This paper presents a generalization of non-uniform B-spline surfaces called T-splines. T-spline control grids permit T-junctions, so lines of control points need not traverse the entire control grid. T-splines support many valuable operations within a consistent framework, such as local refinement, and the merging of several B-spline surfaces that have different knot vectors into a single gap-free model. The paper focuses on T-splines of degree three, which are C 2 (in the absence of multiple knots). T-NURCCs (Non-Uniform Rational Catmull-Clark Surfaces with T-junctions) are a superset of both T-splines and Catmull-Clark surfaces. Thus, a modeling program for T-NURCCs can handle any NURBS or Catmull-Clark model as special cases. T-NURCCs enable true local refinement of a Catmull-Clark-type control grid: individual control points can be inserted only where they are needed to provide additional control, or to create a smoother tessellation, and such insertions do not alter the limit surface. T-NURCCs use stationary refinement rules and are C 2 except at extraordinary points and features.

This paper presents a generalization of non-uniform B-spline surfaces called T-splines. T-spline control grids permit Tjunctions, so lines of control points need not traverse the entire control grid. T-splines support many valuable operations within a consistent framework, such as local refinement, and the merging of several B-spline surfaces that have different knot vectors into a single gap-free model. The paper focuses on T-splines of degree three, which are C 2 (in the absence of multiple knots). T-NURCCs (Non-Uniform Rational Catmull-Clark Surfaces with T-junctions) are a superset of both T-splines and Catmull-Clark surfaces. Thus, a modeling program for T-NURCCs can handle any NURBS or Catmull-Clark model as special cases. T-NURCCs enable true local refinement of a Catmull-Clark-type control grid: individual control points can be inserted only where they are needed to provide additional control, or to create a smoother tessellation, and such insertions do not alter the limit surface. T-NURCCs use stationary refinement rules and are C 2 except at extraordinary points and features.

This newly inaugurated research database for 12-lead electrocardiogram signals was created under the auspices of Chapman University and Shaoxing People’s Hospital (Shaoxing Hospital Zhejiang University School of Medicine) and aims to enable the scientific community in conducting new studies on arrhythmia and other cardiovascular conditions. Certain types of arrhythmias, such as atrial fibrillation, have a pronounced negative impact on public health, quality of life, and medical expenditures. As a non-invasive test, long term ECG monitoring is a major and vital diagnostic tool for detecting these conditions. This practice, however, generates large amounts of data, the analysis of which requires considerable time and effort by human experts. Advancement of modern machine learning and statistical tools can be trained on high quality, large data to achieve exceptional levels of automated diagnostic accuracy. Thus, we collected and disseminated this novel database that contains 12-lead ECGs of 10,646 patients with a 500 Hz sampling rate that features 11 common rhythms and 67 additional cardiovascular conditions, all labeled by professional experts. The dataset consists of 10-second, 12-dimension ECGs and labels for rhythms and other conditions for each subject. The dataset can be used to design, compare, and fine-tune new and classical statistical and machine learning techniques in studies focused on arrhythmia and other cardiovascular conditions.

Doo-Sabin and Catmull-Clark subdivision surfaces are based on the notion of repeated knot insertion of uniform tensor product B-spline surfaces. This paper develops rules for non-uniform Doo-Sabin and Catmull-Clark surfaces that generalize non-uniform tensor product Bspline surfaces to arbitrary topologies. This added flexibility allows, among other things, the natural introduction of features such as cusps, creases, and darts, while elsewhere maintaining the same order of continuity as their uniform counterparts.

A typical NURBS surface model has a large percentage of superfluous control points that significantly interfere with the design process. This paper presents an algorithm for eliminating such superfluous control points, producing a T-spline. The algorithm can remove substantially more control points than competing methods such as B-spline wavelet decomposition. The paper also presents a new T-spline local refinement algorithm and answers two fundamental open questions on T-spline theory.