CAD关键技术在口腔修复体咬合调整中的应用基础研究
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摘要
CAD/CAM技术在口腔修复体设计与制造中的应用,引发了口腔修复学的第三次技术革命。它彻底改变了传统的义齿制作方法,是实现高效率、高精度义齿制作的唯一途径。修复体 面咬合调整是整个口腔修复体CAD系统中的关键问题和技术难点。目前国内欠缺对口腔修复体咬合调整CAD技术的深入研究,而国外虽已开发出实用系统,但 面咬合调整也存在尚未较好解决的问题。本文对口腔修复体咬合调整的CAD关键技术进行了系统、深入的研究,主要创新性成果如下:
(1)设计了口腔修复体三角网格模型拓扑重建的数据结构,给出了快速建立拓扑结构的算法流程。三角网格模型顶点查找时,通过使用中间文件记录无重复的顶点及点和面的拓扑信息,提高了原直接法的查找速度,并将平衡二叉树法和哈希表法应用于顶点查找过程,也快速、有效地去除了STL文件记录的大量重复顶点。对三种顶点查找方法的比较分析表明,哈希表法更适用于含有海量无规则散乱点的修复体模型的拓扑重建。
(2)提出了以简单 架为媒介,通过上下颌模型在正中 状态下的虚拟对位获取被修复体对颌约束的方法。首先采用改进的圆柱面特征识别方法计算 架转轴的轴线位置,然后通过构建上下颌模型OBB包围盒树,并在下颌模型绕 架轴线转动过程中对包围盒树进行更新,以及遍历上下颌模型包围盒树,实现了上下颌模型在采样位置的实时碰撞检测,从而建立了整个牙列在正中 位的咬合接触关系,为被修复体同名标准冠调控咬合面提供了准确的静态对颌约束。
(3)提出了上下颌模型咬合面方向和法方向两种距离图的概念,以及基于图像空间碰撞检测算法的咬合面方向距离图计算方法和基于OpenGL选择模式的法向距离图计算方法。前者通过对上下颌模型在咬合面方向视景体内的绘制,从图像的深度缓存和模板缓存中获得 面间沿咬合面方向的距离值。后者通过在牙颌模型顶点法方向视景体内绘制对颌模型,从选择缓存中获得牙颌模型上顶点沿法向到对颌模型的距离值。由于充分发挥了图形硬件的运算功能,这两种基于图像空间的距离计算方法可快速、准确获得牙齿模型 面间距离,为指导标准冠 面的咬合调整提供了 面间的距离变化情况。
(4)提出了以上下颌模型的距离图为依据,通过对 面间冲突距离进行体样条插值实现冲突区域调整的方法。该方法首先选取位于和邻近标准冠模型的控制顶点,并采用变分求解方法建立 面间冲突距离体样条插值函数,然后使用该函数对标准冠模型上顶点的冲突距离进行插值计算,最后依据计算结果对标准冠 面的冲突区域进行调整。调整后的标准冠 面能够符合与对颌牙的咬合关系,并保持 面的固有形态,满足 面光顺性要求。
(5)提出了适用于口腔修复体的分片光滑B样条曲面拟合算法。详细讨论了修复体三角网格模型的Voronoi区域划分、三边界区域划分、四边界区域合并及重新采样,和分片光滑B样条曲面拟合过程。通过对左上颌第一磨牙、尖牙和中切牙的三角网格模型进行曲面拟合,充分验证了算法的有效性,表明了该拟合算法拓扑适应性强,能够生成高质量的样条曲面,符合临床使用的要求。最后在拟合曲面基础上设计加工出了烤瓷冠基底冠,进一步验证了该算法的实用性。
The applications of CAD/CAM technologies to dental restorations’design and fabrication evoked the third technological revolution of prosthodontics. It is changing the traditional method of false tooth fabrication, and is the only way to realize the false tooth fabrication with high efficiency and precision. Adjustment of occlusal surface is a crucial problem and a technical difficult in the whole CAD system of dental restorations. At present, the domestic study of dental restorations’CAD/CAM is deficient. Furthermore, although many practical systems have been developed abroad, there are still some issues about the adjustment of occlusal surface not solved well so far. In this thesis, the key CAD technologies for adjusting the occlusal surface are studied deeply and systemically. The main creative achievements are as follows:
(1) The data structure for reconstructing the topology of dental restorations’triangular meshes is designed, and the algorithm flow for fast topology reconstruction is presented. When searching the vertexes of the triangular meshes model, a media file is introduced to record non-repeated vertexes and the topology of triangles and vertexes. It increases the searching speed of the direct method. Furthermore, AVL trees and Hash table are applied to the process of vertex searching, both of which effectively wiped off the massive repeated vertexes with high speed as well. The comparison of the three vertex searching methods demonstrates that the Hash table method is most applicable to the topology reconstruction of dental restorations, which have massive irregular vertexes.
