Treating trauma to the cranio-maxillofacial region is a great challenge and requires expert clinical skills and sophisticated radiological imaging. The aim of reconstruction of the facial fractures is to rehabilitate the patient both functionally and aesthetically. Bio-modeling is an important tool for constructing surfaces using 2D cross sections. The aim of this manuscript was to show 3D construction using 2D CT scan contours. The fractured part of the cranial vault were constructed using a Ball curve with two shape parameters, later the 2D contours were flipped into 3D with an equidistant z component. The surface created was represented by a bi-cubic rational Ball surface with $C^2$ continuity. At the end of this article, we present two real cases, in which we had constructed the frontal and parietal bone fractures using a bi-cubic rational Ball surface. The proposed method was validated by constructing the non-fractured part.

中文翻译：

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二维轮廓的表面建模及其在颅面骨折中的应用

治疗颅颌面部区域的创伤是巨大的挑战，需要专业的临床技能和先进的放射成像。重建面部骨折的目的是在功能上和美学上使患者康复。生物建模是使用2D横截面构造曲面的重要工具。该手稿的目的是显示使用2D CT扫描轮廓进行3D构造。使用具有两个形状参数的Ball曲线构造颅穹顶的断裂部分，然后将2D等高线翻转为具有等距z分量的3D 。产生的表面由双三次有理球表面表示，$C^2$连续性。在本文的最后，我们介绍了两个真实的案例，其中我们使用双三次有理球表面构造了额骨和顶骨骨折。通过构造非断裂部分验证了该方法的有效性。