Geometric texturing using level sets

We present techniques for warping and blending (or subtracting) geometric textures onto surfaces represented by high resolution level sets. The geometric texture itself can be represented either explicitly as a polygonal mesh or implicitly as a level set. Unlike previous approaches, we can produce topologically connected surfaces with smooth blending and low distortion. Specifically, we offer two different solutions to the problem of adding fine-scale geometric detail to surfaces. Both solutions assume a level set representation of the base surface which is easily achieved by means of a mesh-to-level-set scan conversion. To facilitate our mapping, we parameterize the embedding space of the base level set surface using fast particle advection. We can then warp explicit texture meshes onto this surface at nearly interactive speeds or blend level set representations of the texture to produce high-quality surfaces with smooth transitions.     

Texture mapping using surface flattening via multidimensionalscaling

Presents a novel technique for texture mapping on arbitrary surfaces with minimal distortion by preserving the local and global structure of the texture. The recent introduction of the fast marching method on triangulated surfaces has made it possible to compute a geodesic distance map from a given surface point in O(n lg n) operations, where n is the number of triangles that represent the surface. We use this method to design a surface flattening approach based on multi-dimensional scaling (MDS). MDS is a family of methods that map a set of points into a finite-dimensional flat (Euclidean) domain, where the only data given is the corresponding distance between every pair of points. The MDS mapping yields minimal changes of the distances between the corresponding points. We then solve an "inverse" problem and map a flat texture patch onto a curved surface while preserving the structure of the texture     

Environment Mapping and Other Applications of World Projections

Various techniques have been developed that employ projections of the world as seen from a particular viewpoint. Blinn and Newell introduced reflection mapping for simulating mirror reflections on curved surfaces. Miller and Hoffman have presented a general illumination model based on environment mapping. World projections have also been used to model distant objects and to produce pictures with the fish-eye distortion required for Omnimax frames. This article proposes a uniform framework for representing and using world projections and argues that the best general-purpose representation is the is projection onto a cube. Surface shading and texture filtering are discussed in the context of environment mapping, and methods are presented for obtaining diffuse and specular surface illumination from prefiltered environment maps. Comparisons are made with ray tracing, noting that two problems with ray tracing?obtaining diffuse reflection and antialiasing specular reflection?can be handled effectively by environment mapping.     

一种应用平面展开完成任意曲面纹理映射的新方法

本文提出一种新的纹理映射方法。该方法在任意曲面和它的平面展开之间定义映射,并用映射特征来评价映射精度,能有效地减少任意曲面纹理映射中的映射变形误差。     

基于两步法的交互式纹理映射研究

两步纹理映射方法将映射过程分解为S映射与O映射两步进行.针对两步纹理映射方法研究中复杂物体表面纹理映射时出现的变形问题,采用B样条曲面代替简单的中间映射媒介,用它近似地包裹在三维物体的外表面,将纹理通过某种方式映射到曲面上实现参数化.基于两步映射方法提出了一种交互式纹理映射的算法.该算法允许用户交互选择贴图范围,通过控制B样条曲面实现对映射效果的调整.实验结果表明,该算法可显著提高纹理映射质量,纹理贴图效果良好.     

消除二次曲面纹理映射的图像失真的方法

二次曲面是一类常用的物体，文章利用三角剖分纹理映射及仿射变换的原理，分别对圆柱曲面、球面实现了纹理映射，有效地消除了二次曲面的纹理映射的图像失真问题。     

Shape from periodic texture using the eigenvectors of local affinedistortion

Shows how the local slant and tilt angles of regularly textured curved surfaces can be estimated directly, without the need for iterative numerical optimization. We work in the frequency domain and measure texture distortion using the affine distortion of the pattern of spectral peaks. The key theoretical contribution is to show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local slant and tilt angles of tangent planes to curved surfaces. In particular, the leading eigenvector points in the tilt direction. Although not as geometrically transparent, the direction of the second eigenvector can be used to estimate the slant direction. The required affine distortion matrices are computed using the correspondences between spectral peaks, established on the basis of their energy ordering. We apply the method to a variety of real-world and synthetic imagery     

带不失真纹理映射的三维Morphing动画研究及实现

介绍了三维Morphing,编程实现了相同顶点数和拓扑结构的物体之间的Morphing,并采用一种带不失真纹理映射的船形曲面造型法,有效地消除了形变曲面的纹理映射的图像失真问题,最后给出了基于任意拓扑结构的物体间Morphing的方法。     

