【作者】 李博；

【导师】 张丽艳；

【作者基本信息】 南京航空航天大学 ， 航空宇航制造工程， 2013， 博士

【摘要】 浮雕在产品包装、外形装饰、纪念币生产等行业有着广泛的应用和大量的市场需求。基于2D图形、图像的浮雕设计方式建模过程复杂、模型表示直观性差，难以胜任具有丰富细节的浮雕设计。近年来，随着3D数字化测量技术与数字几何处理技术的不断发展，使得利用3D实物数字化模型进行浮雕设计成为CAD领域的研究热点。本文以离散微分几何理论和数字几何处理技术为基础，对基于实物模型的浮雕数字化设计理论和方法进行了深入的研究，分别从浮雕的结构形态和设计制作过程的角度，提出了适合以3D实物数字化模型为设计起点的浮雕数字化定义，并据此展开了对平面浅浮雕、曲面浅浮雕、线刻浮雕及浮雕重用设计的研究。本文的主要内容和创新点总结如下：1、针对平面浅浮雕的生成，在几何信号的空域上提出了两种方法：基于形状特征分解的方法和基于微分坐标变形的方法。前者利用Laplace-Beltrami算子和低通滤波将源几何形状分解为模型大样和两个尺度上的细节，通过在各尺度上实施有针对性的压缩实现浮雕生成，算法效率高且生成的浮雕有很好的细节。后者利用微分坐标这一曲面局部形状度量，将目标浮雕隐式地表达为满足边界约束条件的Poisson方程的最优解。这两种方法克服了已有从3D数字化模型设计浮雕需要重采样的缺点，实验表明在网格顶点数量相同的条件下，本文方法产生的浮雕效果优于应用重采样方法得到的浮雕。2、首次在频域上展开了对平面浅浮雕生成方法的研究，分别提出了基于曲面流形调和变换和基于Fourier变换的方法。前者以曲面流形调和变换的特征函数为一组正交基，将源模型由空域变换到频域，利用提出的几何频谱分割方法获得低频和高频信号，通过对各频段信号的压缩和流形调和逆变换实现浮雕生成。该方法对细节较少或网格分辨率较低的模型同样可以得到较好的浮雕效果。后者通过Fourier变换和高通滤波在频域实现形状压缩，利用所提出的绝对变差函数进一步检测形状的不连续位置并压缩其深度，最终生成浮雕。该方法具有较高的时间效率，对具有较强边缘特征的源模型生成的浮雕效果尤为突出。3、提出了一种保持细节的曲面浅浮雕设计方法。该方法将曲面浮雕的生成转化为目标浮雕曲面与背景曲面满足一阶几何连续性约束的最小二乘问题，在梯度域中对模型依次采用Canny算子、双边滤波算子和非锐化掩模方法保持浮雕细节，并通过约束条件的松弛因子控制浮雕在曲面上的立体感。该方法解决了浮雕在背景曲面上的光滑过渡问题，得到的曲面浅浮雕不但很好地保持了源模型的细节，且在算法给定的控制参数下具有很好的形状可控性。4、提出了一种线刻风格的浮雕设计方法。该方法包括视觉相关的初始特征点提取、基于分离-连接度的骨架提取算子的特征点优化，给定线宽参数的特征线提取、深度压缩等步骤，生成的线刻浮雕很好地表达了源模型的形状信息，有较好的视觉效果。5、针对浮雕设计过程中存在重复性设计的问题，研究并提出基于法矢调整的浮雕黏贴方法。以原浮雕模型与目标背景曲面作为输入，通过参数域对齐、浮雕映射、法矢调整等过程实现新浮雕模型的快速设计。该方法能有效减小浮雕在黏贴过程中产生的变形。更多还原

【Abstract】 Bas-Relief is widely used in packaging, shapes decoration, coinage industry. Digital bas-reliefdesign based on2D images and sketches is not proper for high-detailed bas-relief, due to thecomplicated processes and abstract representation of model. In recent years, with the development of3D measurement technology and digital geometry processing technology, digital bas-relief designfrom3D model is becoming to a hot research spot in the field of CAD. In this paper, an intensivestudy based on the discrete differential geometry and digital geometry processing technology iscarried out on the theory and methods of digital bas-relief design from3D object models, Definitionsof digital bas-relief are proposed in view of the bas-relief structure and the design process respectively,which are suitable for bas-relief design from3D digital models. Afterwards, four contents arethoroughly studied including planar bas-relief design, curved surface bas-relief design, line-basedbas-relief design and bas-relief reapplication.The main contents and innovations are summarized as follows:Two algorithms for planar bas-relief design are proposed in spatial domain of geometry signal. Oneis based on shape features decomposition, the other is based on differential coordinate deformation.For the first one, a shape is decomposed into one base part and two detailed parts at different scalesusing low-pass filtering and Laplace-Beltrima operator, subsequently, a detail-preserving bas-relief isachieved efficiently by applying different compression manner to those parts accordingly. For thesecond one, the object bas-relief is expressed to the optimum solution of a Poisson equation with thefixed boundary condition implicitly by using differential coordinate which measured the localgeometry shape. These two methods solved the resample disadvantage of the existing bas-reliefgeneration algorithm. The experiments show that relief generated by methods in this paper is betterthan the relief obtain by resample method if they have the same number of vertices.The first try to design the plane bas-relief in frequency domain is made in this paper, twoalgorithms are provided including an algorithm based on manifold harmonic transforming and analgorithm based on Fourier transforming. For the first one, the geometry signal is transformed fromspatial domain to frequency domain by using the eigenfunctions of manifold harmonic transformingas a set of orthogonal basis. And then the signal is divided into high frequency and low frequency bygeometry frequency cutting method raised in this paper. By compressing the two bands respectivelyand using the inverse manifold harmonic transform, a bas-relief is obtained. Even for the modelwithout too much detail feature or mesh with low resolution, the algorithm can still support a good result. For the second one, shape is compressed by high-pass filter on the frequency domain after FFT.After that, discontinuity in shape is further detected based on proposed absolute variation function andthen eliminated. By the process, a bas-relief is finally generated. The second method is quite efficient,and has a better result for the model with strong edge feature.A detail preserving curved surface bas-relief algorithm is provided in this paper. In this method, thegeneration of curved surface bas-relief is converted to a constrained least squares equation whichguaranteed surfaces of object relief has the first order geometry continuity at the boundary where itintersection with the background surface. Canny operator, bilateral filter, unsharp masking are actingon the gradient domain of source model in order to fulfill the aim of detail preserving. Thestereoscopic impression of relief can be toned by the relaxation factor of the constrain condition. Thealgorithm properly solved the smooth blending problem, the generated relief has a fine detail, andfurthermore, it has a well control of the relief’s shape feature under the system parameters.A line-style bas-relief generation method is proposed by this paper. The main procedure includes:vision-dependent feature point extraction, separate-and-connect-based skeleton extraction operatorbased feature point optimize, feature line extraction with a user selected line width and depth rangecompression. The relief generated by this algorithm has a good visual effect and properly conveyedthe shape of source model.A relief paste algorithm based on normal adjustment is proposed to handle the repeated work inbas-relief design. The algorithm’s input includes an original relief model and a target model, and theoutput is a new relief composed from them. The main process includes parametric corresponding,relief mapping and normal-adjustment. This algorithm decreases the deformation during the reliefpasting process, and supports a new solution for rapid relief design based on the existed relief model.更多还原