外文参考文献译文及原文一种设计三维形状的工具

目录
1 引言 ........................................................................................................ 错误!未定义书签。

2 目前做法 ................................................................................................ 错误!未定义书签。

3 相关工作 ................................................................................................ 错误!未定义书签。

4 游艇的绘制 ............................................................................................ 错误!未定义书签。

5 特点和数据结构 .................................................................................... 错误!未定义书签。

6 成立曲线 ................................................................................................ 错误!未定义书签。

自由曲线 ........................................................................................... 错误!未定义书签。

约束曲线 ........................................................................................... 错误!未定义书签。

反射曲线 ........................................................................................... 错误!未定义书签。

结论 ............................................................................................................ 错误!未定义书签。

Contents
1 Introduction ............................................................................................. 错误!未定义书签。

2 Current practice ....................................................................................... 错误!未定义书签。

3 Related work ............................................................................................ 错误!未定义书签。

4 Sketch of a 12-meter yacht ...................................................................... 错误!未定义书签。

5 Features and data structures ..................................................................... 错误!未定义书签。

6 Curve creation.......................................................................................... 错误!未定义书签。

Free-form curves................................................................................ 错误!未定义书签。

Constrained curves ............................................................................ 错误!未定义书签。

Reflected curves ................................................................................ 错误!未定义书签。

Conclusions ................................................................................................ 错误!未定义书签。

