Knot Placement of B-spline Curves with Equally Spaced Geometric Information

受每个节点区间应该具有相同建模能力的启发,提出一种基于几何信息均分的B样条曲线节点设置算法.首先放置少量节点,以每个节点区间具有相等的几何信息量; 准则来确定节点的位置;为了提高样条的建模能力,根据上一次迭代中的拟合误差确定加细节点区间并使新节点均分该节点区间的几何信息.该算法可以快速有效地; 得到用户指定精度的逼近曲线.通过对一些具有不同几何复杂度的实例进行实验的结果表明,文中算法是有效的;与现有的2种算法相比,; 该算法在相同控制顶点的情况下能够得到更高精度的逼近结果.Motivated by the observation that each knot interval should be of the; same modeling ability, a knot placement algorithm based on equally; spaced geometric information for B-spline curves is proposed. In the; algorithm, a few of knots are determined according to the principle that; each knot interval is of the same amount of geometric information at the; initial iteration. In order to improve the modeling ability of the; B-splines, the knot interval needed to be refined is determined by the; last fitting errors and the new knot inserted is placed to equally space; the accumulated geometric information in the knot interval. Via the; adaptive knot placement algorithm, approximated curve with specified; tolerance can be produced rapidly and efficiently. Several models with; distinct geometric complexities are tested to demonstrate the efficacy; of our algorithm in fitting curves. Comparing to other two available; methods, more accurate results can be obtained by our method with the; same number of control points.国家自然科学基金; 福建省自然科学基金; 中央高校基本科研业务费专项资

An approach to construct a three-dimensional isogeometric model from µ-CT scan data with an application to the bridge of a violin

We present an algorithm to build a ready to use isogeometric model from scan data gained by a µ-CT scan. Based on a three-dimensional multi-patch reference geometry, which includes the major topological features, we fit the outline, then the cross-section and finally the three-dimensional geometry. The key step is to fit the outline, where a non-linear least squares problem is solved with a Gauss-Newton approach presented by Borges and Pastva (2002). We extend this approach by a regularisation and a precise interpolation of selected data points. The resulting NURBS geometry is ready for applying isogeometric analysis tools for efficient numerical simulations. As a particular example we examine the scan data of a violin bridge and present the complete workflow from the µ-CT scan up to the numerical simulation based on isogeometric mortar methods. We illustrate the relevance of the constructed geometry with a vibro-acoustical application