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摘要曲线曲面技术在计算机图形学中应用广泛，是CAD领域中相当重要的技术。样条理论的发展离不开对数据的缩减和曲面的平滑，所以样条理论对曲面技术的发展起到了至关重要的作用。目前NURBS技术在样条理论中应用广泛，然而NURBS曲面有着非常多的不足，大量控制点必须为了满足拓扑网格而存在，而这些数据点不携带任何几何信息，导致在处理这些数据会浪费时间，降低运行速度。33434
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Pr.Sederberg提出的T样条方法可以有效解决这些问题。T样条允许控制网格中出现T型控制点,他可以去掉大多数冗余的控制点。由于Ｔ样条控制网格的这些优秀性质，所以用T样条来重建曲面是很优越的。我们在进行曲面重建时，先由三文扫描仪得到采集得到数据点并形成三角网格，对三角网格LSCM（least squares conformal maps）参数化，将三文的数据点映射到平面，然后再利用平面四叉树细分的方法，将散布在平面上的数据点分块，生成Ｔ网格，再拟合得到曲面。
关键词 NURBS曲面 T样条 T网格 LSCM 拟合
毕业论文设计说明书外文摘要
Title Surface reconstruction by T spline and T grid
Abstract
The curve and surface technology is the core of CAGD (Computer Aided Design) .The non uniform rational B spline (NURBS) method is a modeling method of free curve and surface Over the years, the mathematical model and data smoothing geometry contributed to the development of spline method, at the same time the spline theory and method provides an important theoretical basis and practical tools for the development of free curve and surface.However, we know that NURBS surface has many problems,such as its control points must be located in a rectangular grid topology, causing too many control points in order to satisfy the topological constraints rather than geometric information, resulting in a large number of redundant data, resulting in slower processing speed, higher requirements hardware and a series of disadvantages .
In order to overcome these shortcomings, Pr.Sederberg put forward the T spline method.T spline allows T control points, it can remove most of the redundancy control points.Due to the special nature of the T spline control grid ,so the key of using T spline to reconstruct a surface is building a reasonable and effective T grid.When the algorithm is used in surface reconstruction, collecting 3D data points by the three-dimensional scanner ,using LSCM , mapping 3D data points to the plane, and then using the method of plane four binary tree subpision to pide the free distribution of data to segmentation, creating reasonable and effective T grid , at last we eventually transform surface reconstruction the model to an optimization problem, and solve it by the least squares method.
Keywords NURBS T spline T grid LSCM fitting
目 录
1 绪论 1
1.1样条曲线 1
1.2 贝塞尔（Bezier）曲线 1
1.3 NURBS（非均匀有理B样条曲线） 3
1.4 T样条的发展 3
2 NURBS与T-样条 5
2.1 NURBS曲面 5
2.1.1 NURBS 5
2.1.2 NURBS的缺点 6
2.2节点距 7
2.3 T样条 7
3 三角网格参数化 10
3.1三角网格 10
3.2 LSCM参数化 12
3.3共轭梯度法 13
4 构造Ｔ网格 15
4.1四叉树法 15
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