一种设计三维形状的工具
1引言
形状设计通过产品不同化，视觉吸引力，符合人体工程学的表现有助于产品的商业竞争力。

遗憾的是，目前的CAD工具是无法达到外形设计专门好，因为它们不能把握快速素描的概念。

因此，设计人员更喜爱利用纸和铅笔进行初步构思。

咱们的目标是成立一个从全然上形成的CAD设计系统的新类型。

咱们希望它足够直观，易于利用，功能壮大以致工业设计人员能够将概念设计权的初始时期通过适当的模式制造它。

咱们依照咱们的方式来塑造一个新的范例，咱们能够称之为“在三维中直接设计。

”
咱们尤其要提供一个对用户友好的CAD界面，许诺用户通过手持的六位自由传感器直接输入三维空间信息来设计复杂自由曲面的形状。

如此的CAD系统将大大提高速度和形状设计质量。

2目前做法
在产品设计的最初时期，工业设计师往往造出粗糙的2D草图，只有最终产品的近似实际尺寸。

一旦设计师一直致力于某一具体方案，草图将转化为更精准的三维模型。

那个进程可能涉及到将粘贴版面编排或输入数据进运算机数据库。

在这两种情形下，从二维草图到三维模型的转变是主观的和临时性的。

该任务需要提取的素描（如剪影线，突出线条，线条和字符）及标注他们从而提供一个三维模型。

咱们能够刻画出他们利用这种“二维到三维”模式的复杂性和目前的CAD系统限制的事实，其中二维形状的输入成立了三维。

用户必需通过利用二维输入设备如鼠标，操纵杆，或牌进行三维信息沟通。

除运用二维到三维范式，今天的CAD系统的大部份人也需要一个超级详细的大体形状的代表性。

因此，用户必需有打算地和有层次地利用今天的三维CAD系统去设计模型，涉及指定层，局部坐标系统，除工作架的坐标必需与样条拟合。

有些系统许诺设计师绘制平面（二维），然后将与样条曲线拟合。

要取得三维曲线，但是，设计者必需通过指定移动的方向和幅度个别操纵点外的平面位移。

这些系统都需要用户在操纵工作点的水平工作，而不是本身的形状。

因此，用户被迫花费更多的时刻和地址如何规定的比例，以完成一项任务，而不是任务本身。

这老是一个“非直线前进”的系统和复杂的用户界面。

3相关工作
几个研究工作重点是开发设计CAD系统的初始时期。

彭特兰开发那个叫Supersketch的CAD工具，在此前提下，人们自然地把看到的物体看为“块状粘土。

”Supersketch的用户进展的原始形状和变形加入他们形成对象模型。

在另一项研究，彭特兰还制定了素描工具，提取二维透视图的三维特点。

编辑能够初步绘制曲线以后。

运算机接口最近的进展之一是三维输入设备。

几个初期的设计纳入附加的机械测量装置之间的联系。

在另一种方式，费尔德曼提供力反馈和位置和方向感应。

他的Joystring 包括一个手持3英寸的T型杆连接到伺服电机的电线杆和一台超级运算机操纵。

这种机械检测工具提供的费用和罚款使得它是为难的和限制自由运动的。

所谓的3D输入设备传感器框架是在一个CRT的周围感觉手指的位置和方向。

利用光学传感器阵列检测手部动作，那个装置能够用来“塑造”在屏幕上的部份。

最近的另一个进展是一个6位的自由度球，目前可从多个供给商取得利用。

那个工具，它类似于换档手柄上的杠杆，利用户能够在虚拟世界操纵的对象。

推，拉，扭力和旋转，转换成翻译。

具有3D输入设备的研究工作有重点关注波默斯三维六位的自由度设备。

这种输入设备采纳磁场，排除之间的手持传感器和运算机机械联系的需要。

在一个项目中，沃尔和杰瑟姆制造了6个自由度的自由度鼠标命名为“蝙蝠”来探讨三维场景操控。

他们发觉，最有效的方法来克服深度感觉模糊的地方是一个关于切换垂直轴90度翻转，同时禁用到屏幕的动作。

他们还发觉，与利用传统的鼠标接口相较，近似安置对象一个简单的任务，他们把那个结果记为手与物体运动之间的动觉对应关系。

该波默斯设备也被用于在图形工作站探讨的空间之间的输入和立体显示的对应关系。

施曼特实施单传感器波默斯6D“魔术棒”。

他的目标是发觉一个清楚投影到空间，让用户在投影图像达到立体影像与棒的立体显示的互动功能。

他第一制定了一个方案，创建三维涂料涂在棒周围地域。

项目到工作区的图像，施曼特用半镀银镜和传统视频监控安装以上，以45度角在用户眼前。

用户戴眼镜，看从镜上CRT反映的时刻复用立体影像。

施曼特的初步结果显示，棒子和投影图像的良好的自然对应产生于棒尖所画的线。

但是，渲染和图形之间的手部动作的检测和时刻距离所造成的磁场干扰有损于该工具的互动感觉。

该波默斯设备也被用于Eyephone和数据手套产品，让用户在虚拟世界内运作的VPL
之研究。

该Eyephone是一个头戴式显示屏，能够提供普遍的周边立体虚拟世界的视觉。

通过采纳一个波默斯传感器跟踪头部运动，Eyephone使运算机匹配观看者在虚拟世界中的位置和用户的头部方向。