Texture Mapping Real‐World Objects with Hydrographics

In the digital world, assigning arbitrary colors to an object is a simple operation thanks to texture mapping. However, in the real world, the same basic function of applying colors onto an object is far from trivial. One can specify colors during the fabrication process using a color 3D printer, but this does not apply to already existing objects. Paint and decals can be used during post‐fabrication, but they are challenging to apply on complex shapes. In this paper, we develop a method to enable texture mapping of physical objects, that is, we allow one to map an arbitrary color image onto a three‐dimensional object. Our approach builds upon hydrographics, a technique to transfer pigments printed on a sheet of polymer onto curved surfaces. We first describe a setup that makes the traditional water transfer printing process more accurate and consistent across prints. We then simulate the transfer process using a specialized parameterization to estimate the mapping between the planar color map and the object surface. We demonstrate that our approach enables the application of detailed color maps onto complex shapes such as 3D models of faces and anatomical casts.     

曲面片的可展切曲面及其映射分析

论文以微分几何可展曲面理论为基础,提出了过曲面曲线构造其可展切曲 面的方法,得出了可展切曲面的表达形式,对可展切曲面进行了分类,通过建立两曲面间的 映射关系,实现了它们间整体与局部的映射分析,较准确地把握曲面的变形情况,并通过实 例对方法进行了验证。曲面片可展切曲面的方法可以应用于曲面设计、曲面近似展开和纹理 映射等方面。     

Texture mapping on surfaces of arbitrary topology using norm preserving-based optimization

A simple and yet highly efficient, high-quality texture mapping method for surfaces of arbitrary topology is presented. The new method projects the given surface from the 3D object space into the 2D texture space to identify the 2D texture structure that will be used to texture the surface. The object space to texture space projection is optimized to ensure minimum distortion of the texture mapping process. The optimization is achieved through a commonly used norm preserving minimization process on edges of the surface. The main difference here is, by using an initial value approach, the optimization problem can be set up as a quadratic programming problem and, consequently, solved by a linear least squares method. Three methods to choose a good initial value are presented. Test cases show that the new method works well on surfaces of arbitrary topology, with the exception of surfaces with exceptionally abnormal curvature distribution. Other advantages of the new method include uniformity and seamlessness of the texture mapping process. The new method is suitable for applications that do not require precise texture mapping results but demand highly efficient mapping process such as computer animation or video games.     

基于样图的纹理合成技术研究

基于样图的纹理合成方法是继纹理映射、过程纹理合成方法后发展起来的一种纹理技术,用于解决传统方法中出现的缝隙、扭曲、变形和参数调整等问题。在大规模场景的生成以及真实感图形绘制和非真实感绘制、计算机动画等方面具有广泛的应用前景;同时对图像编辑、数据压缩、网络数据的快速传输也有一定的指导意义。该文首先简要回顾了纹理技术的发展历程,总结出基于样图的纹理合成技术的基本原理,从基于Markov模型、侧重逼真显示、任意曲面等几个方面,对基于样图的纹理合成技术进行了较全面的总结和分析,对该领域未来的研究和应用前景做出了有益的探讨。     

Shape from texture for smooth curved surfaces in perspective projection

Projective distortion of surface texture observed in a perspective image can provide direct information about the shape of the underlying surface. Previous theories have generally concerned planar surfaces; this paper presents a systematic analysis of first- and second-order texture distortion cues for the case of a smooth, curved surface. In particular, several kinds of texture gradients are analyzed and are related to surface orientation and surface curvature. The local estimates obtained from these cues can be integrated to obtain a global surface shape, and it is shown that the two surfaces resulting from the well-known tilt ambiguity in the local foreshortening cue typically have qualitatively different shapes. As an example of a practical application of the analysis, a shape-from-texture algorithm based on local orientation-selective filtering is described, and some experimental results are shown.     

