Real-Time Texture Synthesis Using s-Tile Set

This paper presents a novel method of generating a set of texture tiles from samples,which can be seamlessly tiled into arbitrary size textures in real-time.Compared to existing methods,our approach is simpler and more advantageous in eliminating visual seams that may exist in each tile of the existing methods,especially when the samples have elaborate features or distinct colors.Texture tiles generated by our approach can be regarded as single-colored tiles on each orthogonal direction border,which are easier for tiling and more suitable for sentence tiling.Experimental results demonstrate the feasibility and effectiveness of our approach.     

On the parallel execution time of tiled loops

Many computationally-intensive programs, such as those for differential equations, spatial interpolation, and dynamic programming, spend a large portion of their execution time in multiply-nested loops that have a regular stencil of data dependences. Tiling is a well-known compiler optimization that improves performance on such loops, particularly for computers with a multilevel hierarchy of parallelism and memory. Most previous work on tiling is limited in at least one of the following ways: they only handle nested loops of depth two, orthogonal tiling, or rectangular tiles. In our work, we tile loop nests of arbitrary depth using polyhedral tiles. We derive a prediction formula for the execution time of such tiled loops, which can be used by a compiler to automatically determine the tiling parameters that minimizes the execution time. We also explain the notion of rise, a measure of the relationship between the shape of the tiles and the shape of the iteration space generated by the loop nest. The rise is a powerful tool in predicting the execution time of a tiled loop. It allows us to reason about how the tiling affects the length of the longest path of dependent tiles, which is a measure of the execution time of a tiling. We use a model of the tiled iteration space that allows us to determine the length of the longest path of dependent tiles using linear programming. Using the rise, we derive a simple formula for the length of the longest path of dependent tiles in rectilinear iteration spaces, a subclass of the convex iteration spaces, and show how to choose the optimal tile shape.     

Activatable tiles for compact robust programmable molecular assembly and other applications

Algorithmic DNA self-assembly is capable of forming complex patterns and shapes, that have been shown theoretically, and experimentally. Its experimental demonstrations, although improving over recent years, have been limited by significant assembly errors. Since 2003 there have been several designs of error-resilient tile sets but all of these existing error-resilient tile systems assumed directional growth of the tiling assembly. This is a very strong assumption because experiments show that tile self-assembly does not necessarily behave in such a fashion, since they may also grow in the reverse of the intended direction. The assumption of directional growth of the tiling assembly also underlies the growth model in theoretical assembly models such as the TAM. What is needed is a means for enforce this directionality constraint, which will allow us to reduce assembly errors. In this paper we describe a protection/deprotection strategy to strictly enforce the direction of tiling assembly growth so that the assembly process is robust against errors. Initially, we start with (1) a single “activated” tile with output pads that can bind with other tiles, along with (2) a set of “deactivated” tiles, meaning that the tile’s output pads are protected and cannot bind with other tiles. After other tiles bind to a “deactivated” tile’s input pads, the tile transitions to an active state and its output pads are exposed, allowing further growth. When these are activated in a desired order, we can enforce a directional assembly at the same scale as the original one. Such a system can be built with minimal modifications of existing DNA tile nanostructures. We propose a new type of tiles called activatable tiles and its role in compact proofreading. Activatable tiles can be thought of as a particular case of the more recent signal tile assembly model, where signals transmit binding/unbinding instructions across tiles on binding to one or more input sites. We describe abstract and kinetic models of activatable tile assembly and show that the error rate can be decreased significantly with respect to Winfree’s original kinetic tile assembly model without considerable decrease in assembly growth speed. We prove that an activatable tile set is an instance of a compact, error-resilient and self-healing tile-set. We describe a DNA design of activatable tiles and a mechanism of deprotection using DNA polymerization and strand displacement. We also perform detailed stepwise simulations using a DNA Tile simulator Xgrow, and show that the activatable tiles mechanism can reduce error rates in self assembly. We conclude with a brief discussion on some applications of activatable tiles beyond computational tiling, both as (1) a novel system for concentration of molecules, and (2) a catalyst in sequentially triggered chemical reactions.     