总之，这两个装置许诺用户通过移动一个虚拟世界，通过互手套的手部动作与对象交互。

最后，VPL手套已被用在探讨立体显示三维曲面造型互动。

德罗斯的3D设计空间利用户能够利用手套和移动三维点，形成了复杂曲面多项式的“操纵网”。

4游艇的绘制
在试图把握3-Draw特性的进程中，咱们开始了一个12米长的游艇样品模型的构建。

下面的文本描述的步骤，设计人员利用3-Draw目前实现的功能完成了该模型。

设计师的进程伴随着数字记录。

第一，设计人员第一次提请两个游艇模型曲线确信右舷甲板和龙骨轮廓（见图）。

他画了一个作为一个独立的空间三维曲线的单手运动的甲板曲线。

接着，他利用Pick-Draw画出龙骨轮廓。

假设要利用Pick-Draw，设计师在右舷甲板预选两点（例如，一点在船头，另一点在船尾）作为新曲线的端点。

预先选择终止点使得设计师能够集中捕捉曲线的形状，而不用在绘制进程中担忧其大小，位置和方向。

以后，并自动绘制曲线折点，以适应终止点，设计师通过扭曲手持笔指定新的曲线方向。

然后，按下触控笔的按钮，设计师在所需的方向释放曲线。

在创建游艇下一步，设计师确信一个反射面来成立了船中心线。

在3-Draw的利用下，默许反射面能够“拿起”手写笔，然后以手写笔的自然动进行导向和定位。

在释放时（松开手写笔按钮），相关于其他对象组成的曲线，反射面仍处于相对固定的位置和方向。

然后，用户通过利用手写笔创建曲线的镜像版本。

图反映了甲板和龙骨曲线成立在船的左舷。

图展现甲板和龙骨曲线
成立船体形状，设计师下一步利用Pick-Draw，通过利用两个预选点绘制右舷舱壁（见图）。

在捕捉每一个舱壁的形状以后，设计人员通过扭曲手写笔设置加入舱壁的轴
的端点的扭量。

然后，他按下手写按钮以画下曲线。

（图还说明了一个前舱壁被扭曲到正确位置。

）另外，设计人员能够通过利用3-Draw的轴扭功能来改变任何曲线的轴旋转量。

在完成舱壁反映整个中心平面轮廓以后，设计师像画龙骨和甲板那样，利用两点绘制出一个舵。

图展现舱壁，注意利用笔完成舱壁曲线的扭转
图展现舵，龙骨和甲板的梁
接下来，设计师开始勾画翼龙骨。

不是预选两个端点，他绘制一个独立的曲线作为右舷剖面，使得他稍后能够利用转换和旋转功能来移动它的位置。

设计者在空间勾画出一条自由曲线作为翼龙骨。

他用镊子和位移枪的功能来微调曲线的形状。

镊子让设计者能够利用虚拟笔抓住一点，并能在手写笔的运动方向拉伸曲线。

当位移枪利历时，3-Draw从该虚拟手写笔尖端呈现半透明圆锥辐射。

当设计师横扫那个圆锥曲线部份，偏转的曲线距离正如从空气枪偏转一个字符串的浮动空间。

类似镊子，位移枪个别点的坐标偏移，以使曲线能理想变形。

一旦变形，曲线维持其新的形状。

在加上翼龙骨的三维轮廓之前，设计人员利用擦除功能削减龙骨基底的一条曲线。

然后，他利用保险丝功能挑选三条曲线联系在一路从而在船体上附上新的曲线。

一旦曲线融合成单一的曲线，它们能够轻松地移动，并反映在一个步骤。

设计者利用两点绘制法增加了一些弯曲过梁来取得图的模型。

图展现翼龙骨的三位轮廓
该游艇模型再加上桅杆，索具，帆，和国旗就能够完成。

设计者利用单一的预选点，通过Pick-Draw绘制桅杆和旗杆。

这使得它在形状确信后在规模，方向，形状和位置确信前很容易锚一曲线的终止。

随着桅杆，那个画图功能，让设计人员很容易维持和旋转游艇，在锁定曲线到位前同时移动桅杆以取得正确的向前或向后倾斜。

锁定桅杆到位后，设计师利用功能Ball和Socket抓住和精细定位桅杆，使得它仿佛是通过一个球窝关节连接在其基底。

5特点和数据结构
3-Draw维持一个三维虚拟世界类似于设计师的工作领域。

当设计师在源周围的移动波默斯传感器，那个动作就被映射到虚拟物体在虚拟世界中的动作。

这致使手部动作和虚拟物体移动产生一一对应。

从波默斯设备发送得来的点坐标当即抵消一个固定转译。

这抵消将绘制波默斯传感器的位置和方向，成为一个描述世界坐标的系统。

传入的信息流也被缩放，使得一个完整的三维手部运动的范围反映在屏幕上的虚拟物体运动。

该系统目前可显示一枝笔，类似于波默斯手写笔，和产品组合的形状相对应的对象传感器。

在一种情形中，对象传感器贴在一个类似剪贴板的调色板的顶部。

由于易于操作，它为绘制一个新模型的前几条三维曲线作为了一个粗略的指导。

该虚拟类似物关于调色板来讲是一个网格线，大小类似调色板。

通常，用户为了实现自己手中持有的曲线组成对象的感觉，会在绘制足足数量的曲线后关闭虚拟片。

参考图5，曲线是存储在3-Draw中关于它们自己的局部坐标系CSline。

另外，组成模型的每一组曲线的集合都有一个局部的坐标系统CScurve-list，正如和和谐系统的虚拟调色板CSobject和虚拟笔CSpen. 巢层次的坐标系统。