一种适用于球面局部区域的纹理映射算法

两步纹理映射和环境映射一般都采用球面作为中介曲面，由于球面映射算法是这两种纹理映射技术的重要组成部分，且球面映射算法还可应用于自由曲面的识别和视景生成等方面，因此，对球面映射算法进行研究具有重要的意义，为了进一步减少球面映射算法产生的纹理形变，从纹理不变形准则出发，分析了传统球面纹理映射算法及其不足之处，并在此基础上提出了一种适用于局部球面的纹理映射新算法，由于该算法考虑了面积等比约束关系，因此可显著提高纹理映射质量，实验结果表明，该算法十分有效，具有一定优势。     

Globally optimal surface mapping for surfaces with arbitrary topology

Computing smooth and optimal one-to-one maps between surfaces of same topology is a fundamental problem in computer graphics and such a method provides us a ubiquitous tool for geometric modeling and data visualization. Its vast variety of applications includes shape registration/matching, shape blending, material/data transfer, data fusion, information reuse, etc. The mapping quality is typically measured in terms of angular distortions among different shapes. This paper proposes and develops a novel quasi-conformal surface mapping framework to globally minimize the stretching energy inevitably introduced between two different shapes. The existing state-of-the-art inter-surface mapping techniques only afford local optimization either on surface patches via boundary cutting or on the simplified base domain, lacking rigorous mathematical foundation and analysis. We design and articulate an automatic variational algorithm that can reach the global distortion minimum for surface mapping between shapes of arbitrary topology, and our algorithm is sorely founded upon the intrinsic geometry structure of surfaces. To our best knowledge, this is the first attempt towards numerically computing globally optimal maps. Consequently, our mapping framework offers a powerful computational tool for graphics and visualization tasks such as data and texture transfer, shape morphing, and shape matching.     

Projective texture atlas construction for 3D photography

The use of attribute maps for 3D surfaces is an important issue in geometric modeling, visualization and simulation. Attribute maps describe various properties of a surface that are necessary in applications. In the case of visual properties, such as color, they are also called texture maps. Usually, the attribute representation exploits a parametrization g:U??²→?³ of a surface in order to establish a two-dimensional domain where attributes are defined. However, it is not possible, in general, to find a global parametrization without introducing distortions into the mapping. For this reason, an atlas structure is often employed. The atlas is a set of charts defined by a piecewise parametrization of a surface, which allows local mappings with small distortion. Texture atlas generation can be naturally posed as an optimization problem where the goal is to minimize both the number of charts and the distortion of each mapping. Additionally, specific applications can impose other restrictions, such as the type of mapping. An example is 3D photography, where the texture comes from images of the object captured by a camera [4]. Consequently, the underlying parametrization is a projective mapping. In this work, we investigate the problem of building and manipulating texture atlases for 3D photography applications. We adopt a variational approach to construct an atlas structure with the desired properties. For this purpose, we have extended the method of Cohen–Steiner et al. [6] to handle the texture mapping set-up by minimizing distortion error when creating local charts. We also introduce a new metric tailored to projective maps that is suited to 3D photography.     

Decorating surfaces with bidirectional texture functions

We present a system for decorating arbitrary surfaces with bidirectional texture functions (BTF). Our system generates BTFs in two steps. First, we automatically synthesize a BTF over the target surface from a given BTF sample. Then, we let the user interactively paint BTF patches onto the surface such that the painted patches seamlessly integrate with the background patterns. Our system is based on a patch-based texture synthesis approach known as quilting. We present a graphcut algorithm for BTF synthesis on surfaces and the algorithm works well for a wide variety of BTF samples, including those which present problems for existing algorithms. We also describe a graphcut texture painting algorithm for creating new surface imperfections (e.g., dirt, cracks, scratches) from existing imperfections found in input BTF samples. Using these algorithms, we can decorate surfaces with real-world textures that have spatially-variant reflectance, fine-scale geometry details, and surfaces imperfections. A particularly attractive feature of BTF painting is that it allows us to capture imperfections of real materials and paint them onto geometry models. We demonstrate the effectiveness of our system with examples.     

Representation of Urban Buildings Using Modified Relief Mapping

This paper describes the real-time mapping displacement of buildings onto the polygon model of base terrain of geo-spatial information,The buildings are represented as height maps,lcading to low memory requirements and not involving changes of the original geometry（i.e.no vertices are created or displaced）.The displacement of buildings is mapped toward the protruding direction,The base of textrue which represents the ground in topography is correctly mapped onto base polygon without any distortion.This approach can exhibit the correct,occlusions between buildings and ground due to parallax and correct self-occlusion.