Many real-world objects are designed by smooth curves, especially in the domain of aerospace and ship, where aerodynamic shapes (e.g., airfoils) and hydrodynamic shapes (e.g., hulls) are designed. To facilitate the design process of those objects, we propose a deep learning based generative model that can synthesize smooth curves. The model maps a low-dimensional latent representation to a sequence of discrete points sampled from a rational B 'ezier curve. We demonstrate the performance of our method in completing both synthetic and real-world generative tasks. Results show that our method can generate diverse and realistic curves, while preserving consistent shape variation in the latent space, which is favorable for latent space design optimization or design space exploration.
Curve synthesis is an important component in aerodynamic or hydrodynamic shape ( , airfoils, hydrofoils, and ship hulls) optimization, where curves representing those shapes are synthesized as design candidates. Splines ( , B-spline and B 'ezier curves) @cite_6 @cite_12 , Free Form Deformation (FFD) @cite_13 , Class-Shape Transformations (CST) @cite_2 @cite_21 , and PARSEC parameterization @cite_18 @cite_17 @cite_21 are used for synthesizing curves in the previous work. Then the control points or parameters for these parameterizations are modified (usually by random perturbation or Latin hypercube sampling @cite_13 ) during optimization to synthesize design candidates. As mentioned previously, these methods suffer from the problems of unknown design parameter limits and the high-dimensionality of the design space. Our proposed data-driven method eliminates these issues by using a low-dimensional latent representation to capture the shape variability and parameter limits of real-world designs.
@cite_18 @cite_21 @cite_6 @cite_2 @cite_13 @cite_12 @cite_17
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The numerical search for the optimum shape of an aerofoil is of great interest for aircraft and turbomachine designers. Unfortunately, this process is very computationally intense and can require a large number of individual flow field simulations resulting in very long CPU run times. One of the core issues that the designer must deal with is how to describe the shape of the airfoil. Clearly, we cannot treat the profile on a point by point basis as the problem would have an infinite number of degrees of freedom. Hence the typical practice is to resort to using a series of curves, such as polynomials and Bezier curves, to describe the profile. This typically reduces the number of degrees of freedom to a much smaller, manageable number. The influence of the selection of the parameterization on the optimization has received relatively little consideration to date. We can anticipate that some parameterizations will be less suitable for describing the profile shape and may result in slower convergence times. Our paper will discuss a new airfoil parameterization, Bezier-PARSEC, that was developed to extend and improve the typical Bezier parameterization found in use. This parameterization was found to fit the known shape of a wide range of existing airfoil profiles as well as resulting in accelerated convergence for aerodynamic optimization using Differential Evolution. Our presentation will present the development and details of the Bezier-PARSEC parameterization and provide evidence that the parameterization is suitable and accelerates convergence. A novel self-adaptive geometric primitive for functional geometric shape synthesis is presented. This novel geometric primitive, for CAD use, is specifically designed to reproduce geometric shapes with functional requirements, such as the aerodynamic and hydrodynamic ones, once the functional parameters are furnished. It produces a typical CAD representation of a functional profile: a set of Bezier curves. The proposed primitive follows a generate-and-test approach and takes advantage of the use of a properly designed artificial neural network (BNN). It combines the properties of a geometric primitive and the capability to manage the engineering knowledge in a specific field of application. The proposed evolutionary primitive is applied to a real engineering application: the automatic synthesis of airfoils. Some examples are simulated in order to test the effectiveness of the proposed method. The results obtained by an original prototypal software are presented and critically discussed. The geometric representation and parameterization used in an aerodynamic wing design process determines the number of design variables and influences the smoothness of the wing representation. In an attempt to reduce the number of design variables while preserving good smoothness properties, the present research investigates the performance of an optimized nonuniform rational B-spline (NURBS) geometrical representation for the aerodynamic design of wings. As a first step, an approach is described whereby optimal spatial positions and weights of a fixed number of NURBS control points is determined using a quasi-Newton optimization algorithm to approximate a general airfoil section. The resulting optimized NURBS representation significantly reduces the number of design variables needed to define accurately a wing section while ensuring good smoothness properties. In a second step, the NURBS control point positions and weights are used as design variables in an aerodynamic optimization problem. This methodology results in a rapid and robust design process, as illustrated by examples of aerodynamic optimization for two- and three-dimensional cases Tracking-by-synthesis is a promising method for markerless vision-based camera tracking, particularly suitable for Augmented Reality applications. In particular, it is drift-free, viewpoint invariant and easy-to-combine with physical sensors such as GPS and inertial sensors. While edge features have been used succesfully within the tracking-by-synthesis framework, point features have, to our knowledge, still never been used. We believe that this is due to the fact that real-time corner detectors are generally weakly repeatable between a camera image and a rendered texture. In this paper, we compare the repeatability of commonly used FAST, Harris and SURF interest point detectors across view synthesis. We show that adding depth blur to the rendered texture can drastically improve the repeatability of FAST and Harris corner detectors (up to 100 in our experiments), which can be very helpful, e.g., to make tracking-by-synthesis running on mobile phones. We propose a method for simulating depth blur on the rendered images using a pre-calibrated depth response curve. In order to fulfil the performance requirements, a pyramidal approach is used based on the well-known MIP mapping technique. We also propose an original method for calibrating the depth response curve, which is suitable for any kind of focus lenses and comes for free in terms of programming effort, once the tracking-by-synthesis algorithm has been implemented.