因此，在一个曲线显示之前，它的点坐标转换第一就说明该模型，然后就说明了虚拟调色板，最后一个关于虚拟世界CSworld。

3-Draw作为第一度持续基数样条呈现曲线。

曲线插值点从波默斯设备取得。

图坐标嵌套系统的树结构
6成立曲线
3-Draw许诺设计人员绘制三种曲线：自由曲线，约束曲线和反射曲线。

6.1自由曲线
3-Draw在目前的实现的要紧任务是绘制三维曲线和在虚拟工作区中相关于其他曲线成立自己的位置和方向。

在这种运作画图模式，用户通过按住手写笔的按钮按他所需的尺寸移动他的手来画一条曲线。

松开按钮曲线就画出来了。

在曲线的绘制进程中，3-Draw 转换直角点的坐标并对从笔传感器来的欧拉角到虚拟对象进行描述。

然后计算和存储新坐标点的位置。

起初，3-Draw 为虚拟对象和新的曲线指定坐标系统是为了与虚拟片制度同步和和谐。

但是，后来由于通过刚体变换曲线和对象被移动，该虚拟片的坐标系统与移动坐标系统进行对齐。

在一个自由形式曲线图，3-Draw不断更新虚拟笔和片剂的位置。

因此，设计者可能在取得多角度视觉的同时移动了牌。

另外，一条曲线的增加完全取决于触笔的移动。

因此，移动牌本身可不能造成画图。

添加最后一个增量点在曲线上确信曲线上增设一个点的位置。

这增量的转变是最后一次波默斯读取到此刻手写笔的位置转变，是关于对虚拟对象的描述。

6.2约束曲线
当创建曲线，设计者能够选择充分利用绘画的六位自由手写笔完全不受约束的规定，制定自由形式曲线。

关于它们的位置，方向，在虚拟工作区的大小，这种自由形式的曲线，确实具有7个自由度：曲线上一点的坐标X、Y、Z的位置，曲线上这点的三维定向，和曲线的缩放。

（固然，曲线的形状是手持式手写笔直接作用的结果。

因此，在形状域所有绘制曲线具有许多额外的自由度。

）
另外，在绘制曲线之前，设计者能够用一种或多种方式限制曲线的7个自由度。

在3-Draw 的目前实现中，用户能够在Pick Draw模式下预先制定一个或曲线的两个端点（如游艇的例子所说那样）。

预先指定限制的益处是抓住了一个曲线的形状，使得曲线的定位，定向，和其它方面的扩展能够与其它曲线脱钩。

用户能够通过单独集中形状取得更精准的形状，没有了在中意位置被限制的负担。

用户利用利用“行对准''采摘技术选择曲线和点。

用户将笔尖对齐屏幕上的对象并点击手写笔按钮。

以后3-Draw 在采摘区搜索RGB颜色的像素字节，为了显示存在的曲线和点的代码。

3-Draw能够从这些颜色字节取得一个点或曲线的数量，因为它呈现每
一个对象都有独特的颜色代码。

线的视线采摘利用户能够确信点的三维位置和曲线，没有实际履行虚拟笔困难的三维线路。

要选择模糊的对象，用户只需简单地移动虚拟片来揭露隐藏的对象。

采摘可用在默许的画图模式下，如此，用户能够通过按住笔按钮和移动手写笔来画曲线，或通过点击笔的按钮来选择一个曲线或点。

6.3反射曲线
在用户需要模型对称性的情形下，只有一半的模型需要被创建，另一半通过反射面反射曲线生成（如游艇的例子所讲）。

结论
3-Draw已经证明，在运算机绘制的三维模型是自然和快速的。

一个熟练的设计家呈现了一个12米长含有近100条曲线的全3D游艇线框模型约需小时。

在某种程度上，这种高水平是同时利用双手提供复杂的三维信息的结果。

3-Draw 提供壮大的动觉反馈给用户，使他们感到他们持有在屏幕上观看的对象，并与他们迅速自然地互动。

咱们也能够归功于利用3-Draw时的简单设计方式，这方式是基于咱们能够把一个复杂的自由曲面的形状制造分成四个步骤。

这四个步骤使纸和铅笔的绘制扩展到三维图形，运算性能够生成无视觉限制的模型，能让设计师简单地执行图像投影。

3-Draw通过使对捕捉形状、缩放和方向脱钩，进一步简化了画图进程。

用户目前能够预先指定的一个或两个曲线的端点位置，在画曲线后再指定剩余的七个自由度。

新手用户需要时刻去了解一个方式如何转换成三维手势，但所需三维图形的和谐远远比绘制角度或成为擅长雕塑所需的技术简单得多。

3-Draw表现了一种形状设计的新方式，该方式许诺直接探讨三维设计和解放设计者在利用二维工具时的限制性。

A Tool for Designing 3D Shapes
1Introduction
Shape design contributes to a product’s commercial competitiveness through product differentiation, visual appeal, and ergonomic performance. Unfortunately, current CAD tools do not serve shape design well because they can’t handle quick sketching of conce pts. As a result, designers prefer to use manual sketching tools such as paper and pencil to rough out their initial ideas.
Our goal is to develop a fundamentally new type of CAD system for designing shape. We want it to be sufficiently intuitive, easy to use, and powerful that industrial designers can and will use it from the initial stages of conceptual design right through to models suitable for manufacturing. We based our approach to shape design on a new paradigm that we could call “design directly in3D. ”
We particularly want to provide a user-friendly CAD interface that allows users to design complex free-form shapes by entering information directly in three dimensions using a pair of hand-held, six-degree-of-freedom sensors. Such a CAD system would significantly increase the speed and quality of shape design.
2Current practice
In the first stages of product design, industrial designers often create rough 2D sketches that only approximate the actual dimensions of the final product. Once a designer has committed to a particular alternative, the sketches are translated into a more precise 3D model. This process may involve clay mockups or entering data into a computer database. In either case, the transformation from 2D sketch to 3D model is subjective and ad hoc. The task requires extracting salient geometric features from the sketches (such as silhouette lines, highlight lines, and character lines) and dimensioning them to provide a 3D model.
We can trace the complexity and limitations of current CAD systems to the fact that they employ this “2D-to-3D” paradigm, in which 3D shape is built up from 2D inputs. The user must communicate 3D information using a 2D input device such as a mouse, joystick, or tablet.
