Optimization of freeform surfaces using intelligent deformation techniques for LED applications

2018 ◽  
Vol 7 (1-2) ◽  
pp. 67-80
Author(s):  
Annie Shalom Isaac ◽  
Cornelius Neumann

AbstractFor many years, optical designers have great interests in designing efficient optimization algorithms to bring significant improvement to their initial design. However, the optimization is limited due to a large number of parameters present in the Non-uniform Rationaly b-Spline Surfaces. This limitation was overcome by an indirect technique known as optimization using freeform deformation (FFD). In this approach, the optical surface is placed inside a cubical grid. The vertices of this grid are modified, which deforms the underlying optical surface during the optimization. One of the challenges in this technique is the selection of appropriate vertices of the cubical grid. This is because these vertices share no relationship with the optical performance. When irrelevant vertices are selected, the computational complexity increases. Moreover, the surfaces created by them are not always feasible to manufacture, which is the same problem faced in any optimization technique while creating freeform surfaces. Therefore, this research addresses these two important issues and provides feasible design techniques to solve them. Finally, the proposed techniques are validated using two different illumination examples: street lighting lens and stop lamp for automobiles.

2019 ◽  
Vol 111 ◽  
pp. 29-43 ◽  
Author(s):  
Konstantinos Gavriil ◽  
Alexander Schiftner ◽  
Helmut Pottmann

2021 ◽  
Vol 54 (3) ◽  
pp. 1-42
Author(s):  
Divya Saxena ◽  
Jiannong Cao

Generative Adversarial Networks (GANs) is a novel class of deep generative models that has recently gained significant attention. GANs learn complex and high-dimensional distributions implicitly over images, audio, and data. However, there exist major challenges in training of GANs, i.e., mode collapse, non-convergence, and instability, due to inappropriate design of network architectre, use of objective function, and selection of optimization algorithm. Recently, to address these challenges, several solutions for better design and optimization of GANs have been investigated based on techniques of re-engineered network architectures, new objective functions, and alternative optimization algorithms. To the best of our knowledge, there is no existing survey that has particularly focused on the broad and systematic developments of these solutions. In this study, we perform a comprehensive survey of the advancements in GANs design and optimization solutions proposed to handle GANs challenges. We first identify key research issues within each design and optimization technique and then propose a new taxonomy to structure solutions by key research issues. In accordance with the taxonomy, we provide a detailed discussion on different GANs variants proposed within each solution and their relationships. Finally, based on the insights gained, we present promising research directions in this rapidly growing field.


Author(s):  
Daniel J. Chapman ◽  
Diego A. Arias

Solar brightness profiles were used to model the optical performance of a parabolic linear solar concentrator. A sensitivity analysis of the sun size on collector performance was completed using analytical methods. Ray traces were created for solar brightness profiles having circumsolar ratios from 0–40%, slope errors of the optical surface from 2–5 mrads, and angles of incidence varying from 0–60 degrees. Using typical meteorological data for two locations, the optical performance was calculated and averaged over a year. Intercept factors of these simulations were compared to simpler analytical models that cast the sun shape as a Gaussian function. Results showed that collector performance is relatively insensitive to solar profile, and that using a representative Gaussian solar profile will tend to underestimate collector performance compared to using exact weighted solar profiles by about 1%. This difference is within the uncertainty propagation of the intercept factor calculated with analytical methods.


Author(s):  
Joanna M. Brown ◽  
Malcolm I. G. Bloor ◽  
M. Susan Bloor ◽  
Michael J. Wilson

Abstract A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.


Author(s):  
Dennis Mosbach ◽  
Katja Schladitz ◽  
Bernd Hamann ◽  
Hans Hagen

Abstract We present a method for approximating surface data of arbitrary topology by a model of smoothly connected B-spline surfaces. Most of the existing solutions for this problem use constructions with limited degrees of freedom or they address smoothness between surfaces in a post-processing step, often leading to undesirable surface behavior in proximity of the boundaries. Our contribution is the design of a local method for the approximation process. We compute a smooth B-spline surface approximation without imposing restrictions on the topology of a quadrilateral base mesh defining the individual B-spline surfaces, the used B-spline knot vectors, or the number of B-spline control points. Exact tangent plane continuity can generally not be achieved for a set of B-spline surfaces for an arbitrary underlying quadrilateral base mesh. Our method generates a set of B-spline surfaces that lead to a nearly tangent plane continuous surface approximation and is watertight, i.e., continuous. The presented examples demonstrate that we can generate B-spline approximations with differences of normal vectors along shared boundary curves of less than one degree. Our approach can also be adapted to locally utilize other approximation methods leading to higher orders of continuity.


Author(s):  
Yuan Yuan ◽  
Shiyu Zhou

B-spline surfaces are widely used in engineering practices as a flexible and efficient mathematical model for product design, analysis, and assessment. In this paper, we propose a new sequential B-spline surface construction procedure using multiresolution measurements. At each iterative step of the proposed procedure, we first update knots vectors based on bias and variance decomposition of the fitting error and then incorporate new data into the current surface approximation to fit the control points using Kalman filtering technique. The asymptotical convergence property of the proposed procedure is proved under the framework of sieves method. Using numerical case studies, the effectiveness of the method under finite sample is tested and demonstrated.


2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
C. H. Garcia-Capulin ◽  
F. J. Cuevas ◽  
G. Trejo-Caballero ◽  
H. Rostro-Gonzalez

B-spline surface approximation has been widely used in many applications such as CAD, medical imaging, reverse engineering, and geometric modeling. Given a data set of measures, the surface approximation aims to find a surface that optimally fits the data set. One of the main problems associated with surface approximation by B-splines is the adequate selection of the number and location of the knots, as well as the solution of the system of equations generated by tensor product spline surfaces. In this work, we use a hierarchical genetic algorithm (HGA) to tackle the B-spline surface approximation of smooth explicit data. The proposed approach is based on a novel hierarchical gene structure for the chromosomal representation, which allows us to determine the number and location of the knots for each surface dimension and the B-spline coefficients simultaneously. The method is fully based on genetic algorithms and does not require subjective parameters like smooth factor or knot locations to perform the solution. In order to validate the efficacy of the proposed approach, simulation results from several tests on smooth surfaces and comparison with a successful method have been included.


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