Development of Algorithms for Geometric Optimization and Data Analysis in Architecute

Architecute 中几何优化和数据分析算法的开发

基本信息

批准号：
13680412
负责人：
KATOH Naoki
金额：
$ 2.18万
依托单位：
KYOTO UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2003
项目状态：
已结题

项目摘要

Over the last three years, we have developed several geometric algorithms for optimization and data analysis in architecture. The summary of the results obtained as follows.1) We considered the problem of triangulating a convex polygon on spheres using n Steiner points that minimizes the overall edge length ratio. The problem arises in an application to approximation of curved surfaces of dome structures by triangular meshes. We establish a relation of this problem to a certain extreme packing problem. Based on this relationship, we develop a heuristic producing 6-approximation for spheres (provided n is chosen sufficiently large). That is, the produced triangular mesh is uniform in this respect.2) We studied the problem of rounding a real-valued matrix into an integer-valued matrix to minimize a n L_p-discrepancy measure between them. To define the L-p-discrepancy measure, we introduce a family of regions (rigid submatrices) of the matrix, and consider a hypergraph defined by the family. We first investigate the rounding problem by using integer programming problems with convex piecewise-linear objective functions, and give some nontrivial upper bounds for the L_p-discrepancy. We propose several interesting family of regions for which an efficient algorithm can be developed. We show that our approach is suitable for developing a high-quality digital-halftoning software.3) We developed an optimization method for finding an optimal floor layout of rooms, passages and door ways in a possibly non-rectangular site, based on mathematical programming as well as genetic algorithm.4) We developed a new method that quantitatively clarifies the relationship between the impression perceived on an photo of an architectural internal space and the phsical features of its color image. The effectiveness of the method was verified through questionnaires and experiments.

在过去的三年里，我们开发了几种用于建筑优化和数据分析的几何算法。所得结果总结如下： 1）我们考虑了使用n个斯坦纳点对球体上的凸多边形进行三角剖分的问题，以最小化总边长比。该问题出现在通过三角形网格近似圆顶结构的曲面的应用中。我们建立了这个问题与某个极端包装问题的关系。基于这种关系，我们开发了一种启发式方法，为球体生成 6 近似值（假设 n 选择足够大）。也就是说，生成的三角形网格在这方面是均匀的。2）我们研究了将实值矩阵舍入为整数值矩阵以最小化它们之间的n L_p-差异度量的问题。为了定义 L-p-差异度量，我们引入矩阵的一系列区域（刚性子矩阵），并考虑由该系列定义的超图。我们首先通过使用具有凸分段线性目标函数的整数规划问题来研究舍入问题，并给出 L_p 差异的一些重要上限。我们提出了几个有趣的区域族，可以为其开发有效的算法。我们证明我们的方法适合开发高质量的数字半色调软件。3) 我们开发了一种优化方法，用于基于数学编程在可能非矩形的场地中找到房间、通道和门道的最佳楼层布局以及遗传算法。4）我们开发了一种新方法，可以定量地阐明建筑内部空间照片上感知的印象与其彩色图像的物理特征之间的关系。通过问卷调查和实验验证了该方法的有效性。