Optimal semi-oblique tiling

For 2D iteration space tiling, we address the problem of determining the tile parameters that minimize the total execution time on a parallel machine. We consider uniform dependency computations tiled so that (at least) one of the tile boundaries is parallel to the domain boundaries. We determine the optimal tile size as a closed form solution. In addition, we determine the optimal number of processors and also the optimal slope of the oblique tile boundary. Our results are based on the BSP model, which assures the portability of the results. Our predictions are justified on a sequence global alignment problem specialized to similar sequences using Fickett's k-band algorithm, for which our optimal semi-oblique tiling yields an improvement of a factor of 2.5 over orthogonal tiling. Our optimal solution requires a block-cyclic distribution of tiles to processors. The best one can obtain with only block distribution (as many authors require) is three times slower. Furthermore, our best running time is within 10 percent of the "predicted theoretical peak" performance of the machine!.     

Polyominoes simulating arbitrary-neighborhood zippers and tilings

This paper provides a bridge between the classical tiling theory and the complex-neighborhood self-assembling situations that exist in practice.The neighborhood of a position in the plane is the set of coordinates which are considered adjacent to it. This includes classical neighborhoods of size four, as well as arbitrarily complex neighborhoods. A generalized tile system consists of a set of tiles, a neighborhood, and a relation which dictates which are the “admissible” neighboring tiles of a given tile. Thus, in correctly formed assemblies, tiles are assigned positions of the plane in accordance with this relation.We prove that any validly tiled path defined in a given but arbitrary neighborhood (a zipper) can be simulated by a simple “ribbon” of microtiles. A ribbon is a special kind of polyomino, consisting of a non-self-crossing sequence of tiles on the plane, in which successive tiles stick along their adjacent edge.Finally, we extend this construction to the case of traditional tilings, proving that we can simulate arbitrary-neighborhood tilings by simple-neighborhood tilings, while preserving some of their essential properties.     

Dart Throwing on Surfaces

In this paper we present dart throwing algorithms to generate maximal Poisson disk point sets directly on 3D surfaces. We optimize dart throwing by efficiently excluding areas of the domain that are already covered by existing darts. In the case of triangle meshes, our algorithm shows dramatic speed improvement over comparable sampling methods. The simplicity of our basic algorithm naturally extends to the sampling of other surface types, including spheres, NURBS, subdivision surfaces, and implicits. We further extend the method to handle variable density points, and the placement of arbitrary ellipsoids without overlap. Finally, we demonstrate how to adapt our algorithm to work with geodesic instead of Euclidean distance. Applications for our method include fur modeling, the placement of mosaic tiles and polygon remeshing.     

A Comparison of Methods for Generating Poisson Disk Distributions

Poisson disk distributions have many applications in the field of computer graphics. Besides sampling, Poisson disk distributions are used in object distribution, non‐photorealistic rendering and procedural texturing. Over the years, a large number of methods for generating Poisson disk distributions have been proposed, making it difficult to choose the right method for a given application. In this paper, we present a detailed comparison of most techniques for generating Poisson disk distributions. The methods we study include dart throwing, relaxation dart throwing, Lloyd's relaxation, Shade's Poisson disk tiles, tiled blue noise samples, fast hierarchical importance sampling with blue noise properties, edge‐based Poisson disk tiles, template Poisson disk tiles, corner‐based Poisson disk tiles and recursive Wang tiles for real‐time blue noise. Analysing all of these methods within a single framework is one of the major contributions of this work.     

一种面向服务器制图可视化的矢量数据多尺度组织方法

提出了一种面向服务器制图可视化的矢量数据多尺度组织方法。基于矢量数据瓦片化思想,将矢量数据按照全球地理空间金字塔索引模型划分为层次化瓦片数据,将服务器制图可视化处理中对数据图层的空间查询操作,转化为对瓦片数据的数据读取操作。实验及应用表明,该方法减少了数据读取时间,降低了I/O代价,提高了矢量数据服务器制图可视化的整体性能。     

The 4-way deterministic tiling problem is undecidable

It is shown that the (infinite) tiling problem by Wang tiles is undecidable even if the given tile set is deterministic by all four corners, i.e. a tile is uniquely determined by the colors of any two adjacent edges. The reduction is done from the Turing machine halting problem and uses the aperiodic tile set of Kari and Papasoglu.     