In addition to employing the 2D-to-3D paradigm, most of today’s CAD systems also require a highly detailed underlying representation for shape. As a result, users must model a shape in a planned and methodical A typical session on today’s 3D CAD systems in volves specifying layers, local coordinate systems, and working planes in addition to point coordinates that must later be fitted with splines. Some systems allow the designer to draw planar (2D) curves that are then approximated with splines. To obtain 3D curves, however, the designer must move individual control points by specifying the direction and magnitude of out-of-plane displacement.
These systems all require the user to work at the control-point level rather than with the shape itself. As a result, the user is forced to spend a greater percentage of time specifying how and where to accomplish a task rather than on the task itself. This invariably results in a “nonstraightforward” system and a complex user interface.
3Related work
Several research efforts have focused on developing CAD systems for the initial stages of design. Pentland developed such a CAD tool, called Supersketch, on the premise that people naturally see objects as “lumps of clay. ” Users of Supersketch develop models by deforming primitive shapes and joining them to form objects. In separate research, Pentland also developed a sketching tool that extracts 3D features from 2D perspective drawing. Editing is possible after drawing the initial curves.
One of the most recent developments in computer interfaces is the 3D input device. Several early designs incorporated mechanical linkages attached to measuring devices. In another approach, Feldman provided force feedback as well as position and orientation sensing. His Joystring consisted of a hand-held three-inch T-bar connected by wires to servomotors and controlled by a supercomputer. Such mechanical sensing tools provided fine resolution at the expense of being awkward and limiting in the freedom of motion.
A 3D input device called the Sensor Frame continuously senses finger position and orientation in the vicinity of a CRT. Using an array of optical sensors to detect hand movements, this device can be used to “sculpt” parts on a screen. ’ Another recent development is a six-degree-of-freedom ball, currently available from several vendors. This tool, which resembles the handle on a gearshift lever, allows users to manipulate objects within a virtual world. Pushing, pulling, and twisting forces are converted into translations and rotations.
Several research efforts with 3D input devices have focused attention on the Polhemus 3Space six-degree-of-freedom device. This input device employs magnetic fields, eliminating the need for mechanical linkages between the hand-held sensors and the computer. In one project, Ware and Jessome created a six-degree-of-freedom mouse named the “Bat” to explore manipulation of 3D scenes. ” They discovered that the most effective way to overcome depth perception ambiguities was to toggle a 90 degree flip about a vertical axis while disabling motion into the screen. They also found that approximate object placement became a trivial task with the Polhemus device compared with using conventional mouse interfaces. They credited this result to the kinesthetic correspondence between hand and object movement.
The Polhemus device has also been used to explore the correspondence between spatial input and stereoscopic display in a graphics workstation. Schmandt implemented a single-sensor Polhemus as a 6D “magic wand.” His goal was to discover the interactive capabilities of stereoscopic displays by projecting stereo images into an unobscured space and letting the user reach into the projected image with the wand. He first developed a 3D paint program that created painted regions in the vicinity of the wand. To project images into the workspace, Schmandt used a half-silvered mirror and a conventional video monitor mounted above and in front of the user at a 45 degree angle. The user wore electrically shuttered glasses and viewed time-multiplexed stereo images reflected from the CRT onto the mirror. Schmandt’s initial results indicated a good natural correspondence between the wand and the projected images of painted lines emanating from the tip. However, magnetic field disturbances from the monitor and the time lag between hand motion and graphic rendering detracted from the interactive feel of the tool.
