This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric role in shape reconstruction. In this paper we address the general problem of global-support parametric surface approximation from clouds of data points for reverse engineering applications. Given a set of measured data points, the approximation is formulated as a nonlinear continuous least-squares optimization problem. Then, a recent metaheuristics called Cuckoo Search Algorithm (CSA) is applied to compute all relevant free variables of this minimization problem (namely, the data parameters and the surface poles). The method includes the iterative generation of new solutions by using the Lévy flights to promote the diversity of solutions and prevent stagnation. A critical advantage of this method is its simplicity: the CSA requires only two parameters, many fewer than any other metaheuristic approach, so the parameter tuning becomes a very easy task. The method is also simple to understand and easy to implement. Our approach has been applied to a benchmark of three illustrative sets of noisy data points corresponding to surfaces exhibiting several challenging features. Our experimental results show that the method performs very well even for the cases of noisy and unorganized data points. Therefore, the method can be directly used for real-world applications for reverse engineering without further pre/post-processing. Comparative work with the most classical mathematical techniques for this problem as well as a recent modification of the CSA called Improved CSA (ICSA) is also reported. Two nonparametric statistical tests show that our method outperforms the classical mathematical techniques and provides equivalent results to ICSA for all instances in our benchmark.

The solar optical telescope onboard the Solar-B is aimed to perform a high precision polarization measurements of the solar spectral lines in visible wavelengths to obtain, for the first time, continuous sets of high spatial resolution (~0.2arcsec) and high accuracy vector-magnetic-field map of the sun for studying the mechanisms driving the fascinating activity phenomena occurring in the solar atmosphere. The optical telescope assembly (OTA) is a diffraction limited, aplanatic Gregorian telescope with an aperture of Φ500mm. With a collimating lens unit and an active folding mirror, the OTA provides a pointing-stabilized parallel beam to the focal plane package (FPP) with a field of view of about 360x200arcsec. In this paper we identify the key technical issues of OTA for achieving the mission goal and describe the basic concepts in its optical, mechanical and thermal designs. The strategy to verify the in-orbit performance of the telescope is also discussed.

Designing aesthetically appealing models is vital for the marketing success of industrial products. In this paper, we propose quasi-Aesthetic Curves that can be used in CAD systems for aesthetic shape design. Quasi-Aesthetic Curves represented in rational cubic Bézier Forms are curves whose logarithmic curvature histograms (LCHs) become nearly straight lines. The monotonicity of curvature of quasi-Aesthetic Curves is checked by the proposed method. We generate quasi-Aesthetic Curves by approximating the Aesthetic Curves whose LCHs are strictly represented by straight lines. We show that one Aesthetic Curve segment whose change of tangential angle is less than 90 deg. can be replaced by one quasi-Aesthetic Curve segment guaranteeing the monotonicity of the curvature in most of practical situations.