离散曲面的近似Poisson盘采样

Poisson盘采样作为计算机图形学的一个重要课题,在重网格化、过程纹理、物体分布、光照计算等方面都有重要应用.虽然最近几年对于2维平面Poisson盘采样的研究比较密集,但是直接对于2维流形表面上的Poisson盘采样的研究却比较少.在本文中,我们提出了一种可以直接在Mesh表面生成近似Poisson盘分布的方法.此方法实现简单,同时可以通过简单修改适用于保特征的采样和自适应采样.文中引入了张量投票的方法来实现特征识别和自适应采样半径的计算,并给出了采样后的重网格化结果,作为此算法的一个后期应用.通过大量实例表明,本文方法快速、鲁棒、适用广泛.     

A robust high-resolution details preserving denoising algorithm for meshes

Poisson disk sampling has been widely used in many applications such as remeshing, procedural texturing, object distribution, illumination, etc. While 2D Poisson disk sampling is intensively studied in recent years, direct Poisson disk sampling on 2-manifold surface is rarely covered. In this paper, we present a novel framework which generates approximate Poisson disk distribution directly on mesh, a discrete representation of 2-manifold surfaces. Our framework is easy to implement and provides extra flexibility to specified sampling issues like feature-preserving sampling and adaptive sampling. We integrate the tensor voting method into feature detection and adaptive sample radius calculation. Remeshing as a special downstream application is also addressed. According to our experiment results, our framework is efficient, robust, and widely applicable.     

A unifying approach to picture grammars

Several old and recent classes of picture grammars, that variously extend context-free string grammars in two dimensions, are based on rules that rewrite arrays of pixels. Such grammars can be unified and extended using an approach, whereby the right part of a rule is formalized by means of a finite set of permitted tiles. We focus on a simple type of tiling, named regional, and define the corresponding regional tile grammars. They include both Siromoney?s (or Matz?s) Kolam grammars and their generalization by Pr?ša, as well as Drewes?s grid grammars. Regionally defined pictures can be recognized with polynomial-time complexity by an algorithm extending the CKY one for strings. Regional tile grammars and languages are strictly included into our previous tile grammars and languages, and are incomparable with Giammarresi-Restivo tiling systems (or Wang systems).     

A pipelined schedule to minimize completion time for loop tiling with computation and communication overlapping

This paper proposes a new method for the problem of minimizing the execution time of nested for-loops using a tiling transformation. In our approach, we are interested not only in tile size and shape according to the required communication to computation ratio, but also in overall completion time. We select a time hyperplane to execute different tiles much more efficiently by exploiting the inherent overlapping between communication and computation phases among successive, atomic tile executions. We assign tiles to processors according to the tile space boundaries, thus considering the iteration space bounds. Our schedule considerably reduces overall completion time under the assumption that some part from every communication phase can be efficiently overlapped with atomic, pure tile computations. The overall schedule resembles a pipelined datapath where computations are not anymore interleaved with sends and receives to nonlocal processors. We survey the application of our schedule to modern communication architectures. We performed two sets of experimental results, one using MPI primitives over FastEthernet and one using the SISCI API over an SCI network. In both cases, the total completion time is significantly reduced.     

Semi‐Stochastic Tilings for Example‐Based Texture Synthesis

We investigate semi‐stochastic tilings based on Wang or corner tiles for the real‐time synthesis of example‐based textures. In particular, we propose two new tiling approaches: (1) to replace stochastic tilings with pseudo‐random tilings based on the Halton low‐discrepancy sequence, and (2) to allow the controllable generation of tilings based on a user‐provided probability distribution. Our first method prevents local repetition of texture content as common with stochastic approaches and yields better results with smaller sets of utilized tiles. Our second method allows to directly influence the synthesis result which—in combination with an enhanced tile construction method that merges multiple source textures—extends synthesis tasks to globally‐varying textures. We show that both methods can be implemented very efficiently in connection with tile‐based texture mapping and also present a general rule that allows to significantly reduce resulting tile sets.     

