Recurrent Modeling

目前的分形工具缺乏对特定自然结构建模所必需的控制水平。例如，已经建立了许多树木的分形模型，但是给定一棵特定的树，使用当前的分形建模模型很难表示树的特定形状。循环建模项目确定了这个问题的三个方面，并试图用几个新的分形建模工具来解决每个方面。目的一：循环模型表示。通过将经典的自指表示转换为标准的隐式和参数形式，循环建模努力将分形表示提升到计算机辅助几何设计中光滑表面所享受的复杂水平。循环建模还尝试了“程序几何实例化”，并增强了经典对象实例化范式，使其能够更有效地表示l系统当前指定的开发分形模型。目的二：交互循环建模。循环建模将计算机辅助几何设计的工具扩展到分形几何。直接操作界面提供了分形建模过程中的实时反馈。前一个目标的隐式公式允许应用专门为自然建模设计的标准混合公式。扩展构造立体几何以包含分形模型支持从基元构造复杂形状。目的三：自动循环建模。循环建模攻击分形几何的逆问题：从基于模型的计算机视觉领域“找到近似给定形状的分形模型的参数”。第二位PI是nsf支持的基于模型的计算机视觉研究员。他对这个问题的独特见解导致了一种新的解决方案，称为“相似性哈希”。相似性哈希在初始测试中成功检测到自相似性并返回自相似模型的参数。循环建模继续这项研究，以开发一种自动系统，用于发现自然结构中的自性。循环建模提出的新工具将影响计算机图形学和森林科学领域。新的工具将表现出非常详细的几何图形，比如森林和农作物。这些模型可以应用于图像合成，特别是在动画、虚拟环境、基于物理的建模和遥感中。计算机辅助几何设计的平滑表示有助于制造商，而通过循环建模表示提出的细节的有效表示将有助于环境的研究。* * *

Current fractal tools lack the level of control necessary to model specific natural structures. For example, many fractal models of trees have been constructed, but given a particular tree, it would be difficult to represent the tree's specific shape using current models of fractal modeling. The recurrent modeling project identifies three aspects to this problem, and attempts to solve each with several new fractal modeling tools. Objective I: Recurrent Model Representation. Recurrent modeling strives to elevate fractal representation to the level of sophistication that smooth surfaces enjoy in computer-aided geometric design by translating their classical self-referential representation into standard implicit and parametric forms. Recurrent modeling also attempts "procedural geometric instancing," and enhancement of the classic object instancing paradigm that enables it to more efficiently represent the development fractal models currently specified by L-systems. Objective II: Interactive Recurrent Modeling. Recurrent modeling extends the tools of computer-aided geometric design to fractal geometry. A direct manipulation interface provides real time feedback in the fractal modeling process. The implicit formulation from the previous objective allows the application of standard blending formulations specifically designed for natural modeling. Extending constructive solid geometry to include fractal models supports the construction of complex shapes from primitives. Objective III: Automatic Recurrent Modeling. Recurrent modeling attacks the inverse problem of fractal geometry: "find the parameters of a fractal model that approximates a given shape" from the domain of model-based computer vision. The second PI is an NSF-supported model-based computer vision researcher. His unique perspective on this problem resulted in a new solution, called "similarity hashing". Similarity hashing successfully detects self-similarity and returns the paramete rs of the selfsimilar model in initial tests. Recurrent modeling continues this research to develop an automated system for discovering selfaffinity in natural structures. The new tools recurrent modeling proposes would impact the fields of computer graphics and forest science. The new tools would represent highly detailed geometrics, such as a forest and crops. Such models would have applications in image synthesis, particularly in animation, virtual environments, physically- based modeling and remote sensing. As the smooth representations of computer-aided geometric design aid manufacturers, the efficient representations of detail proposed by recurrent modeling representations would aid the study of the environment. ***