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题名:
基于几何的发型造型方法研究
作者: 张晓鹏
答辩日期: 1999
专业: 计算机软件
授予单位: 中国科学院软件研究所
授予地点: 中国科学院软件研究所
学位: 博士
关键词: 局部坐标架 ; 纹元 ; 体纹理 ; Bezier曲线 ; Bezier曲面 ; 圆柱体 ; 棱柱体 ; 台体 ; 螺线 ; 子分 ; 插值 ; 绘制
摘要: 毛发的造型和绘制技术是当今计算机图形学中的一个突出难题。因为头发形状精细,数量庞大,传统的造型和绘制技术很难达到令人满意的效果。近年来国际上已经有十多篇关于头发的造型、绘制和动画的论文发表,但它们有一个共同缺点:没有精确地描述出头发的结构组织。它们有的只处理直发,有的把每根头发按个体处理,有的虽然指出了头发的整体构造思想但没有给出头发结构的表示式,因而在造型控制、绘制效率、动画控制和内存节省上有不足之处,特别是它们无法描述出卷发型和波浪发型。我们针对头发提出了两种描述工具:弯曲纹元和弯曲体纹理,并给出了它们的数学表达式以及对不同发型的描述方法。弯曲纹元表示了形状近似的一簇头发,弯曲纹元按照头发的特性分成两种形式:心定弯曲纹元和棱定弯曲纹元。心定弯曲纹元是一个给定的三角形或四边形沿某条曲线,按照与局部坐标架所保持的特定关系进行移动而形成的几何体,三角形或四边形内每一个点经过移动而形成的轨迹就是这种纹元中头发中心的曲线,因而心定弯曲纹元由起始三角形或四边形和中心曲线决定,当然也要包含移动规则。棱定弯曲纹元是空间中三条或四条互相保持一定距离的参数曲线所张成的几何体,在给定三点或四点的内插形式之后就构成一簇插值曲线,这簇曲线便是棱定弯曲纹元中头发的中心曲线,因而棱定弯曲纹元由棱线决定,而插值方法一般取为局部重心坐标方法。弯曲体纹理是体纹理的推广形式,描述了一个弯曲几何体内曲线曲面的变化情况,适用于表现具有比较大的聚散变化的发簇,其特点在于曲线曲面的变化的自由度更宽。弯曲体纹理是多项式曲面的各个控制顶点各自沿着形状相近的曲线运动而形成的几何体,同样也可以看成是多项式曲面的各个控制顶点各自沿着形状相近的曲线运动而形成的几何体。由于拼接的三次曲线曲面可以实现各种几何特征,我们用三次Bezier曲线和三次Bezier曲面表示变化中的曲线曲面,得到的弯曲体纹理就是三次Bezier体。弯曲体纹理和弯曲纹元是弯曲状三维纹理的结构。我们认为复杂三维纹理的景物是由弯曲体纹理和弯曲纹元构成的,因而指明了三维纹理空间的结构,并解决了弯曲纹理曲面的描述问题、结构问题和造型问题。为了构造基本发型,我们用曲面插值方法将头皮曲面予以信息加细,用球面四边化的方法通过投影手段将头皮进行四边化处理,通过头皮曲面上相邻多边形之间的关系对头皮四边形重新组合等特别处理。参照理发师制作发型的过程,提出头发的分批构造方法,并且以人头部的形状为依据,给出头发自然分布的表示方式和纹元特征曲线造型的思想,进而给出简单发型的构造方法。然后根据头皮曲面上四边形的结构关系和纹元起始向量的插值方法,将简单造型予以修正和发展,给出几个发型的构造方法和实例。为了构造复杂发型,例如卷发发型和波浪发型,我们首先构造了五种曲面和三种曲线:弯曲圆柱面、弯曲圆台面、弯曲棱柱面、弯曲棱台面和弯曲旋转抛物面,以及弯曲圆柱螺线、弯曲圆台螺线和弯曲旋转抛物螺线,并且给出了这些曲线曲面上适合于拼接的点和向量的表示方式。然后给出了这些曲线曲面的拼接条件和拼接方法,并将它们用于构造弯曲纹元拼接起来的螺旋状发型。作为造型效果的显示手段,我们给出了局部光照绘制头发的简单方法,针对用弯曲纹元和弯曲全纹理描述的不同头发有不同的处理,这种方法虽然效果较差但速度快。为了绘制出造型的最终效果,我们给出了弯曲纹元和弯曲体纹理离散成直形纹元的具体方法。对于直形纹元,研究了直线元体内法线的局部相对坐标方程,和影射到纹元空间后的具体形状,并给出拟合纹元空间中光线曲线的方法以及它投影到纹元底面的曲线的形状,以便使用快速方法判断光线与头发的相交情况,进而给出在整体上具有发光滑效果的直纹元的绘制方法。最终实现了用光线跟踪绘制发型的方法,并得到了具有真实效果的发型图象。
英文摘要: Furry surface modeling and rendering is a prominent and difficult problem in modern Computer Graphics. It is not an easy work by traditional modeling and rendering techniques to get satisfactory effects, due to the fine shapes and the great quantity of human hairs. More than ten papers about hairs or furry surfaces have been published in international journals and conferences in recent years, but they have a common drawback: no precise specification was given for the structural organizations of hairs. Some of them only deal with short straight hairs, and some treat hairs individually, but some others, although indicate wisp ideas, present no structural expressions for hairs, so that they all show shortage in modeling control, rendering efficiency, and animation control, especially in describing curly style and wavy hairs. In the thesis we put forward description tools for hairs in terms of curved texel and curved volumetric texture. Also we give mathematical expressions for them and their applications for different hair styles. A curved texel is a set of hairs with similar shapes. Texels can be divided into two types in accordance with hairs styles, centrally controlled texels and edge controlled texels. A centrally controlled texel is a geometric body generated by triangles or quadrilaterals moving through the central curve according to some specific relation to local frames of the central curve, in which the track of a point in the moving triangle or the moving quadrilateral is the hair curve in the texel. Therefore, a centrolled texel is determined by the base triangle or quadrilateral and the central curve, including moving regulations. An edge controlled texel is a geometric body generated by three or four spatial parametric curves keeping mutual distances. After specifying a three point or four point interpolation, a cluster of curves or hair curves are constructed. The spatial parametric curves are known as the edges of the texel in an edge controlled texel. So an edge controlled texel is determined by edges, and the