(2) A method able to acquire the opposite occlusal restriction of prepared tooth is proposed. It makes use of the virtual orientation of the lower and upper jaws model on the position of centric occlusion, during which the simple articulator is used as a medium. Firstly, an improved method for feature identification of the cylinder is used to compute the rotation axis equation of the simple articulator. Then, by constructing OBB trees for the lower and upper jaws model, updating the bounding box trees during the rotation of the lower jaw around the axis of the articulator, and traversing these trees, real-time collision detection between lower and upper jaws at sample positions is realized. As a result, the occlusal relationship between the lower and upper jaws on the position of centric occlusion is built. It provides accurate static opposite occlusal restriction for the occlusal surface adjustment of the prepared tooth’s standard crown.
(3) The concepts of two distance maps defined along the occlusal surface’s direction and the normal direction respectively, along with the calculation methods of the distance maps are proposed for the lower and upper jaws model. The calculation of the distance map along the occlusal surface’s direction is based on the collision detection algorithm in the image space, in which the distances are obtained from the depth buffer and stencil buffer by rending the lower and upper jaws model in camera along the occlusal surface’s direction. The calculation of the distance map along the normal direction utilizes the selection mode of OpenGL, in which the distances from the vertexes on the model to the opposite model are achieved from the selection buffer by rending the opposite occlusal model along the normal direction of vertexes on the tooth model. Because the two calculation methods for the distance map fully utilize the good computation performance of the graphics hardware, they have high efficiency and accuracy. And they provide distance changes between occlusal surfaces for conducting the adjustment of the standard crown’s occlusal surface.
(4) A method for adjusting the conflict areas is proposed. According to the distance map of the lower and upper jaws model, the method realizes the adjustment by interpolating the conflict distance between occlusal surfaces using a volume spline function. Firstly, control points on or nearby the standard crown model are selected, and the volume spline interpolation function is calculated by variational methods. Then the conflict distances of the vertexes on the standard crown model are computed using the interpolation function. Finally, the conflict areas on the occlusal surface of the standard crown are adjusted according to the results. The adjusted occlusal surface can accord with the opposite tooth. The shape inherent to the occlusal surface is well maintained, and the requirement of occlusal surface’s smoothness is satisfied.
(5) A surface fitting algorithm suitable to the dental restorations is proposed, which fits surface by using patches of smooth B-spline surfaces. For the triangular meshes model of the restoration, its Voronoi partition, delaunay domain partition, quadrilateral domain combination and resampling, and the surface fitting using patches of smooth B-spline surfaces are discussed in succession detailedly. The fitting results of triangular meshes models of the first molar, canine and central incisor in left maxillary fully demonstrate the effectiveness of the proposed algorithm. They show that the algorithm has a strong adaptability of topology and a capability of producing high quality spline surface. Therefore it satisfies the clinical applications. At last, a base of porcelain fused to metal crown is designed and processed based on the reconstructed surface, which further verifies the practicability of the algorithm.
(1)设计了口腔修复体三角网格模型拓扑重建的数据结构,给出了快速建立拓扑结构的算法流程。三角网格模型顶点查找时,通过使用中间文件记录无重复的顶点及点和面的拓扑信息,提高了原直接法的查找速度,并将平衡二叉树法和哈希表法应用于顶点查找过程,也快速、有效地去除了STL文件记录的大量重复顶点。对三种顶点查找方法的比较分析表明,哈希表法更适用于含有海量无规则散乱点的修复体模型的拓扑重建。
(2)提出了以简单 架为媒介,通过上下颌模型在正中 状态下的虚拟对位获取被修复体对颌约束的方法。首先采用改进的圆柱面特征识别方法计算 架转轴的轴线位置,然后通过构建上下颌模型OBB包围盒树,并在下颌模型绕 架轴线转动过程中对包围盒树进行更新,以及遍历上下颌模型包围盒树,实现了上下颌模型在采样位置的实时碰撞检测,从而建立了整个牙列在正中 位的咬合接触关系,为被修复体同名标准冠调控咬合面提供了准确的静态对颌约束。
(3)提出了上下颌模型咬合面方向和法方向两种距离图的概念,以及基于图像空间碰撞检测算法的咬合面方向距离图计算方法和基于OpenGL选择模式的法向距离图计算方法。前者通过对上下颌模型在咬合面方向视景体内的绘制,从图像的深度缓存和模板缓存中获得 面间沿咬合面方向的距离值。后者通过在牙颌模型顶点法方向视景体内绘制对颌模型,从选择缓存中获得牙颌模型上顶点沿法向到对颌模型的距离值。由于充分发挥了图形硬件的运算功能,这两种基于图像空间的距离计算方法可快速、准确获得牙齿模型 面间距离,为指导标准冠 面的咬合调整提供了 面间的距离变化情况。
(4)提出了以上下颌模型的距离图为依据,通过对 面间冲突距离进行体样条插值实现冲突区域调整的方法。该方法首先选取位于和邻近标准冠模型的控制顶点,并采用变分求解方法建立 面间冲突距离体样条插值函数,然后使用该函数对标准冠模型上顶点的冲突距离进行插值计算,最后依据计算结果对标准冠 面的冲突区域进行调整。调整后的标准冠 面能够符合与对颌牙的咬合关系,并保持 面的固有形态,满足 面光顺性要求。
(5)提出了适用于口腔修复体的分片光滑B样条曲面拟合算法。详细讨论了修复体三角网格模型的Voronoi区域划分、三边界区域划分、四边界区域合并及重新采样,和分片光滑B样条曲面拟合过程。通过对左上颌第一磨牙、尖牙和中切牙的三角网格模型进行曲面拟合,充分验证了算法的有效性,表明了该拟合算法拓扑适应性强,能够生成高质量的样条曲面,符合临床使用的要求。最后在拟合曲面基础上设计加工出了烤瓷冠基底冠,进一步验证了该算法的实用性。
