Smooth quasi-developable surfaces bounded by smooth curves

Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not adequate for generating smooth quasi-developable surfaces. We propose the first method which is capable of exploring the full solution space of continuous input curves to compute a smooth quasi-developable ruled surface with as large developability as possible. The resulting surface is exactly bounded by the input smooth curves and is guaranteed to have no self-intersections. The main contribution is a variational approach to compute a continuous mapping of parameters of input curves by minimizing a function evaluating surface developability. Moreover, we also present an algorithm to represent a resulting surface as a B-spline surface when input curves are B-spline curves.Comment: 18 page

Fast B-spline Curve Fitting by L-BFGS

We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the L-BFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to perform either matrix computation or foot point projection in every iteration. As a result, our method is much faster than existing methods

Developable B-spline surface generation from control rulings

An intuitive design method is proposed for generating developable ruled B-spline surfaces from a sequence of straight line segments indicating the surface shape. The first and last line segments are enforced to be the head and tail ruling lines of the resulting surface while the interior lines are required to approximate rulings on the resulting surface as much as possible. This manner of developable surface design is conceptually similar to the popular way of the freeform curve and surface design in the CAD community, observing that a developable ruled surface is a single parameter family of straight lines. This new design mode of the developable surface also provides more flexibility than the widely employed way of developable surface design from two boundary curves of the surface. The problem is treated by numerical optimization methods with which a particular level of distance error is allowed. We thus provide an effective tool for creating surfaces with a high degree of developability when the input control rulings do not lie in exact developable surfaces. We consider this ability as the superiority over analytical methods in that it can deal with arbitrary design inputs and find practically useful results.Comment: 13 pages, 12 figrue

Highly-accurate 5-axis flank CNC machining with conical tools

A new method for $5$-axis flank computer numerically controlled (CNC) machining using a predefined set of tappered ball-end-mill tools (aka conical) cutters is proposed. The space of lines that admit tangential motion of an associated truncated cone along a general, doubly curved, free-form surface is explored. These lines serve as discrete positions of conical axes in 3D space. Spline surface fitting is used to generate a ruled surface that represents a single continuous sweep of a rigid conical milling tool. An optimization based approach is then applied to globally minimize the error between the design surface and the conical envelope. Our computer simulation are validated with physical experiments on two benchmark industrial datasets, reducing significantly the execution times while preserving or even reducing the milling error when compared to the state-of-the-art industrial software

Gastrodin Rescues Autistic-Like Phenotypes in Valproic Acid-Induced Animal Model

Autism spectrum disorder (ASD) is an immensely challenging developmental disorder characterized by impaired social interaction, restricted/repetitive behavior, and anxiety. GABAergic dysfunction has been postulated to underlie these autistic symptoms. Gastrodin is widely used clinically in the treatment of neurological disorders and showed to modulate GABAergic signaling in the animal brain. The present study aimed to determine whether treatment with gastrodin can rescue valproic acid (VPA) induced autistic-like phenotypes, and to determine its possible mechanism of action. Our results showed that administration of gastrodin effectively alleviated the autistic-associated behavioral abnormalities as reflected by an increase in social interaction and decrement in repetitive/stereotyped behavior and anxiety in mice as compared to those in untreated animals. Remarkably, the amelioration in autistic-like phenotypes was accompanied by the restoration of inhibitory synaptic transmission, α5 GABAA receptor, and type 1 GABA transporter (GAT1) expression in the basolateral amygdala (BLA) of VPA-treated mice. These findings indicate that gastrodin may alleviate the autistic symptoms caused by VPA through regulating GABAergic synaptic transmission, suggesting that gastrodin may be a potential therapeutic target in autism

Free-form surface modeling with developables and cyclides

published_or_final_versionComputer ScienceDoctoralDoctor of Philosoph

A graph-based method for fitting planar B-spline curves with intersections

The problem of fitting B-spline curves to planar point clouds is studied in this paper. A novel method is proposed to deal with the most challenging case where multiple intersecting curves or curves with self-intersection are necessary for shape representation. A method based on Delauney Triangulation of data points is developed to identify connected components which is also capable of removing outliers. A skeleton representation is utilized to represent the topological structure which is further used to create a weighted graph for deciding the merging of curve segments. Different to existing approaches which utilize local shape information near intersections, our method considers shape characteristics of curve segments in a larger scope and is thus capable of giving more satisfactory results. By fitting each group of data points with a B-spline curve, we solve the problems of curve structure reconstruction from point clouds, as well as the vectorization of simple line drawing images by drawing lines reconstruction

Burning Rate Enhancement Analysis of End-Burning Solid Propellant Grains Based on X-Ray Real-Time Radiography

Unexpected pressure rise may occur in the end-burning grain solid rocket motor. It is generally believed that this phenomenon is caused by the nonparallel layer combustion of the burning surface, resulting in the increase of burning rate along the inhibitor. In order to explain the cause of this phenomenon, the experimental investigation on four different end configurations were carried out. Based on the X-ray real-time radiography (RTR) technique, a new method for determining the dynamic burning rate of propellant and obtaining the real-time end-burning profile was developed. From the real-time images of the burning surface, it is found that there was a phenomenon of nonuniform burning surface displacement in the end-burning grain solid rocket motor. Through image processing, the real-time burning rate of grain center line and the real-time cone angle are obtained. Based on the analysis of the real-time burning rate at different positions of the end surface, the end face cone burning process in the motor working process is obtained. The closer to the shell, the higher the burning rate of the propellant. Considering the actual structure of this end-burning grain motor, it is speculated that the main cause of the cone burning of the grain may be due to the heat conduction of the metal wall. By adjusting the initial shape of the grain end surface, the operating pressure of the combustion chamber can be basically unchanged, so as to meet the mission requirements. The results show that the method can measure the burning rate of solid propellant in real time and provide support for the study of nonuniform combustion of solid propellant