interpolations are generally the barycentric method. A curved volumetric texture is a generalization of volumetric texture, describing the variety of curves and surfaces in it. It is used to exhibit the cluster of hairs with great convergence and divergence, having the characteristic of great freedom for expressing hair shapes. A curved volumetric texture is a geometric body generated by a polynomial surface with each control point moving along corresponding polynomial curves. In another word, it can be also regarded as being generated by a moving polynomial curve with each control point moving along corresponding polynomial surfaces. Because composite cubic curves and composite cubic surfaces can achieve every geometric property of curves and surfaces, we use cubic Bezier curves and cubic Bezier surfaces to represent moving curves and surfaces, and the resultant curved volumetric texture becomes a Bezier solid. Curved texels and curved volumetric textures are structures of volumetric textures with curved shapes. We think scenes with complex volumetric textures are made up of curved texels and curved volumetric textures, which indicates the structure of volumetric textures, and the specification, structure and modeling problem of curved volumetric textures are achieved in the thesis. In order to model basic hair styles, we use surface interpolation method to refine scalp information, and use sphere quadrilateralization and the projection of a sphere to the head polyhedron to quadrilateralize the head, and use neighboring relationship of scalp polygons to reorganize scalp groups. ON reference of the process of barbers in making hair style, we bring forward the modeling method of hair style by group. Relying on geometric shape of human head, we give the natural distribution mode and the ideas of texel characteristic curve modeling, and present a modeling method for simple hair styles. Based on the structural relationship of quadrilaterals on a scalp and the interpolation of texel starting vectors, we further modify and improve the simple hair styles. In order to model complex hair styles, such as curly hairs and wavy hairs, we first construct five types of surfaces and three curves: curved cylinder, curved circular frustum, curved prism, curved edged frustum, curved revolving paraboloid, and curved cylinder helix, curved circular frustum helix and curved revolving paraboloid helix. Then we give the expressions for points and normal vectors on these surfaces, suitable to composition. At last, we present composite conditions and composite methods for all the curves and methods,and use them to construct helix hair styles of curved texel composition. For rendering the models, we present a local illuminance hair rendering method, dealing with hairs in curved texels and curved volumetric textures separately. The method is advantageous in speed though the quality of rendered image is not quite good. In order to render the final modeling result, methods are given to discretilize curved texels and curved volumetric textures to straight texels. As to straight texels, we study the local relative coordinate equation of a light line in a texel coordinate system, and the concrete shape of light line when mapped to texel space, so that quick check could be made for the intersection of light line with hairs. This becomes the straight texel rendering method of global smoothness for all hairs and can be used to long hairs. Finally the ray tracing hair style rendering method is applied to produce realistic images.
语种: 中文
内容类型: 学位论文
URI标识: http://ir.iscas.ac.cn/handle/311060/7214
Appears in Collections:中科院软件所

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Recommended Citation:
张晓鹏. 基于几何的发型造型方法研究[D]. 中国科学院软件研究所. 中国科学院软件研究所. 1999-01-01.
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