黄磊 侯增选 李楠楠 张迪靖 苏金辉

摘   要：针对汽车工业中虚拟油泥模型外观设计问题，采用一种六自由度输入设备并基于实时力反馈交互技术，提出一种新型的变刚度画笔模型以及触觉装饰方法，实现在虚拟三维物体表面实时触觉绘制与外观装饰.基于变刚度弹性理论，深入研究虚拟3D画笔的触觉行为.首先，采用一种弯曲弹簧振子模型来构建3D画笔的力学模型，并分析虚拟画笔实时变形与承受的绘制力之间的内在关系;接着，基于一种加权平均距离的碰撞算法，研究虚拟画笔与虚拟3D物体之间的碰撞检测问题;采用一种球扩展操作以获得弯曲画笔的最小包围球，进而计算得到虚拟投影平面;根据在一个采样点处的画笔变形，得到虚拟投影平面上的二维笔触;通过将二维画笔笔触实时地映射到三维对象表面，便可以得到三维笔触;沿着三维绘制方向，通过控制绘制力矩并叠加不同大小、形状的3D笔触便可得到3D笔道.仿真对比实验结果表明，所采用的画笔模型及方法可以有效增强用户虚拟绘制时的真实性.

关键词：计算机触觉;人机交互;实时力反馈;变刚度;碰撞检测

中图分类号：TP23                             文獻标志码：A   文章编号：1674—2974（2020）08—0049—11

Abstract：For the exterior design of virtual clay model in automotive industry， a novel variable stiffness brush model and haptic decorating method are proposed using a six DOF input device and based on real-time force feedback technology， and the haptic behavior of virtual 3D brush based on variable stiffness is studied in detail. Firstly， the relationship between brush deformation and endured force is examined by employing the bending spring-mass model to construct the 3D brush mechanical model. Then， the collision detection between virtual hairy brush and virtual 3D object is studied based on a collision algorithm of Weighted Average Distance. An effective ball expanding operation is used to compute the smallest bounding sphere of the bent brush  and then to determine the projection plane. The 2D footprint produced between the brush and the projection plane is calculated according to the deformation of the brush at a sampling point， and then， the 3D brush footprint can be obtained by projecting the 2D brush footprint onto the 3D object surface. The 3D brush stroke is formed by controlling the exerted force and superimposing 3D brush footprints along the direction of painting. Experiment results show that the adopted method can effectively enhance the reality to users.

Key words：computer haptics; human-computer interaction; real-time force feedback; variable stiffness; collision detection

无论是从企业层面还是从普通消费者的层面来讲，产品外观设计阶段在工业零部件或消费产品的概念设计阶段都占有非常重要的位置.产品外观设计，包括产品形状设计和产品外表面的装饰，通常采用计算机……