The Polhemus device has also been used by VPL Research in the Eyephone and DataGlove products to enable users to operate within virtual worlds. The Eyephone is a head-mounted display that provides wide peripheral stereoscopic views of virtual worlds. By incorporating a Polhemus sensor to track head motions, the Eyephone enables the computer to match the position and orientation of the viewer in the virtual world with the position and orientation of the user’s head. Together, these two devices allow a user to move through a virtual world and interact with objects via the hand motions of the glove.
Finally, the VPL glove has been used in conjunction with a stereoscopic display to explore interactive modeling of 3D surfaces. DeRose’s 3D Design Space lets users reach in using the glove and move 3D points that form the “control nets” of complex polynomial surfaces.
4Sketch of a 12-meter yacht
In an attempt to capture the flavor of 3-Draw, we initiated construction of a sample model of a 12-meter yacht. The following text describes the steps the designer took to complete the model using 3-Draw’s currently implemented features.Accompanying figures trace the designer’s progress.
To begin, the designer first drew two curves of the yacht model to establish the starboard deck and keel contours (see Figure . He drew the deck curve with a single hand motion as an unattached 3D curve in space. Next he drew the keel contour using Pick-Draw. To use Pick-Draw, the designer preselected two points on the starboard deck (for example, one at the bow, the other at the stern) as the new curve’s endpoints. Preselecting endpoints in advance allowed the designer to concentrate on capturing the shape of the curve without worrying about its scale, placement, and orientation during the drawing process. After the curve was drawn and automatically snapped to fit the endpoints, the designer specified th e new curve’s orientation about the axis joining its endpoints by twisting the hand-held stylus. Then, by pressing the stylus button, the designer released the curve in the desired orientation.
In the next step of creating the yacht, the designer positioned a reflection plane to establish the center line of the boat. In 3-Draw, a default reflection plane can be “picked up” with the stylus, then positioned and oriented with natural motions of the hand holding the stylus. When released (by releasing the stylus button), the reflection plane remains fixed in its position and orientation relative to the other curves comprising the object. The user then creates mirrored versions of curves by picking them with the stylus. Figure illustrates the reflected deck and keel curves that establish the port side of the boat.
Figure 3-Draw image showing newly reflected port deck and keel curves To establish shape in the hull, the designer next drew the starboard bulkheads using the Pick-Draw method with two preselected points (see Figure . After capturing the shape of each bulkhead, the designer set the amount of twist through the axis joining the bulkhead’s endpoints by twisting the stylus. He then pressed the stylus button to release the curve. (Figure also illustrates one of the bulkheads prior to being twisted into the proper position.) Additionally, the designer can later alter the amount of axis twist of any curve by using the 3-Draw feature Axis-Twist.
After reflecting the bulkheads across the center plane to complete the port contour, the designer added a rudder as well as a keel and deck crosspieces using two-point Pick-Draw (see Figure .
Figure 3-Draw image showing bulkheads. Note the twisting of a bulkhead curve,
accomplished using the pen
Figure 3-Draw image showing rudder as well as keel and deck crosspieces Next, the designer began to sketch the winged keel. Rather than preselect two endpoints, he drew the starboard profile as a freestanding curve so that he could later move it into position using the features Translate and Rotate.
