Photometry is a well-known method for 3D reconstruction of objects using images taken in different lighting conditions. In this method, by knowing the light sources' direction, the normal vectors of the surface are recovered in a dense grid through the intensities recorded in the captured images. Each normal vector is then converted to the height difference in two orthogonal directions, and the simultaneous estimation of the heights for the dense grid is done by solving a system of linear, overdetermined and inconsistent equations. The miss-alignment of the coordinate system represents normal vectors and the dense grid frame of 3D reconstruction causes a systematic error in the estimation of the gridded heights map. Photometric self-calibration methods for determining the light sources’ direction are one of the causes of miss-alignments in object and surface normal vectors coordinate systems. In this paper, a sequential and iterative process is proposed to estimate and perform an appropriate rotation to the surface normal vectors. In each iteration of this method, a portion of the necessary rotation is identified in order to parallelize of the two object coordinate systems and surface normal vectors through fitting a geometric transformation to the estimated residuals of the 3D reconstruction process. The results of using the proposed method in various experiments have demonstrated a noticeable improvement in the precision and accuracy of 3D reconstruction.

Point-based models have been analyzed for different applications and depending on the demand, features are extracted by various algorithms. Surfacerecognition from point clouds is most applicable problem in machine vision and reverse engineering. In this research for estimating design parameters, planes and cylinders in point clouds are investigated and new algorithm for detecting these surfaces and calculate their parameters is proposed. According to proposed method, at first surface normal vector by using nearest neighbors must be estimated. By using surface normal vector homogeneous neighborhood is selected. Umbrella curvature is then calculated using homogeneous neighbors. The points are grouping by umbrella curvature as a criterion. Planes and Cylinders are detected by analyzing umbrella curvature values and pattern of homogeneous neighbors. A new method for calculation of planes and cylinders parameters is proposed. This method used fordetermining parameters of eachgroup of points. For evaluation that the proposed algorithm, the calculated parameters are compared with parameters are measured by coordinate measuring machine (CMM). Analyzing results shows that the proposed algorithm performs well and has appropriate abilities on automatic detection of cylinders and planes and calculation their parameters.

SPH method is one of the most used numerical mesh-free methods in CFD simulations which can easily model problems with free surfaces. Considering the importance of surface tension in most engineering applications and the capability of SPH method in simulating free surfaces, a single-phase method for implementing surface tension is introduced in this study. Unlike time-consuming multi-phase simulations, this method does not need to model the second lighter fluid, which reduces the CPU-time and memory requirements substantially. Mirror imaginary particles are used near the free surface to obtain surface properties such as surface normal vector and curvature, which are required in surface tension calculation. The advantages of using these imaginary particles are explained qualitatively through the use of some examples of droplet dynamics. This method is applied to several benchmark problems in surface tension simulations, and acceptable results are obtained.

With the rapid development of 3D laser scanners, point-based discrete shape modeling is being widely used in many engineering applications, e.g. quality control, reverse engineering, computer graphics and machine vision. Point cloud discrete curvature estimation is considered basic operation in point cloud operations and is used in many applications related to cloud points. This paper presents a novel method for point clouds surface curvature estimation. One of the key components of point clouds surface curvature calculation is neighbor coordinates of query point. For selecting neighbors homogeneous neighborhood method is used. This method of choosing neighbors, in addition to the distance takes into consideration the directional balance by improving the k nearest neighbors. Surface normal vector is estimated by neighbors coordinates. In this paper surface curvature is calculated based on normal vector and homogeneous neighbors coordinates. Surface curvature calculated using the novel method is called umbrella curvature. To evaluate how this method performs, umbrella curvature values are calculated for a number of cloud points and the results are used in some different applications. The results show that the proposed method performs well in point clouds curvature estimation.

Polishing is considered as the last and most important step in the manufacturing of optical component. Computer control polishing (CCP) methods are usually used to polish complex surfaces. In this method, material removal is controlled at each point, depending on error at that point. In contact polishing mechanism, tool feed rate is often controlled to eliminate local errors. It means that the higher tool feed rate, the lower material removal would be and vice versa. Tool influence function (TIF) which is defined as the instantaneous material removal under the polishing tool for a given tool motion, is the most important parameter in CCP and its predictability during the polishing process leads to reliable result. In this study, a new spherical tool which can polish complex surfaces by using a 3- axis CNC machine is presented. Because of spherical geometry of both tool and workpiece, tool material removal rate is variable because of changing the angle between tool axis and surface normal vector that leads to variation of relative speed. Tool influence function which depends on tool engagement’s angle was modeled based on Pereston equation. Moreover, the simulation is modeled based on discretization of tool path. To evaluate the methodology, some polishing experimental testes were performed. The experimental results show that a 130 mm spherical convex lens with initial surface roughness of 1.114 micrometer for PV was decreased to 395 nm for PV using the CCP method developed in this study.

Point based 3D modeling has recently received greater attention، mainly due to its simplicity. One of the most fundamental operations for point set processing is to find the neighbors of each point in point clouds. This paper presents a new method called homogeneous neighborhood for determining neighbors in point clouds. This method of choosing neighbors، in addition to the distance takes into consideration the directional balance by improving the k nearest neighbors. The directional balance describes whether the neighbors are well spread around the point of concern. In this study effects of selecting neighbors on normal vector estimation are investigated. Normal vector is calculated using homogeneous neighborhood. For evaluation of the proposed method in determining neighbors، normal vector are calculated using the k nearest neighbors. The results show that the homogeneous neighborhood method is more accurate in normal vector estimation than the k nearest method. For evaluation of the homogeneous neighborhood method، it was employed in point cloud registration application. The results of registration by using the homogeneous neighborhood show that this method of neighbor selection yields reduced registration errors.

