• Korean Journal of Computational Design and Engineering
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• v.18 no.1
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• pp.49-57
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• 2013

In this paper, orthogonal projection of a point onto a 2D planar curve is discussed. The problem is formulated as finding a point on a curve where the tangent of the curve is perpendicular to the vector connecting the point on the curve and a point in the space. Existing methods are compared and novel approaches to solve the problem are presented. The proposed methods are tested with examples.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.73-86
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• 2007

The general stereographic projection which maps a point on a sphere with arbitrary radius to a point on a plane stereographically and its inverse projection have the pythagorean-hodograph (PH) preserving property in the sense that they map a PH curve to another PH curve. Upon this fact, for given spatial $C^1$ Hermite data, we construct a spatial PH curve on a sphere that is a $C^1$ Hermite interpolant of the given data as follows: First, we solve $C^1$ Hermite interpolation problem for the stereographically projected planar data of the given data in $\mathbb{R}^3$ with planar PH curves expressed in the complex representation. Second, we construct spherical PH curves which are interpolants for the given data in $\mathbb{R}^3$ using the inverse general stereographic projection.

• Journal of Computational Design and Engineering
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• v.1 no.2
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• pp.116-127
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• 2014

This paper aims to review methods for computing orthogonal projection of points onto curves and surfaces, which are given in implicit or parametric form or as point clouds. Special emphasis is place on orthogonal projection onto conics along with reviews on orthogonal projection of points onto curves and surfaces in implicit and parametric form. Except for conics, computation methods are classified into two groups based on the core approaches: iterative and subdivision based. An extension of orthogonal projection of points to orthogonal projection of curves onto surfaces is briefly explored. Next, the discussion continues toward orthogonal projection of points onto point clouds, which spawns a different branch of algorithms in the context of orthogonal projection. The paper concludes with comments on guidance for an appropriate choice of methods for various applications.

• Nuclear Engineering and Technology
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• v.54 no.3
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• pp.917-925
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• 2022

Steam generator (SG) tubes in a nuclear power plant can undergo rapid changes in pressure and temperature during an accident; thus, an accurate model to predict short-term creep damage is essential. The theta (𝜃) projection method has been widely used for modeling creep-strain behavior under constant stress. However, many creep test data are obtained under constant load, so creep rupture behavior under a constant load cannot be accurately simulated due to the different stress conditions. This paper proposes a novel methodology to obtain the creep curve under constant stress using a modified 𝜃 projection method that considers the increase in true stress during creep deformation in a constant-load creep test. The methodology is validated using finite element analysis, and the limitations of the methodology are also discussed. The paper also proposes a creep-strain model for alloy 690 as an SG material and a novel creep hardening rule we call the damage-fraction hardening rule. The creep hardening rule is applied to evaluate the creep rupture behavior of SG tubes. The results of this study show its great potential to evaluate the rupture behavior of an SG tube governed by creep deformation.

• Journal of the Korean Chemical Society
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• v.21 no.5
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• pp.362-371
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• 1977

In this paper application of the projection operator technique to the study of NMR absorption line shape and free induction decay curve is explored. It is found that the projection operator technique can provide a convenient means for deriving a set of hierarchy equations which may serve as a good starting point for theoretical calculation of the absorption line and free induction decay function by successive approximation or by an appropriate decoupling approximation. A brief review of linear response theory of NMR line shape and the relation between the absorption line shape and free induction decay function are also described.

• Investigative Magnetic Resonance Imaging
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• v.9 no.1
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• pp.36-42
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• 2005

Purpose : To develop a novel approach to calculate the sensitivity profiles of the phased array coil for use in non-uniform intensity correction. Materials and Methods : The proposed intensity correction method estimates the sensitivity profile of the coil to extract intensity variations that represent the scanned image. The sensitivity profile is estimated by fitting a non-linear curve to various angles of projections through the imaged object in order to eliminate the high-frequency image content. Filtered back projection is then used to compute the estimates of the sensitivity profile of each coil. The method was applied both to phantom and brain images from 8-channel phased-array coil and 4-channel phased-array coil, respectively. Results : Intensity-corrected images from the proposed method have more uniform intensity than those from the commonly used 'sum-of-squares' approach. By using the proposed correction method, the intensity variation was reduced to $6.1\%$ from $13.1\%$, acquired from the 'sum-of-squares'. Conclusion : The proposed method is more effective at correcting the intensity non-uniformity of the phased-array surface-coil images than the conventional 'sum-of-squares' method.

• Korean Journal of Soil Science and Fertilizer
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• v.32 no.3
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• pp.211-214
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• 1999

To acknowledge the differences in soil physical properties of cultivated land derived from major parent rocks in Yeong-nam areas, we investigated Riley's projection sphericity(one of the morphological properties) of sand and made up Soil Moisture Characteristics Curve(SMCC). The averages in Riley s projection sphericity range from 0.63 to 0.67 in soils derived from Sedimentary rocks than 0.56 to 0.61 in soils derived from igneous rocks. In case of soils derived from igneous rocks, the Riley's projection sphericity is lower as the particle size get to be smaller. The differences of SMCC were larger in the fine loamy soils than in coarse loamy soils. The moisture retention was higher in the soils derived from Sedimentary rocks than in the soils derived from Igneous rocks. After we transformed the water retention into dimensionless scale value by available water ratio, the SMCC was nearly unchangeable in the tested soils except for fine loamy soils derived from Sedimentary rock, but was not correlated with soil texture or parent rocks.

• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.821-834
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• 2019

The reductivity of a spherical curve is the minimal number of times a particular local transformation called an inverse-half-twisted splice is required to obtain a reducible spherical curve from the initial spherical curve. It is unknown if there exists a spherical curve whose reductivity is four. In this paper, an unavoidable set of configurations for a spherical curve with reductivity four is given by focusing on 5-gons. It has also been unknown if there exists a reduced spherical curve which has no 2-gons and 3-gons of type A, B and C. This paper gives the answer to this question by constructing such a spherical curve.

• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.127-134
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• 1998

This paper presents d new algorithm to compute the offlet curve of a given planar parametric curve. We reduce the problem of computing an offset curve to that of intersecting a surface to a paraboloid. Given an input curve C(t)=(x(t), y(t))∈R², the corresponding surface D/sub c(t)/ is constructed symbolically as the envelope surface of a one-parameter family of tangent planes of the paraboloid Q:z=x²+y²along a lifted curve C(t)=(x(t), y(t), x(t)²+y(t)²∈Q. Given an offset distance d∈R, the offset curve C/sub d/(t) is obtained by the projection of the intersection curve of D/sub c(t)/ and a paraboloid Q:z=x²+y²-d² into the xy-plane.

• Proceedings of the KIPE Conference
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• 2018.07a
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• pp.126-128
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• 2018

Solar array simulator (SAS) is a special DC power supply that regulates the output voltage or current to emulate characteristics of photovoltaic (PV) panels. Especially, the control of SAS is a challenging task due to the nonlinearity in the output curve, which is dependent on irradiance as well as temperature and is determined by panel materials. Conventionally, both current-mode control and voltage-mode control should be alternated by partitioning the operating curve into multiple sections, which is not only for the measurement noise problem with the feedback sensing but also for the control stability issue near the maximum power point. However, the occurrence of transition among different controllers may deteriorate the overall performance. To eliminate the mode transitions, a novel single controller scheme has been introduced in this paper, where the reference operating projection technique enables simple, smooth and numerically stable control. Theoretical consideration on the loop stability issue is discussed and the performance is verified experimentally for the emulation of a PV panel data in view of stability and response speed.