基于OpenGL的等角插补明暗处理的软件实现

等角插补明暗处理具有Phong明暗处理的视觉效果,而且具有较Phong明暗处理更快的渲染效率,基于标准图形渲染管道,用Ｃ语言实现了OpenGL渲染管道的硬件计算部分,同时用Ｃ语言实现了等角插补明暗处理,并给出了实验结果。该方法的实现可为渲染算法的研究和实现提供参考。     

Phong shading by binary interpolation

This paper presents a new vector interpolation method for Phong shading, referred to as binary interpolation. It can calculate the reflection model by a scalar method. A pre-defined table is used to convert scan lines into segments, each of which is a power of two in length. Then binary interpolation is carried out in each segment. The new method has been tested in two situations; firstly with various sizes of right angled triangles, secondly with the Utah teapot. The results show that, excluding plot to screen time, binary interpolation can decrease the calculation time for a reflection model by about 20%.     

Improved quadratic normal vector interpolation for realistic shading

Published online: 19 July 2001     

Shape aware normal interpolation for curved surface shading from polyhedral approximation

Independent interpolation of local surface patches and local normal patches is an efficient way for fast rendering of smooth curved surfaces from rough polyhedral meshes. However, the independently interpolating normals may deviate greatly from the analytical normals of local interpolating surfaces, and the normal deviation may cause severe rendering defects when the surface is shaded using the interpolating normals. In this paper we propose two novel normal interpolation schemes along with interpolation of cubic Bézier triangles for rendering curved surfaces from rough triangular meshes. Firstly, the interpolating normal is computed by a Gregory normal patch to each Bézier triangle by a new definition of quadratic normal functions along cubic space curves. Secondly, the interpolating normal is obtained by blending side-vertex normal functions along side-vertex parametric curves of the interpolating Bézier surface. The normal patches by these two methods can not only interpolate given normals at vertices or boundaries of a triangle but also match the shape of the local interpolating surface very well. As a result, more realistic shading results are obtained by either of the two new normal interpolation schemes than by the traditional quadratic normal interpolation method for rendering rough triangular meshes.     

Stabilized finite elements with equal order of interpolation for soil dynamics problems

Summary The accurate prediction of the behaviour of geostructures is based on the strong coupling between the pore fluid and the solid skeleton. If the relative acceleration of the fluid phase to the skeleton is neglected, the equations describing the problem can be written in terms of skeleton displacements (or velocities) and pore pressures. This mixed problem is similar to others found in solid and fluid dynamics. In the limit case of zero permeability and incompressibility of the fluid phase, the restrictions on the shape functions used to approximate displacements and pressures imposed by Babuska-Brezzi conditions or the Zienkiewicz-Taylor patch test hold. As a consequence, it is not possible to use directly elements with the same order of interpolation for the field variables. This paper proposes two alternative methods allowing us to circumvent the BB restrictions in the incompressibility limit, making it possible to use elements with the same order of interpolation. The first consists on introducing the divergence of the momentum equation of the mixture as an stabilization term, the second is a generalization of the two step-projection method introduced by Chorin for fluid dynamics problems.     

Faster search by lackadaisical quantum walk

In the typical model, a discrete-time coined quantum walk searching the 2D grid for a marked vertex achieves a success probability of \(O(1/\log N)\) in \(O(\sqrt{N \log N})\) steps, which with amplitude amplification yields an overall runtime of \(O(\sqrt{N} \log N)\). We show that making the quantum walk lackadaisical or lazy by adding a self-loop of weight 4 / N to each vertex speeds up the search, causing the success probability to reach a constant near 1 in \(O(\sqrt{N \log N})\) steps, thus yielding an \(O(\sqrt{\log N})\) improvement over the typical, loopless algorithm. This improved runtime matches the best known quantum algorithms for this search problem. Our results are based on numerical simulations since the algorithm is not an instance of the abstract search algorithm.     

