A Geometrical Analysis of Aesthetic Free-form Surface and Its Application to Surface Design

本研究的目的是分析和可视化美学曲面的属性，并构造出满足设计者意图的形状。为了明确这些属性，引入了自由曲面的曲面边的概念。曲面边具有与多面体边相似的性质，并由等高线的高度、距离、坡度、主曲率等方程导出的微分方程来定义。曲面边分为两类：固有曲面边和环境相关曲面边。曲面的固有边由与曲面垂直的主曲率来定义，因此可以用它来揭示曲面的内在特征。依赖于环境的曲面边由曲面上依赖于视点灯光位置的值定义。这种类型的曲面边直接影响曲面的外观。这个…的结果S的更多研究给出了根据造型设计者的感觉生成美学造型的基础技术。为了满足设计师构造汽车车身等美学造型的意图，我们提出了一种曲线构造法作为自由造型设计的第一步。在表面设计过程中，设计者根据自己的感觉来确定形状，这与周围场景的阴影线、高光线和反射图像密切相关。由于反射和明暗效果受曲面曲率变化的影响，曲率变化是一个重要的影响因素，应按设计者的要求进行分配。通过前面的实验，我们发现设计者希望曲线的曲率曲线是单调的，并且有不到两个拐点。为了合成这类曲线，我们提出了一种基于其渐开线的曲线生成方法。从边界条件出发，将渐开线表示为一条Bezier曲线，并求出其渐开线，然后用G^2NURBS将其拟合为目标曲线。我们还讨论了一种曲线修改方法，以及在曲面构造中的应用，并对该方法进行了评估。较少

The purpose of this research is analize and visualize properties of aesthetic surfaces, and to construct shapes which satisfy designer's intention.In order to make clear the properties, a new concept, which we call surface edges of free-form surface, is introduced. The surface edges have similar properties as edges of a polyhedron, and are defined by the differential equations which are derived from equations for contour curves for height, distance, gradient, principal curvature and so on. The surface edges are classified into two types : inherent surface edge and environments-dependent surface edge. The inherent surface edge is defined by principle curvature which is perculiar to the surface, therefore with it we can reveal intrinsic characteristics to the surface. The environments-dependent surface edge is defined by the value on the surface that depend on a view points a light position. This kinds of surface edges affect directly to the appearance of the surfaces. The results of thi … More s research give fundamental technology to generate an aesthetic shape according to styling designers'feeling.To satisfy designer's intention for constructing aesthetic shapes such as automotive bodies, we have proposed a curve contruction method as the first step of free-form-shape design. In surface design process, designers determine shapes according to their feeling which is greatly concerned to shade lines, high-light lines and reflected images of the surrounding scene. Since the reflection and shading is affected by the curvature variation of the surfaces the curvature variation is important factor and should be distributed as designers want. By our previous experiments we found that designer wants the curve whose curvature plot is monotone and has less than two inflection points. To synthesis such curves we develope a curve generation method based on its evolute. From the boundary conditions we represent the evolute as a Bezier curve, and obtain its involute and then fit the curve by G^2NURBS as an objective curve. And we also treat a method of curve modification, an application to surface construction and evaluation of our method. Less