全冠和全冠桥数字化设计关键技术研究与应用
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摘要
随着计算机技术、信息技术和图形学技术的发展，口腔CAD/CAM数字化修复技术，凭借高效率、高精度和智能化的特点，正逐步取代传统的口腔修复体手工设计、制造方式，掀起口腔修复领域的一次技术革命。本文以口腔数字化修复中全冠和全冠桥的数字化设计为研究对象，综合应用生物医学工程、计算机辅助设计、离散数学、微分几何和曲面曲线造型等学科的理论，系统分析了全冠和全冠桥数字化设计流程中涉及的若干关键技术，并对这些关键技术进行了深入研究、探索，提出了新的方法。本文主要研究内容和成果如下：
（1）针对全冠修复体标准冠和内冠网格曲面光滑拼接的问题，提出了基于隐式曲面和波前法的网格过渡技术。首先根据提取的标准冠和内冠网格曲面的边界曲线，在边界之间双向搭桥将网格曲面过渡转化为网格补洞问题，然后使用波前法在孔洞内生成新的填充网格，并根据空间圆球规则优化网格以提升三角片质量。为提高过渡边界连续性，根据网格边界顶点法矢生成隐式曲面，然后把过渡网格的顶点投影到隐式曲面上，用投影点更新原来的网格顶点坐标，保证了过渡的光滑性。
（2）针对修复体个性化设计的需要，提出了两种局部变形算法：基于特征曲线驱动的局部变形和基于能量最小约束的局部变形。特征曲线驱动变形根据变形扩散原理，设计了合理的变形密度函数，由设定的变形半径和“近似投影点算法”，快速建立特征曲线和局部曲面的映射关系，利用曲线的编辑驱动曲面变形，适用于调整修复体的轮廓形态。基于能量最小约束提出的局部变形算法，将网格曲面划分为不同的区域，移动控制区域顶点会使变形区域的顶点在最小能量约束下发生变化，适用于编辑修复体的局部特征形态。
（3）提出了基于蒙皮剖分的全冠桥数字化设计框架，包括连接体网格曲面的生成算法和全冠桥各部分的网格融合算法，并且对桥体的数字化设计作了简要说明。传统全冠桥设计方法是将连接体数据保存在系统数据库中，设计时调用连接体数据并通过布尔运算形成全冠桥，存在编辑能力差、效率低的问题。根据定义的截面模版，使用蒙皮剖分算法自动生成连接体网格曲面，然后通过裁剪、缝合算法与两侧牙冠融合成一体，具有很强的形态编辑功能，而且编辑过程中能实时检测连接体中间截面的面积，确保设计的连接体具有足够的强度。
（4）根据牙齿修复中模型不同的属性和咬合、接触关系的特点，提出了基于动态混合包围盒的碰撞检测技术，可快速查询模型的碰撞区域；根据碰撞检测结果，又研究了模型刺穿深度的计算方法，并将深度数值用色阶图的方式显示出来，为牙齿修复体的数字化设计提供了直观的操作依据。
With the development of the computer and graphics technology, dental CAD/CAM repairtechnology which is efficient, accurate and intelligent is gradually replacing the traditional dentalrepair mode, and has led to a revolution in dental repair field. With the comprehensive application ofbiomedical engineering, computer aided design, mathematics, differential geometry and threedimension geometry modeling, several key technology about the digital design of the full crown andbridge are studied deeply in this dissertation. Main contents and achievements are as follows:
1. New mesh blending algorithm based on the implicit surface and advancing front method ispresented for the smoothly splicing outer and inner mesh surface of full crown restoration. Thealgorithm first extracts two boundary curves and bridginges between them to convert mesh blendingproblem into mesh hole filling problem; then fills the holes with advancing front method. The fillingmesh surface would be optimized according to the space sphere rules to enhance the quality oftriangles. The implicit surface is generation as control surface making use of vertex normal vectors onthe boundary, and vertexes in the blending mesh are then projected on the implicit surface andreplaced by projected points, which ensures the smoothness of mesh transition.
2. For the demand of individual design restoration, two local mesh deformation algorithms areproposed: local deformation driven by characteristic curves and local deformation based on surfaceminimum energy principle. According to the deformation diffusion principle, the reasonabledeformation density function is designed; Combining with deformation radius and approximateprojected points algorithm, curve-driven deformation method could build curve and local surfacemapping relations quickly and achieve deformation, which is applicable to adjust outline form ofrestoration. The other local deformation algorithm divides the selected mesh surface into differentareas, and deformation could be achieved when the control hand is translated,which is applicable toedit local characteristic of restoration.
3. The digital design framework of full crown bridge based on skin subdivision is realized,including of connector mesh surface generation algorithm and mesh fusion algorithm, and brieflyintroducing pontic’s digital design. Traditional design method is to store connector model in systemdatabase and edits them in designing progress, and form full crown bridge through boolean operationat last, but the editing ability is poor and the efficiency is low. However, the skin subdivisionalgorithm could automatically generate connector surface rapidly between two projected curves and then be merged with fixed full crown through proposed cutting and stitching algorithms. Its editingability is strong and the section area could be calculated to detect the strength of connector further.
