• Transactions of the Korean Society of Automotive Engineers
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• v.6 no.4
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• pp.129-140
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• 1998

A numerical method is proposed to optimize automotive cam profiles. An acceleration curve of a cam follower motion is described by Hermite spline curves. Because of the intrinsic characteristics of the Hermite curve, it is possible to design an acceleration curve with arbitrary shape. Design variables in the optimization problem are location of control points which define the acceleration curve. Objective function includes dynamic performances as well as kinematic properties of a valve train. Similar optimization procedure was also performed using Polydyne cam profile synthesis method. Optimized profiles using the Hermite curve are proved to be superior to those using the Polydyne method.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.65-71
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• 2006

Based on the smoothness criterion of minimum curvature variation of the curve, tangent angle constraints guaranteeing an optimized geometric Hermite (OGH) curve both mathematically and geometrically smooth is given, and new methods for constructing composite optimized geometric Hermite (COH) curves are presented in this paper. The comparison of the new methods with Yong and Cheng's methods based on strain energy minimization is included.

• 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 applied mathematics & informatics
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• v.20 no.1_2
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• pp.575-584
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• 2006

In this paper we introduce a discrete tangent vector of a polygon defined on each vertex by a linear combination of forward difference and backward difference, and show that if the polygon is originated from a smooth curve then direction of the discrete tangent vector is a second order approximation of the direction of the tangent vector of the original curve. Using this discrete tangent vector, we also introduced the geometric cubic Hermite interpolation of a polygon with controlled initial and terminal speed of the curve segments proportional to the edge length. In this case the whole interpolation is $C^1$. Experiments suggest that about $90\%$ of the edge length is the best fit for the initial and terminal speeds.

• Transactions of the Korean Society of Automotive Engineers
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• v.3 no.5
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• pp.90-99
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• 1995

A numerical method is proposed to synthesize automotive cam profiles. An arbitrary acceleration profile for the cam follower motion is divided into several segments, each of them is described by a Hermite curve. A cam profile is defined by control point locations and control variables assigned to each segment. Closed form equations are derived for velocity and displacement constraints which should be satisfied for the curve to be a cam profile. Because the method is flexible and provide arbitrary local controllability, any types of cam acceleration profile can be reproduced by the method. The method is expecially useful for the design of roller type OHC valve trains which need precise local control in the cam profile design to avoid under-cutting problems.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.175-195
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• 2012

Representing planar Pythagorean hodograph (PH) curves by the complex roots of their hodographs, we standardize Farouki's double cubic method to become the undetermined junction point (UJP) method, and then prove the generic existence of solutions for general $C^1$ Hermite interpolation problems. We also extend the UJP method to solve $C^2$ Hermite interpolation problems with multiple PH cubics, and also prove the generic existence of solutions which consist of triple PH cubics with $C^1$ junction points. Further generalizing the UJP method, we go on to solve $C^2$ Hermite interpolation problems using two PH quintics with a $C^1$ junction point, and we also show the possibility of applying the modi e UJP method to $G^2[C^1]$ Hermite interpolation.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.805-823
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• 2019

We introduce polynomial PH-MPH transitive mappings which transform planar PH curves to MPH curves in ${\mathbb{R}}^{2,1}$, and prove that parameterizations of Enneper surfaces of the 1st and the 2nd kind and conjugates of Enneper surfaces of the 2nd kind are PH-MPH transitive. We show how to solve $C^1$ Hermite interpolation problems in ${\mathbb{R}}^{2,1}$, for an admissible $C^1$ Hermite data-set, by using the parametrization of Enneper surfaces of the 1st kind. We also show that we can obtain interpolants for at least some inadmissible data-sets by using MPH biarcs on Enneper surfaces of the 1st kind.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.331-347
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• 2002

We characterize the best geometric conic approximation to regular plane curve and verify its uniqueness. Our characterization for the best geometric conic approximation can be applied to degree reduction, offset curve approximation or convolution curve approximation which are very frequently occurred in CAGD (Computer Aided Geometric Design). We also present the numerical results for these applications.

• Journal of Korean Institute of Industrial Engineers
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• v.20 no.1
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• pp.87-98
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• 1994

This paper describes a method of constructing VC2 Chord-length spline surface from semi-evenly spaced 3D point array. The suface uses Hermite interpolant as Ferguson surface, and it is an extention of chord-length spline curve to surface The proposed surface may be widely used in interpolating smoothly 3D point data obtaind by measurement or engineering design.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.4
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• pp.32-40
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• 1994

This paper describes a smooth surface interpolating method of ship hull using a three-dimensional currie net that comes from the mesh curve fairing process. Geometric continuity(($GC^1$) is preserved across the boundary curve between patches. The three-dimensional curve net can have nonrectangular topologies, such as triangular and pentagonal topology. Among the boundary curve interpolation methods, Hermite blended Coons patch, Convex combination, and Gregory patch interpolation method are used to generate the ship hull surface. To check the fairness of the surface, the numerical method of surface/surface intersection problem is adopted. An application to an actual ship hull is given as an example.