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.

在过去的三年中，我们开发了几种几何算法，用于在体系结构中进行优化和数据分析。 1）我们考虑了使用n个steiner点在球体上进行三角调节的问题的问题，该问题是将整个边缘长度比最小化的N型施泰纳点。该问题是在三角形网格中应用于圆顶结构弯曲表面的近似。我们建立了这个问题与某些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生产的球形（规定n可以足够大）。也就是说，在这方面，生成的三角形网格是统一的。2）我们研究了将实值矩阵四舍五入到整数值矩阵中，以最大程度地减少它们之间的n l_p-discrespancy量度。为了定义L-P-discrepancy措施，我们介绍了矩阵的一个区域（刚性一材）家族，并考虑家庭定义的超图。我们首先通过使用凸面分段线性目标函数的整数编程问题来调查舍入问题，并为L_P-拨款提供一些非平凡的上限。我们提出了一些有趣的区域系列，可以开发有效的算法。我们表明我们的方法适合开发高质量的数字速度软件。3）我们开发了一种优化方法，以在可能非划分的位点找到最佳的房间，通道和门方式的最佳地板布局，基于数学编程以及遗传算法。图像。该方法的有效性通过问卷和实验验证。