公路真三维设计：基于体感交互和三维空间曲线的方法

Geometric design is an important phase in the highway design process that is directly related to traffic safety. However, although the 3-D nature of highways is a well-known fact, highways are still designed as separate 2-D horizontal and vertical alignments. This design way is the main reason lead to the unmatched in features between geometric and vehicle and driver, hence two-dimensional (2-D) analysis that does not guarantee a satisfactory design. The aim of this project is build a renew design system, called "true 3-D" geometric design of highway alignment. First of all, an entirely new design interact system from point of view of 3D is proposed. In this system, the handle gesture is capture to use be operation of road alignment design which is totally different from the 2-D "mouse" system. Then, under 3-D spatial, the sight distance, vehicle stability, driver comfort, drainage, and aesthetics is reconstructed. The analyze model and it's constrain model hence are builder to support the renew 3-D design. At the same time, an extended Pythagorean Hodograph curve is used to model the uniform the horizontal and vertical alignments in the 3-D space. Connected with the constraint model of design elements and the 3-D curve model, a control points based 3-D curve fast fitting method is proposed. Finally, a G2 continued 3-D curve is generated to satisfy the highway geometric design. This project tries to rebuild highway geometric design theory under basic from separate 2-D alignments to 3-D uniform alignments. We trust our research will make people review the highway geometric design from a total new viewpoint and will bring a new revolution in the highway geometric design theory.

传统的将公路空间线形分割为平、纵组合的方法，忽视公路"三维"自然本质，导致公路几何特性与车辆行驶特性、驾驶人特性三者之间的不匹配，诱发严重的安全隐患，是公路线形设计面临的主要困境之一。本项目着重研究公路"真三维"设计问题，力图突破传统的将公路空间线形分割为平、纵组合的方法，回归公路几何设计"三维"自然本质，从三维空间的角度考察设计的人机交互问题，利用手势识别，提出基于体感的全新三维交互设计，重新在三维空间下的视距分析，排水分析，汽车行驶轨迹分析，建立其解析模型及其对应的设计约束模型，并将公路二维的平面线形和竖直线形归结到一个统一的三维空间曲线，构建精确的三维空间公路线形模型，发展出控制点约束下的空间曲线快速拟合求解方法，形成G2连续的公路三维空间曲线。本项目力图从"根源"上重构"真三维"公路几何线形设计理论，为后续的真三维几何设计及其优化奠定基础，实现公路几何设计理论的根本性的变革。

公路真三维设计面临 “三维人机交互”与“公路三维空间曲线数学描述模型”两个关键问题。本研究取得如下成果：.1）提出了基于体感交互的公路真三维设计思路，通过人体运动感知，采用手势在带有真实地形景观的三维虚拟环境中直接进行公路空间曲线交互设计。.2）建立了面向公路空间曲线设计的手势三维自然用户界面，对用户界面的功能目标、组成、交互手势系统、控制参数系统与手势识别方法进行研究与设计。根据交互任务的不同，创造性的采用Kinect与肢体手势进行三维虚拟导航，采用Leap Motion与手指手势进行三维线形实体对象操控，实现了高效舒适导航与精确线形设计的兼顾。.3）从公路三维线形本质出发，依据微分几何曲线论，采用曲率和挠率这两个指标对空间曲线的几何特性进行描述，曲率、挠率作为空间曲线的内在几何不变量，可以完全确定曲线的几何形状。.4）发现公路线形设计时平纵线形的叠加并不能保证组合线形在三维空间中的连续性，当二维线形要素变化时，空间曲线的几何连续性会存在不同程度地衰减。.5）在车辆坐标系（即Frenet活动标架）的基础上，将汽车视为刚体，对汽车空间运动进行了研究分析，从微观角度建立了以三维线形指标曲率、挠率为控制量的汽车空间运动模型，综合线形几何连续性、车辆稳定性、行车舒适性等要求，建立了公路三维线形设计指标的工程约束模型。.6）从线形本身的几何特性、计算需求和信息传递三个方面对3-D样条曲线、组合曲线和PH曲线进行了综合对比，确定采用五次PH曲线进行公路三维几何线形设计和构造。采用五阶Bezier多项式形式表示PH曲线，可将三维PH曲线求解问题转换为确定多项式系数问题，此时曲线的路径长度、曲率和挠率均可用多项式表达式表示，可精确计算而不是估计值。本文给出了详细的PH曲线模型的求解过程。