The applications of CAD/CAM technologies to dental restorations’design and fabrication evoked the third technological revolution of prosthodontics. It is changing the traditional method of false tooth fabrication, and is the only way to realize the false tooth fabrication with high efficiency and precision. Adjustment of occlusal surface is a crucial problem and a technical difficult in the whole CAD system of dental restorations. At present, the domestic study of dental restorations’CAD/CAM is deficient. Furthermore, although many practical systems have been developed abroad, there are still some issues about the adjustment of occlusal surface not solved well so far. In this thesis, the key CAD technologies for adjusting the occlusal surface are studied deeply and systemically. The main creative achievements are as follows:
(1) The data structure for reconstructing the topology of dental restorations’triangular meshes is designed, and the algorithm flow for fast topology reconstruction is presented. When searching the vertexes of the triangular meshes model, a media file is introduced to record non-repeated vertexes and the topology of triangles and vertexes. It increases the searching speed of the direct method. Furthermore, AVL trees and Hash table are applied to the process of vertex searching, both of which effectively wiped off the massive repeated vertexes with high speed as well. The comparison of the three vertex searching methods demonstrates that the Hash table method is most applicable to the topology reconstruction of dental restorations, which have massive irregular vertexes.
(2) A method able to acquire the opposite occlusal restriction of prepared tooth is proposed. It makes use of the virtual orientation of the lower and upper jaws model on the position of centric occlusion, during which the simple articulator is used as a medium. Firstly, an improved method for feature identification of the cylinder is used to compute the rotation axis equation of the simple articulator. Then, by constructing OBB trees for the lower and upper jaws model, updating the bounding box trees during the rotation of the lower jaw around the axis of the articulator, and traversing these trees, real-time collision detection between lower and upper jaws at sample positions is realized. As a result, the occlusal relationship between the lower and upper jaws on the position of centric occlusion is built. It provides accurate static opposite occlusal restriction for the occlusal surface adjustment of the prepared tooth’s standard crown.
(3) The concepts of two distance maps defined along the occlusal surface’s direction and the normal direction respectively, along with the calculation methods of the distance maps are proposed for the lower and upper jaws model. The calculation of the distance map along the occlusal surface’s direction is based on the collision detection algorithm in the image space, in which the distances are obtained from the depth buffer and stencil buffer by rending the lower and upper jaws model in camera along the occlusal surface’s direction. The calculation of the distance map along the normal direction utilizes the selection mode of OpenGL, in which the distances from the vertexes on the model to the opposite model are achieved from the selection buffer by rending the opposite occlusal model along the normal direction of vertexes on the tooth model. Because the two calculation methods for the distance map fully utilize the good computation performance of the graphics hardware, they have high efficiency and accuracy. And they provide distance changes between occlusal surfaces for conducting the adjustment of the standard crown’s occlusal surface.
(4) A method for adjusting the conflict areas is proposed. According to the distance map of the lower and upper jaws model, the method realizes the adjustment by interpolating the conflict distance between occlusal surfaces using a volume spline function. Firstly, control points on or nearby the standard crown model are selected, and the volume spline interpolation function is calculated by variational methods. Then the conflict distances of the vertexes on the standard crown model are computed using the interpolation function. Finally, the conflict areas on the occlusal surface of the standard crown are adjusted according to the results. The adjusted occlusal surface can accord with the opposite tooth. The shape inherent to the occlusal surface is well maintained, and the requirement of occlusal surface’s smoothness is satisfied.
(5) A surface fitting algorithm suitable to the dental restorations is proposed, which fits surface by using patches of smooth B-spline surfaces. For the triangular meshes model of the restoration, its Voronoi partition, delaunay domain partition, quadrilateral domain combination and resampling, and the surface fitting using patches of smooth B-spline surfaces are discussed in succession detailedly. The fitting results of triangular meshes models of the first molar, canine and central incisor in left maxillary fully demonstrate the effectiveness of the proposed algorithm. They show that the algorithm has a strong adaptability of topology and a capability of producing high quality spline surface. Therefore it satisfies the clinical applications. At last, a base of porcelain fused to metal crown is designed and processed based on the reconstructed surface, which further verifies the practicability of the algorithm.
引文
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