移动设备上基于Wang tiles的双向纹理合成算法

为了在移动设备上实现纹理合成,首先在总结了PC平台上纹理合成技术特点的基础上,指出基于Wang tiles的纹理合成适合在资源受限的移动平台上实现;然后通过深入分析Cohen随机贴片算法中的不足,提出了改进的基于Wang tiles的双向纹理合成新算法,即包括样本纹理子图的选取、片填充和基于双向扫描的贴片算法。该算法不仅扩大了最佳切割线的搜索范围和增加了贴片的随机性,同时也减少了计算和存储需求。实验结果表明,该算法不仅能够运行在移动设备上,而且与随机贴片算法相比,还提高了非周期性视觉效果。     

A New Genetic Algorithm for Loop Tiling

Tiling is a known problem especially in the field of computational geometry and its related engineering branches. In fact, a tile is a set of points in the Cartesian space. The goal is to partition the space of the points as tiles with optimal dimensions and shapes such that a number of predefined semantic relations holds amongst the tiles. So far, this problem has been solved in special cases with two or three dimensions. The problem of determining the optimal tile is an NP-Hard problem. Presenting a novel constraint genetic algorithm in this paper, we have been able to solve the tiling problem in Cartesian spaces with more than two dimensions, for the loop parallelization problem.     

A parallel algorithm for improving the maximal property of Poisson disk sampling

This paper presents a simple yet effective algorithm to improve an arbitrary Poisson disk sampling to reach the maximal property, i.e., no more Poisson disk can be inserted. Taking a non-maximal Poisson disk sampling as input, our algorithm efficiently detects the regions allowing additional samples and then generates Poisson disks in these regions. The key idea is to convert the complicated plane or space searching problem into a simple searching on circles or spheres, which is one dimensional lower than the original sampling domain. Our algorithm is memory efficient and flexible, which generates maximal Poisson disk sampling in an arbitrary 2D polygon or 3D polyhedron. Moreover, our parallel algorithm can be extended from the Euclidean space to curved surfaces in an intrinsic manner. Thanks to its parallel structure, our method can be implemented easily on modern graphics hardware. We have observed significance performance improvement compared to the existing techniques.     

Tileable BTF

This paper presents a modular framework to efficiently apply the bidirectional texture functions (BTF) onto object surfaces. The basic building blocks are the BTF tiles. By constructing one set of BTF tiles, a wide variety of objects can be textured seamlessly without resynthesizing the BTF. The proposed framework nicely decouples the surface appearance from the geometry. With this appearance-geometry decoupling, one can build a library of BTF tile sets to instantaneously dress and render various objects under variable lighting and viewing conditions. The core of our framework is a novel method for synthesizing seamless high-dimensional BTF tiles, which are difficult for existing synthesis techniques. Its key is to shorten the cutting paths and broaden the choices of samples so as to increase the chance of synthesizing seamless BTF tiles. To tackle the enormous data, the tile synthesis process is performed in a compressed domain. This not only allows the handling of large BTF data during the synthesis, but also facilitates the compact storage of the BTF in a GPU memory during the rendering.     

An efficient code generation technique for tiled iteration spaces

This paper presents a novel approach for the problem of generating tiled code for nested for-loops, transformed by a tiling transformation. Tiling or supernode transformation has been widely used to improve locality in multilevel memory hierarchies, as well as to efficiently execute loops onto parallel architectures. However, automatic code generation for tiled loops can be a very complex compiler work, especially when nonrectangular tile shapes and iteration space bounds are concerned. Our method considerably enhances previous work on rewriting tiled loops, by considering parallelepiped tiles and arbitrary iteration space shapes. In order to generate tiled code, we first enumerate all tiles containing points within the iteration space and, second, sweep all points within each tile. For the first subproblem, we refine upon previous results concerning the computation of new loop bounds of an iteration space that has been transformed by a nonunimodular transformation. For the second subproblem, we transform the initial parallelepiped tile into a rectangular one, in order to generate efficient code with the aid of a nonunimodular transformation matrix and its Hermite Normal Form (HNF). Experimental results show that the proposed method significantly accelerates the compilation process and generates much more efficient code.