• Journal of Information Processing Systems
• /
• v.4 no.4
• /
• pp.153-158
• /
• 2008

This paper deals with the geometric fitting algorithms for parametric curves and surfaces in 2-D/3-D space, which estimate the curve/surface parameters by minimizing the square sum of the shortest distances between the curve/surface and the given points. We identify three algorithmic approaches for solving the nonlinear problem of geometric fitting. As their general implementation we describe a new algorithm for geometric fitting of parametric curves and surfaces. The curve/surface parameters are estimated in terms of form, position, and rotation parameters. We test and evaluate the performances of the algorithms with fitting examples.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.867-883
• /
• 2019

The canal surfaces foliated by pseudo spheres $\mathbb{S}_1^2$ along a space curve in Minkowski 3-space are studied. The geometric properties of such surfaces are shown by classifying the linear Weingarten canal surfaces, the developable, minimal and umbilical canal surfaces are discussed at the same time.

• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1139-1171
• /
• 1996

The purpose of our research is to understand geometric and topological aspects of real projective structures on surfaces. A real projective surface is a differentiable surface with an atlas of charts to $RP^2$ such that transition functions are restrictions of projective automorphisms of $RP^2$. Since such an atlas lifts projective geometry on $RP^2$ to the surface locally and consistently, one can study the global projective geometry of surfaces.

• ETRI Journal
• /
• v.35 no.6
• /
• pp.1115-1125
• /
• 2013

This paper presents a scheme for geometric correction of projected content for planar and quadratic projection surfaces. The scheme does not require the projection surface to be perfectly quadratic or planar and is therefore suitable for uneven low-cost commercial and home projection surfaces. An approach based on the recursive subdivision of second-order B$\acute{e}$zier patches is proposed for the estimation of projection distortion owing to surface imperfections. Unlike existing schemes, the proposed scheme is completely automatic, requires no prior knowledge of the projection surface, and uses a single uncalibrated camera without requiring any physical markers on the projection surface. Furthermore, the scheme is scalable for geometric calibration of multi-projector setups. The efficacy of the proposed scheme is demonstrated using simulations and via practical experiments on various surfaces. A relative distortion error metric is also introduced that provides a quantitative measure of the suppression of geometric distortions, which occurs as the result of an imperfect projection surface.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.9 no.2
• /
• pp.119-124
• /
• 2000

In this paper based on geometric optics and geometric modeling aspheric surface of the side mirror mold with dead angle reduced have been designed and machined in a CNC machining center, Surface roughness of the mold was evaluat-ed by usin the surface shaping system. Surface generating simulation of a ball endmill process is investigated. Through the simulation based on the surface-shaping system 3-D engineered surfaces and properties of engineered surfaces are obtained, Computer simulation provides the effective working conditions through the prediction of geometric properties of engineered surfaces. The rear view mirror and room mirror play important role on the safe driving condition as a observation of environment but the rear view mirror can not provide complete information of driving environments due to the existence of the dead angle. The analysis on the shape of formed mirror shows that the proposed me？ improves range of a driver's sight.

• Journal of Advanced Marine Engineering and Technology
• /
• v.18 no.1
• /
• pp.92-100
• /
• 1994

For generating NC machining data automatically, it is important to handle computer models such as geometric shape data including engineering specifications for the mechanical part to be manufactured. We proposed unique CAM system for a personal computer that can define the geometric shape in an ease manner and machine the sculptured surfaces of a mold cavity. In this paper, the theoretical basis of generation of high precision machining data for a mold cavity is obtained. The first is geometric modelling, and the second is high precision machining with an optimized tool path algorithm satisfying given tolerance limits. Especially, the bicubic Bezier basis function is adopted for a geometric modelling.

• Proceedings of the KSME Conference
• /
• 2003.11a
• /
• pp.1328-1333
• /
• 2003

In the present study, an integrated framework of geometric modeling, analysis, and design optimization is proposed. Geometric modeling is based on B-spline surface representation. Geometrically-exact shell finite element is implemented in analysis module. Control points of the surface are selected as design variables for optimization, which can make the interaction easier between analysis and surface representation. Sequential linear programming(SLP) is adopted for the shape optimization of surfaces. For the computation of shape sensitivities, semi-analytical method is used. The developed integrated framework should serve as a powerful tool for the geometric modeling, analysis, and shape design of surfaces.

• Journal of Mechanical Science and Technology
• /
• v.14 no.10
• /
• pp.1104-1113
• /
• 2000

This paper proposes an efficient reverse engineering technique for compound surfaces using a boundary detection method. This approach consists in extracting geometric edge information using a vision system, which can be used in order to drastically reduce geometric errors in the vicinity of compound surface boundaries. Through the image-processing technique and the interpolation process, boundaries are reconstructed by either analytic curves (e. g. circle, ellipse, line) or parametric curves (B-spline curve). In other regions, except boundaries, geometric data are acquired on CMM as points inspected using a touch type probe, and then they are interpolated on several surfaces using a B-spline skinning method. Finally, the boundary edge and the skinned surfaces are combined to reconstruct the final compound surface. Through simulations and experimental works, the effectiveness of the proposed method is confirmed.

• Honam Mathematical Journal
• /
• v.44 no.2
• /
• pp.259-270
• /
• 2022

This paper is devoted to the geometry of vector fields and timelike flows in terms of anholonomic coordinates in three dimensional Lorentzian space. We discuss eight parameters which are related by three partial differential equations. Then, it is seen that the curl of tangent vector field does not include any component in the direction of principal normal vector field. This implies the existence of a surface which contains both s - lines and b - lines. Moreover, we examine a normal congruence of timelike surfaces containing the s - lines and b - lines. Considering the compatibility conditions, we obtain the Gauss-Mainardi-Codazzi equations for this normal congruence of timelike surfaces in the case of the abnormality of normal vector field is zero. Intrinsic geometric properties of these normal congruence of timelike surfaces are obtained. We have dealt with important results on these geometric properties.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.7 no.9
• /
• pp.2299-2311
• /
• 2013

As portable multimedia devices become more popular and smaller, the use of portable projectors is also rapidly increasing. However, when portable projectors are used in mobile environments in which a dedicated planar screen is not available, the problem of geometric distortion of the projected image often arises. In this paper, we present a geometric image compensation method for portable projectors to compensate for geometric distortions of images projected on various types of planar or nonplanar projection surfaces. The proposed method is based on extraction of the two-dimensional (2D) geometric information of a projection area, setting of the compensation area, and prewarping using 2D homography. The experimental results show that the proposed method allows effective compensation for waved and arbitrarily shaped projection areas, as well as tilted and bent surfaces that are often found in the mobile environment. Furthermore, the proposed method is more computationally efficient than conventional image compensation methods that use 3D geometric information.