Faster plots by fan data compression

A fan data compression method is presented that tripled laser printer speed for Bode and simulation plots with many points. This reduced printer delays without the expense of a faster laser printer, and it saved computer time as well. The authors describe their problem, solution, and conclusions. They give the fan algorithm and present its performance for several applications. They include a pseudocode implementation     

Faster convergence by means of fitness estimation

Evolutionary algorithms usually require a large number of objective function evaluations before converging to a good solution. However, many real-world applications allow for only very few objective function evaluations. To solve this predicament, one promising possibility seems to not evaluate every individual, but to just estimate the quality of some of the individuals. In this paper, we estimate an individuals fitness on the basis of previously observed objective function values of neighboring individuals. Two estimation methods, interpolation and regression, are tested and compared. The experiments show that by using fitness estimation, it is possible to either reach a better fitness level in the given time, or to reach a desired fitness level much faster (roughly half the number of evaluations) than if all individuals are evaluated.     

基于边角插值法的图形渐变避免自交算法研究

提出了一种新的算法,该算法根据图形渐变序列中出现的局部自交点,先判断出这些点的位置并计算出自交区域所占整个图形面积的比例,根据设定的阈值,采用合理的微调整算法,在尽可能保持源图形形态的基础上,将自交点剔除,达到渐变序列中图形全部为简单多边形的目的。结果表明提出的算法能够很好地将图形渐变中的自交点剔除,实现比单独采用边角插值法更理想的图形渐变效果。     

Faster learning by reduction of data access time

Nowadays, the major challenge in machine learning is the ‘Big Data’ challenge. The big data problems due to large number of data points or large number of features in each data point, or both, the training of models have become very slow. The training time has two major components: Time to access the data and time to process (learn from) the data. So far, the research has focused only on the second part, i.e., learning from the data. In this paper, we have proposed one possible solution to handle the big data problems in machine learning. The idea is to reduce the training time through reducing data access time by proposing systematic sampling and cyclic/sequential sampling to select mini-batches from the dataset. To prove the effectiveness of proposed sampling techniques, we have used empirical risk minimization, which is commonly used machine learning problem, for strongly convex and smooth case. The problem has been solved using SAG, SAGA, SVRG, SAAG-II and MBSGD (Mini-batched SGD), each using two step determination techniques, namely, constant step size and backtracking line search method. Theoretical results prove similar convergence for systematic and cyclic sampling as the widely used random sampling technique, in expectation. Experimental results with bench marked datasets prove the efficacy of the proposed sampling techniques and show up to six times faster training.     

Learning shape from shading by a multilayer network

The multilayer feedforward network has often been used for learning a nonlinear mapping based on a set of examples of the input-output data. In this paper, we present a novel use of the network, in which the example data are not explicitly given. We consider the problem of shape from shading in computer vision, where the input (image coordinates) and the output (surface depth) satisfy only a known differential equation. We use the feedforward network as a parametric representation of the object surface and reformulate the shape from shading problem as the minimization of an error function over the network weights. The stochastic gradient and conjugate gradient methods are used for the minimization. Boundary conditions for either surface depth or surface normal (or both) can be imposed by adjusting the same network at different levels. It is further shown that the light source direction can be estimated, based on an initial guess, by integrating the source estimation with the surface estimation. Extensions of the method to a wider class of problems are discussed. The efficiency of the method is verified by examples of both synthetic and real images.     

Constructing spherical curves by interpolation

Based on a composite conical surface patch, we develop new simple methods for up to G² continuous interpolation of an arbitrary sequence of points on a sphere with a specified tangent direction and curvature vector at every point. The resulting interpolation curve is the intersection of the given sphere and the composite conical surface patch. Unlike some existing methods, introduced into the method are several free parameters that can be used in subsequent interactive modification such that the resulting curve’s shape hits our demand, and the resulting curve can be expressed explicitly. Experiments demonstrate the method is effective and potentially useful in pattern design on sphere, sphere trim, robot, and other industrial and research fields.     