4. According to the different property of tooth models and the characteristics of bite and contactrelationship in dental repair, the collision detection algorithm based on dynamic hybrid boundingboxes is presented, which could query model collision domains quickly. Next puncture depth ofmodels that happen to collide is calculated and the result will be displayed in the color map to guideoperation intuitively.
（1）针对全冠修复体标准冠和内冠网格曲面光滑拼接的问题，提出了基于隐式曲面和波前法的网格过渡技术。首先根据提取的标准冠和内冠网格曲面的边界曲线，在边界之间双向搭桥将网格曲面过渡转化为网格补洞问题，然后使用波前法在孔洞内生成新的填充网格，并根据空间圆球规则优化网格以提升三角片质量。为提高过渡边界连续性，根据网格边界顶点法矢生成隐式曲面，然后把过渡网格的顶点投影到隐式曲面上，用投影点更新原来的网格顶点坐标，保证了过渡的光滑性。
（2）针对修复体个性化设计的需要，提出了两种局部变形算法：基于特征曲线驱动的局部变形和基于能量最小约束的局部变形。特征曲线驱动变形根据变形扩散原理，设计了合理的变形密度函数，由设定的变形半径和“近似投影点算法”，快速建立特征曲线和局部曲面的映射关系，利用曲线的编辑驱动曲面变形，适用于调整修复体的轮廓形态。基于能量最小约束提出的局部变形算法，将网格曲面划分为不同的区域，移动控制区域顶点会使变形区域的顶点在最小能量约束下发生变化，适用于编辑修复体的局部特征形态。
（3）提出了基于蒙皮剖分的全冠桥数字化设计框架，包括连接体网格曲面的生成算法和全冠桥各部分的网格融合算法，并且对桥体的数字化设计作了简要说明。传统全冠桥设计方法是将连接体数据保存在系统数据库中，设计时调用连接体数据并通过布尔运算形成全冠桥，存在编辑能力差、效率低的问题。根据定义的截面模版，使用蒙皮剖分算法自动生成连接体网格曲面，然后通过裁剪、缝合算法与两侧牙冠融合成一体，具有很强的形态编辑功能，而且编辑过程中能实时检测连接体中间截面的面积，确保设计的连接体具有足够的强度。
（4）根据牙齿修复中模型不同的属性和咬合、接触关系的特点，提出了基于动态混合包围盒的碰撞检测技术，可快速查询模型的碰撞区域；根据碰撞检测结果，又研究了模型刺穿深度的计算方法，并将深度数值用色阶图的方式显示出来，为牙齿修复体的数字化设计提供了直观的操作依据。
With the development of the computer and graphics technology, dental CAD/CAM repairtechnology which is efficient, accurate and intelligent is gradually replacing the traditional dentalrepair mode, and has led to a revolution in dental repair field. With the comprehensive application ofbiomedical engineering, computer aided design, mathematics, differential geometry and threedimension geometry modeling, several key technology about the digital design of the full crown andbridge are studied deeply in this dissertation. Main contents and achievements are as follows:
1. New mesh blending algorithm based on the implicit surface and advancing front method ispresented for the smoothly splicing outer and inner mesh surface of full crown restoration. Thealgorithm first extracts two boundary curves and bridginges between them to convert mesh blendingproblem into mesh hole filling problem; then fills the holes with advancing front method. The fillingmesh surface would be optimized according to the space sphere rules to enhance the quality oftriangles. The implicit surface is generation as control surface making use of vertex normal vectors onthe boundary, and vertexes in the blending mesh are then projected on the implicit surface andreplaced by projected points, which ensures the smoothness of mesh transition.
2. For the demand of individual design restoration, two local mesh deformation algorithms areproposed: local deformation driven by characteristic curves and local deformation based on surfaceminimum energy principle. According to the deformation diffusion principle, the reasonabledeformation density function is designed; Combining with deformation radius and approximateprojected points algorithm, curve-driven deformation method could build curve and local surfacemapping relations quickly and achieve deformation, which is applicable to adjust outline form ofrestoration. The other local deformation algorithm divides the selected mesh surface into differentareas, and deformation could be achieved when the control hand is translated,which is applicable toedit local characteristic of restoration.
3. The digital design framework of full crown bridge based on skin subdivision is realized,including of connector mesh surface generation algorithm and mesh fusion algorithm, and brieflyintroducing pontic’s digital design. Traditional design method is to store connector model in systemdatabase and edits them in designing progress, and form full crown bridge through boolean operationat last, but the editing ability is poor and the efficiency is low. However, the skin subdivisionalgorithm could automatically generate connector surface rapidly between two projected curves and then be merged with fixed full crown through proposed cutting and stitching algorithms. Its editingability is strong and the section area could be calculated to detect the strength of connector further.
4. According to the different property of tooth models and the characteristics of bite and contactrelationship in dental repair, the collision detection algorithm based on dynamic hybrid boundingboxes is presented, which could query model collision domains quickly. Next puncture depth ofmodels that happen to collide is calculated and the result will be displayed in the color map to guideoperation intuitively.
引文
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