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

A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe

08221 Abstracts Collection -- Geometric Modeling

From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Feasible Form Parameter Design of Complex Ship Hull Form Geometry

This thesis introduces a new methodology for robust form parameter design of complex hull form geometry via constraint programming, automatic differentiation, interval arithmetic, and truncated hierarchical B- splines. To date, there has been no clearly stated methodology for assuring consistency of general (equality and inequality) constraints across an entire geometric form parameter ship hull design space. In contrast, the method to be given here can be used to produce guaranteed narrowing of the design space, such that infeasible portions are eliminated. Furthermore, we can guarantee that any set of form parameters generated by our method will be self consistent. It is for this reason that we use the title feasible form parameter design. In form parameter design, a design space is represented by a tuple of design parameters which are extended in each design space dimension. In this representation, a single feasible design is a consistent set of real valued parameters, one for every component of the design space tuple. Using the methodology to be given here, we pick out designs which consist of consistent parameters, narrowed to any desired precision up to that of the machine, even for equality constraints. Furthermore, the method is developed to enable the generation of complex hull forms using an extension of the basic rules idea to allow for automated generation of rules networks, plus the use of the truncated hierarchical B-splines, a wavelet-adaptive extension of standard B-splines and hierarchical B-splines. The adaptive resolution methods are employed in order to allow an automated program the freedom to generate complex B-spline representations of the geometry in a robust manner across multiple levels of detail. Thus two complementary objectives are pursued: ensuring feasible starting sets of form parameters, and enabling the generation of complex hull form geometry

Piecewise algebraic surface computation and fairing from a discrete model

This paper describes a constrained fairing method for implicit surfaces defined on a voxelization. This method is suitable for computing a closed smooth surface that approximates an initial set of face connected voxels.Preprin

Component-based Geometry Manipulation for Aerodynamic Shape Optimization with Overset Meshes

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143082/1/6.2017-3327.pd

Key Challenges and Opportunities in Hull Form Design Optimisation for Marine and Offshore Applications

New environmental regulations and volatile fuel prices have resulted in an ever-increasing need for reduction in carbon emission and fuel consumption. Designs of marine and offshore vessels are more demanding with complex operating requirements and oil and gas exploration venturing into deeper waters and hasher environments. Combinations of these factors have led to the need to optimise the design of the hull for the marine and offshore industry. The contribution of this paper is threefold. Firstly, the paper provides a comprehensive review of the state-ofthe- art techniques in hull form design. Specifically, it analyses geometry modelling, shape transformation, optimisation and performance evaluation. Strengths and weaknesses of existing solutions are also discussed. Secondly, key challenges of hull form optimisation specific to the design of marine and offshore vessels are identified and analysed. Thirdly, future trends in performing hull form design optimisation are investigated and possible solutions proposed. A case study on the design optimisation of bulbous bow for passenger ferry vessel to reduce wavemaking resistance is presented using NAPA software. Lastly, main issues and challenges are discussed to stimulate further ideas on future developments in this area, including the use of parallel computing and machine intelligence