Inversion of polynomial matrices by interpolation

Known polynomial interpolation methods to polynomial matrices are generalized to obtain new algorithms for the computation of the inverse of such matrices. The algorithms use numerically stabilizable manipulations of constant matrices. Among the three methods investigated Lagrange's interpolation seems especially suitable for the purpose     

On computer generation of random vectors by transformations of uniformly distributed vectors

The paper discusses a general method of computer generation of random vectors based on transformations of uniformly distributed vectors. This method is then applied to build up efficient algorithms for generatingq-exponential random vectors and multivariate normal ort-distributed vectors. Comparisons and connections with other similar algorithms are also presented.     

Shape preserving interpolation by space curves

Shape preserving interpolation for planar data has been well studied while little has been done for shape preserving curve interpolation in space. We consider some criteria for shape preserving interpolation by space curves: convexity and inflections of the projections of the curve onto certain planes, the sign of the torsion, coplanarity and collinearity. Based upon these criteria we then derive an algorithm for interpolating given points in space with a shape preserving piecewise rational cubic curve. The scheme is local and produces curves which are unit tangent continuous and also continuous in curvature magnitude apart from some exceptional cases where the curve contains linear segments. We illustrate the scheme with some graphical examples.     

Surface interpolation of meshes by geometric subdivision

Subdivision surfaces are generated by repeated approximation or interpolation from initial control meshes. In this paper, two new non-linear subdivision schemes, face based subdivision scheme and normal based subdivision scheme, are introduced for surface interpolation of triangular meshes. With a given coarse mesh more and more details will be added to the surface when the triangles have been split and refined. Because every intermediate mesh is a piecewise linear approximation to the final surface, the first type of subdivision scheme computes each new vertex as the solution to a least square fitting problem of selected old vertices and their neighboring triangles. Consequently, sharp features as well as smooth regions are generated automatically. For the second type of subdivision, the displacement for every new vertex is computed as a combination of normals at old vertices. By computing the vertex normals adaptively, the limit surface is G¹ smooth. The fairness of the interpolating surface can be improved further by using the neighboring faces. Because the new vertices by either of these two schemes depend on the local geometry, but not the vertex valences, the interpolating surface inherits the shape of the initial control mesh more fairly and naturally. Several examples are also presented to show the efficiency of the new algorithms.     

基于泊松填充的纹理自适应插值方法

针对新图形技术条件下的纹理合成问题,提出一种纹理插值方法,可将源纹理图像自适应拉伸为不同尺寸的纹理图像并保持其清晰度不改变。首先,采用高维图像插值算法将源纹理裂变为目标纹理分辨率,作为中间过渡纹理;其次,利用自然图像的自相似性,依据中间纹理像素特征随机从源纹理中选取像素块;最后,使用泊松图像编辑算法将源纹理像素块平滑嵌入到中间纹理的间隙区域,得到最终的合成纹理。通过与现有算法的大量对比实验表明,该算法对静态和非静态纹理合成问题都能适用,且合成结果与源纹理具有较高的视觉一致性。另外,该算法逻辑简单、计算快速,无法复杂优化计算或者学习训练步骤,适合在低硬件配置的移动平台应用。     

Edge-detector resolution improvement by image interpolation

Most step-edge detectors are designed to detect locally straight edge-segments which can be isolated within the operator kernel. While it can easily be demonstrated that a cross-sectional support of at least 4 pixels is required for the unambiguous detection of a stepedge, edges which cannot be isolated within windows having this width can nevertheless be resolved. This is achieved by preceding the stepedge detection process by image-intensity interpolation. Although resolution can be improved in this fashion, the step-edge position and intensity estimates thus determined may be subject to systematic biases. Also, the higher resolution performance is accompanied by lower robustness to noise.     

Approximation by a smooth interpolation spline

The properties of a smooth continuous spline approximation are considered. The existence conditions are established and an algorithm is proposed to determine the parameters of such a spline with segments as the sum of a polynomial and an exponent. The errors of approximating a function and its derivative by such a spline with polynomial segments and segments in the form of the sum of a polynomial and an exponent are estimated.     

Uniform convergence of interpolation by cubic splines

For a sequence of meshes on [0, 1] sufficient conditions are given to obtain uniform convergence of cubic spline interpolants for continous functions respectively for the third derivatives of cubic spline interpolants for functions fromC ³ [0, 1].