Appropriate fixture design for manufacturing a product with quality and in accordance with the requirements is important task and depends on the designer’s experience and skills. In fixture design, the appropriate locating and clamping surfaces automatic selection is the most important of design step. Computer aided fixture design softwares ease the fixture design. In this paper, a new method is presented for automatic selection of appropriate clamping and locating surfaces based on the normal vector graph and linear algebra. At first, locating and clamping surfaces are classified with normal vector graph. Then, the best surfaces among the classified locating and clamping surfaces has been selected with the use of linear algebra method. The results for several sample parts have been tested. The obtained results of this study are applied in computer aided fixture design automation.

In statistical common population, common or normal distribution is often governed and so that using Gaussian or normal probability density function and arithmetic averaging is appropriate. But if the statistical population has been formed from a number of spatial arbitrary directions, then common or normal distribution is not governed. In this condition Fisher probability density function and vector averaging can be used (Fisher is the name of the scientist who proposed the mentioned density function for the first time). In this function, each direction is shown as a point on a sphere with unit radius. The mentioned function shows the probability of having a particular direction in unit angular area of a particular area that has a definite central direction. This central direction shows the angular difference with the real average direction. In Fisher function, the distribution of the azimuth angles around the real vector average direction is symmetrical. The azimuth and the declination angles are the same and being symmetrical around the their distribution of the real average direction is logical. One of the statistical directional populations is the statistical population of different directions of the magnetization of rocks (Each magnetization direction is specified by two angles. First the angle between the magnetization direction and the surface of the horizon (inclination angle) and second the angle between the magnetization direction projection on the surface of the horizon and the geographic north direction (declination angle)). In this paper after an introduction, both normal and Fisher distributions (the latter is used for directional population) are discussed for better understanding of the difference between normal and directional statistical populations. Then the algorithm for calculating the vector averaging is presented. After that a software having vector averaging ability that is produced in this research is presented and then the vector and arithmetic averages are compared for magnetization data. During this research, it is clear that there is a weakness in the vector averaging and that weakness is that in some conditions the result of the vector averaging is not unique (this non uniqueness is because of the functions used in vector averaging algorithm). For example for calculating the declination angle, the function arc-tangent is used and we know that the result of this function is not unique. For example arctan (0.5637) is equal to both 29.41 and -150.9 degrees). The proposed method for the treatment of this weakness in this research is that, it would be proper to perform an arithmetic averaging beside the vector averaging and by which in the cases of having non unique results for vector averaging, the true result can be detectable (The result of the arithmetic averaging is unique) Between different results of the vector averaging, that result is true which is more similar to the arithmetic averaging. For example if there is a directional population which their declination angles are between -170 to -140 degrees and their arithmetic average is -150.67 degrees and the results of their vector averaging are 29.41 and -150.59 degrees, then the correct vector average is -150.59.

In this study, we introduce a new type of surface curves called $D$-type curve. This curve is defined by the property that the unit Darboux vector $vec{W}_{0} $ of a surface curve $vec{r}(s)$ and unit surface normal $vec{n} $ along the curve $vec{r}(s)$ satisfy the condition $leftlangle vec{n} ,vec{W}_{0} rightrangle =text{constant}$. We point out that a $D$-type curve is a geodesic curve or an asymptotic curve in some special cases. Then, by using the Frenet vectors and parametric representation of a surface pencil as a linear combination of the Frenet vectors, we investigate necessary and sufficient condition for a curve to be a $D$-type curve on a surface pencil. Moreover, we introduce some corollaries by considering the $D$-type curve as a helix, a Salkowski curve or a planar curve. Finally, we give some examples for the obtained results.

Cystic fibrosis (CF) is an autosomal recessive disorder caused by mutations in CFTR genes that affect chloride ion channel. The CF is a good nominee for gene therapy as the asymptomatic carriers are phenotypically normal, and the desired cells are accessible for vector delivery. Gene therapy shows promising effects involving the correction of gene or replacement of the mutant gene with the functional one. Accordingly, various viral and non-viral carriers have been investigated. Although viral vectors are efficient, they have some problems, including mutagenesis, host immune response, higher toxicity, and costliness. On the other hand, non-viral vectors have less toxicity and immunogenic response and are easier to prepare. For a successful gene therapy, the cargo must be delivered to the target site. However, various barriers are faced by non-viral vectors, which make the gene delivery to the target site difficult. Extracellular barrier, which is the first barrier, include nucleases, negatively charged serum proteins, blood cells, and activated immune system. Ciliated epithelium, mucus gel, apical surface glycocalyx, and plasma membrane come in the second category of the barriers. Furthermore, the third category, which is related to the intracellular barriers, includes endosome and lysosome, cytoplasmic nucleases, viscous environment of cytoplasm with different proteins, and finally nuclear membrane. Various approaches have been proposed to increase the systematic delivery of vectors and enhance their efficiency. Some of these approaches include surface coating with inert polymers, modification of surface charge with anionic polymers, and enhancement of endocytosis and reduction of toxicity by using polyethylene glycol. This review paper was conduct to highlight the barriers faced by non-viral vectors when carrying a genetic payload to the lungs. This study also involved the investigation of the strategies and different types of modifications targeted toward the improvement of the efficiency of non-viral vectors.