The designer sketched the winged keel as a free-form curve in space. He used the features Tweezers and Displacement Gun to fine-tune the curve’s shape. Tweezer s allows the designer to grab a point with the virtual pen and stretch the curve in the stylus’s direction of
motion. When the Displacement Gun is executed, 3-Draw renders a translucent cone radiating from the tip of the virtual stylus. As the designer sweeps this cone through portions of curves, the curves are deflected away as if from an air gun deflecting a string floating in space. Similar to Tweezers, the Displacement Gun offsets individual point coordinates in order to bring about the desired deformation of the curve. Once deformed, a curve retains its new shape.
Before attaching the 3D profile of the winged keel, the designer cut one of the curves at the base of the keel using Erase Point. He deleted the internal curve segment using Erase Line. Then he attached the new curve to the hull by picking the three curves to be linked with the feature Fuse. Once curves are fused into single curves, they can be moved and reflected easily in one step. The designer added some curved crosspieces using twopoint Pick-Draw to obtain the model shown in Figure .
Figure 3-Draw image showing outline of 3D winged keel The model of the yacht was finished with the addition of mast, rigging, sails, and flag . The designer drew the mast and flagpole with Pick-Draw, using a single preselected point. This made it easy to anchor one end of the curve before drawing and finalize the scale, orientation, and position after the shape was captured. With the mast, this drawing feature made it easy for the designer to hold and turn the yacht, and simultaneously move the mast to obtain the proper rake fore and aft before locking the curve into place. After locking the mast in place, the designer used the feature Ball and Socket to grab and finely position the mast as if it were attached at its base via a ball and socket joint.
5Features and data structures
3-Draw maintains a 3D virtual world analogous to the designer's work area. As the designer moves the Polhemus sensors in the vicinity of the source, this motion is mapped into similar motion of virtual objects in the virtual world. This results in a one-to-one mapping of hand motions to virtual object motions.
Point coordinate data sent from the Polhemus device is immediately offset by a fixed translation. This offset maps the positions and orientations of the Polhemus sensors into a description with respect to the world coordinate system. The stream of incoming information is also scaled so that a full range of 3D hand motions causes the movement of the virtual objects to fill the screen.
The system currently can display a pen, analogous to the Polhemus stylus, and an assortment of shapes corresponding to the object sensor. In one case, the object sensor is affixed to the top of a flat palette resembling a clipboard (see Figure 4). Easy to manipulate, it serves as a rough guide for drawing the first few 3D curves of a new model. The virtual analogue to this palette is a tablet with grid lines, similar in size to the palette. Often, users will "turn off" the virtual tablet after drawing a sufficient number of curves to achieve the feeling of holding in their hands the curves comprising the object.
Referring to Figure 10, curves are stored in 3-Draw with respect to their own local coordinate systems, CSline. Additionally, a local coordinate system exists for each set of curves comprising a model, CScurve-list, as well as coordinate systems for the virtual palette, CSobject, and virtual pen, CSpen. The coordinate systems nest hierarchically. Thus, before a curve is displayed, its point coordinates are transformed first to a description with respect to the model, then to a description with respect to the virtual palette, and finally to one with respect to the virtual world, CSworld. 3-Draw renders curves as first-degree continuous cardinal splines. The curves interpolate the points obtained from the Polhemus device.。