• Honam Mathematical Journal
• /
• v.19 no.1
• /
• pp.107-116
• /
• 1997

In this paper, we get some properties of curves of constant relative breadth in the Minkowski plane.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.15-23
• /
• 1999

We obtain an efficient upper bound of the area of convex curves of constant relative breadth in the Minkowski plane. The estimation is given in terms of the Minkowski are length of pedal curve of original curve.

• Journal of applied mathematics & informatics
• /
• v.26 no.1_2
• /
• pp.121-133
• /
• 2008

In this article, we define Minkowski Pythagorean-hodograph (MPH) curves in the Minkowski plane $\mathbb{R}^{1,1}$ and obtain $C^1$ Hermite interpolations for MPH quintics in the Minkowski plane $\mathbb{R}^{1,1}$. We also have the envelope curves of MPH curves, and make surfaces of revolution with exact rational offsets. In addition, we present an example of $C^1$ Hermite interpolations for MPH rational curves in $\mathbb{R}^{2,1}$ from those in $\mathbb{R}^{1,1}$ and a suitable MPH preserving mapping.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.3
• /
• pp.521-529
• /
• 2003

In this paper, we get the measure of strips and lines in the Minkowski plane $M^2$ that meet a fixed compact convex body in $M^2$. From this we also investigate the probability that strips and lines meet a fixed compact convex body in $M^2$.

• East Asian mathematical journal
• /
• v.10 no.2
• /
• pp.255-260
• /
• 1994

• Honam Mathematical Journal
• /
• v.36 no.3
• /
• pp.475-492
• /
• 2014

In this study, we have investigated the possibility of whether any spacelike Frenet plane of a given space curve in Minkowski 3-space $\mathbb{E}_1^3$ also is any spacelike Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.

• Journal of the Korea Computer Graphics Society
• /
• v.23 no.1
• /
• pp.39-48
• /
• 2017

We present penetration depth (PD) computation algorithms using explicit Minkowski sum construction ($PD_e$) and implicit Minkowski sum construction ($PD_i$). Minkowski sum construction is the most time consuming part in fast PD computation. In order to address this issue, we find a candidate solution using a centroid difference and motion coherence. Then, $PD_e$ constructs or updates partial Minkowski sum around the candidate solution. In contrast, $PD_i$ constructs only a tangent plane to the Minkowski sums iteratively. In practice, our algorithms can compute PD for complicated models consisting of thousands of triangles in a few milli-seconds. We also discuss the benefits of using different construction of Minkowski sums in the context of PD.

• Honam Mathematical Journal
• /
• v.17 no.1
• /
• pp.41-47
• /
• 1995

• Kyungpook Mathematical Journal
• /
• v.60 no.2
• /
• pp.375-385
• /
• 2020

Minkowski spaces have long been investigated with respect to certain properties and substructues such as hyperbolic curves, hyperbolic angles and hyperbolic arc length. In 2009, based on these properties, Chung et al. [3] defined the basic concepts of special relativity, and thus; they interpreted the geometry of the Minkowski spaces. Then, in 2017, E. Nesovic [6] showed the geometric meaning of pseudo angles by interpreting the angle among the unit timelike, spacelike and null vectors on the Minkowski plane. In this study, we show that hyperbolic angle depends on time, t. Moreover, using this fact, we investigate the angles between the unit timelike and spacelike vectors.

• Journal of the Korea Computer Graphics Society
• /
• v.6 no.1
• /
• pp.37-50
• /
• 2000

Using the complex formulation of plane curves which R. T. Farouki introduced, we can identify any plane polynomial curve with only a polynomial with complex coefficients. In this paper, using the well-known fundamental theorem of algebra, we completely factorize the polynomial over the complex number field C and from the completely factorized form of the polynomial, we find a new necessary and sufficient condition for a plane polynomial curve to be a Pythagorean-hodograph curve, obseving the set of all roots of the complex polynomial corresponding to the plane polynomial curve. Applying this method to space polynomial curves in the three dimensional Minkowski space $R^{2,1}$, we also find the necessary and sufficient condition for a polynomial curve in $R^{2,1}$ to be a PH curve in a new finer form and characterize all possible curves completely.