标量场的三角网格切割算法.对于给定的任意网格,通过求解泊松方程构造标量场来选取临界点,并采用最速下降法给出临界点到边界或者初始点的切割路径;对于亏格不为零的网格,基于Morse理论,通过构造一个调和标量场来得到鞍点,并将它们连接到边界.该方法把任意亏格网格切割成与圆盘同胚的单边界网格,减小了在网格展开过程中产生的扭曲.实验结果表明,在给定临界点的情况下,采用文中算法得到的切割路径能很好地逼近最短路径,而且不受网格限制,适用于任意亏格的开或闭网格.     

Visualizing the Uncertainty of Graph‐based 2D Segmentation with Min‐path Stability

This paper presents a novel approach to visualize the uncertainty in graph‐based segmentations of scalar data. Segmentation of 2D scalar data has wide application in a variety of scientific and medical domains. Typically, a segmentation is presented as a single unambiguous boundary although the solution is often uncertain due to noise or blur in the underlying data as well as imprecision in user input. Our approach provides insight into this uncertainty by computing the “min‐path stability”, a scalar measure analyzing the stability of the segmentation given a set of input constraints. Our approach is efficient, easy to compute, and can be generally applied to either graph cuts or live‐wire (even partial) segmentations. In addition to its general applicability, our new approach to graph cuts uncertainty visualization improves on the time complexity of the current state‐of‐the‐art with an additional fast approximate solution. We also introduce a novel query enabled by our approach which provides users with alternate segmentations by efficiently extracting local minima of the segmentation optimization. Finally, we evaluate our approach and demonstrate its utility on data from scientific and medical applications.     

Vertical backscatter profile of forests predicted by a macroecological plant model

This study describes a new application of a macroecological model to describe the vertical profile of radar backscatter through forest canopy. Given layers of equally sized cylindrical scatterers, the model predicts that one layer within the forest canopy dominates the backscatter profile. This prediction is based on first-order theoretical approximations, in addition to results from a radiative transfer model parameterized by the macroecological model. This model is used to pre-empt specific backscatter trends with results predicting that Rayleigh and Optical backscatter follow negative and positive exponential trends respectively when plotted with respect to backscattering coefficient and branching level through the canopy. A maximum value is predicted by the model associated with the branching level located at the transitional zone between Rayleigh and Optical scattering. This finding follows directly from the size density distribution within a forest combined with dramatic reductions in cross-sectional trends exhibited through the transition. It is a result unrelated to resonant scattering or the effects of penetration depth. The feasibility of describing radar interactions using geometric optics is explored when limits are imposed on the physical optics scattering solution.

The findings offer a significantly new way of understanding the distribution of scattering from differently sized elements in a canopy, and challenge the widely held assumption that backscatter–biomass relationships saturate due to increased opacity of the canopy.     

Automatic Registration of Multi‐Projector Domes Using a Single Uncalibrated Camera

In this paper we present a novel technique for easily calibrating multiple casually aligned projectors on spherical domes using a single uncalibrated camera. Using the prior knowledge of the display surface being a dome, we can estimate the camera intrinsic and extrinsic parameters and the projector to display surface correspondences automatically using a set of images. These images include the image of the dome itself and a projected pattern from each projector. Using these correspondences we can register images from the multiple projectors on the dome. Further, we can register displays which are not entirely visible in a single camera view using multiple pan and tilted views of an uncalibrated camera making our method suitable for displays of different size and resolution. We can register images from any arbitrary viewpoint making it appropriate for a single head‐tracked user in a 3D visualization system. Also, we can use several cartographic mapping techniques to register images in a manner that is appropriate for multi‐user visualization. Domes are known to produce a tremendous sense of immersion and presence in visualization systems. Yet, till date, there exists no easy way to register multiple projectors on a dome to create a high‐resolution realistic visualizations. To the best of our knowledge, this is the first method that can achieve accurate geometric registration of multiple projectors on a dome simply and automatically using a single uncalibrated camera.