• Korean Journal of Computational Design and Engineering
• /
• v.15 no.2
• /
• pp.115-123
• /
• 2010

We present an efficient algorithm for computing the Hausdorff distance between two planar curves. The algorithm is based on an efficient trimming technique that eliminates the curve domains that make no contribution to the final Hausdorff distance. The input curves are first approximated with biarcs within a given error bound in a pre-processing step. Using the biarc approximation, the distance map of an input curve is then approximated and stored into the graphics hardware depth-buffer by rendering the distance maps (represented as circular cones) of the biarcs. We repeat the same procedure for the other input curve. By sampling points on each input curve and reading the distance from the other curve (stored in the hardware depth-buffer), we can easily estimate a lower bound of the Hausdorff distance. Based on the lower bound, the algorithm eliminates redundant curve segments where the exact Hausdorff distance can never be obtained. Finally, we employ a multivariate equation solver to compute the Hausdorff distance efficiently using the remaining curve segments only.

• Communications of the Korean Mathematical Society
• /
• v.22 no.4
• /
• pp.641-648
• /
• 2007

In this paper, we present the exact Hausdorff distance between the offset curve of quadratic $B\'{e}zier$ curve and its quadratic $GC^1$ approximation. To illustrate the formula for the Hausdorff distance, we give an example of the quadratic $GC^1$ approximation of the offset curve of a quadratic $B\'{e}zier$ curve.

• International Journal of Contents
• /
• v.11 no.2
• /
• pp.9-14
• /
• 2015

We propose a new distance measure between 2-dimensional points to provide a total order for an entire point set and to reflect the correct geometric meaning of the naturalness of the point ordering. In general, there is no total order for 2-dimensional point sets, so curve reconstruction algorithms do not solve the self-intersection problem because the distance used in the previous methods is the Euclidean distance. A natural distance based on Brownian motion was previously proposed to solve the self-intersection problem. However, the distance reflects the wrong geometric meaning of the naturalness. In this paper, we correct the disadvantage of the natural distance by introducing a polar-natural distance, and we also propose a new curve reconstruction algorithm that is based on the polar-natural distance. Our experiments show that the new distance adequately reflects the correct geometric meaning, so non-simple curve reconstruction can be solved.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.13 no.4
• /
• pp.257-265
• /
• 2009

In this paper we find an explicit form of upper bound of Hausdorff distance between given cubic spline curve and its quadratic spline approximation. As an application the approximation of offset curve of cubic spline curve is presented using our explicit error analysis. The offset curve of quadratic spline curve is exact rational spline curve of degree six, which is also an approximation of the offset curve of cubic spline curve.

• Communications of the Korean Mathematical Society
• /
• v.28 no.3
• /
• pp.571-580
• /
• 2013

In this paper, we extend the familiar limit curve theorem in [2] to a situation where each causal curve lies in a sequence of compact interpolating spacetimes converging to a limit Lorentz space in the sense of Lorentzian Gromov-Hausdorff distance.

• Journal of Korean Society for Quality Management
• /
• v.32 no.4
• /
• pp.265-273
• /
• 2004

We got the growth distance curve by spline smoothing method with observed marketing data and the growth velocity curve by the derivation of the growth distance curve. Using this growth velocity curve, we defined the several characteristic points which describe the variation of marketing data. In this paper, to specify several patterns of marketing data, we suggested characteristic function by using these characteristic points. In addition, we applied characteristic function to the seventeen brands of electric home products data.

• Korean Journal of Food Science and Technology
• /
• v.29 no.2
• /
• pp.273-278
• /
• 1997

In order to investigate the punch properties of some vegetables-cucumber, radish, garlic, ginger and potato-force, distance, and time were measured with a texturometer, and the correlations between compositions and cell characteristics of samples were characterized. Many reflection and rupture points on the force-distance and distance-time curve were observed, and these points appeared when the cells of sample were resisted and yielded against the applied force. They were big and clear at the slow crosshead speed. The regression analysis for force-time and distance-time to the rupture point showed $R^{2}>0.95$. The rupture time and rupure force were 5.63 sec, 4.88 N in ginger and 4.15 sec, 2.00 N in cucumber. The rupture forces become large values at the fast crosshead speed. As cell sizes were increased, the moisture content and rupture distance were increased, while the viscosity of juice, density, regularity of cell, and slope of force-time were decreased. Rupture force, time and distance were decreased at the large specific gravity of samples. The slopes of distance-time curve were inversely proportional to slope of force-time curve.

• Journal for History of Mathematics
• /
• v.28 no.5
• /
• pp.249-262
• /
• 2015

Simon Stevin, a mathematician active in the Netherlands in early seventeenth century, parlayed his mathematical talents into improving navigation skills. In 1605, he introduced a technique of calculating the distance of loxodrome employed in long-distance voyages in his book, Navigation. He explained how to calculate distance by 8 different angles, and even depicted how to make a copper loxodrome model for navigators. Particularly, Stevin clarified in the 7th copper loxodrome model on the unique features of equiangular spiral curve that keeps spinning and gradually accesses from the vicinity to the center. These findings predate those of Descartes on equiangular spiral curve by more than 30 years. Navigation, a branch of actual mathematics devised for the survival of sailors on the bosom of the ocean, was also the first step to the discovery of new mathematical object.

• Journal of the Korea Computer Graphics Society
• /
• v.17 no.3
• /
• pp.33-42
• /
• 2011

We present a new technique for removing interior knots of parametric B-spline curves. An initial curve is constructed by continuous $L_{\infty}$ approximation proposed by Eck and Hadenfeld. We employ Hausdorff distance to measure the shape difference between the original curve and the initial one. The final curve is obtained by minimizing their Hausdorff distance. We demonstrate the effectiveness of our technique with experimental results on various types of planar and spatial curves.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.7 no.5
• /
• pp.178-185
• /
• 1999

Recently, Collision Warning System is developed to improve vehicle safety. This system chiefly uses radar. But the detected vehicle from radar must be decide whether it is the vehicle in the same lane of my vehicle or not. Therefore, Vision System is needed to detect traffic lane. As a preparative step, this study presents the development of algorithm to recognize traffic lane curve direction. That is, the Neural Network that can recognize traffic lane curve direction is constructed by using the information of short distance, middle distance, and decline of traffic lane. For this procedure, the relation between used information and traffic lane curve direction must be analyzed. As the result of application to sampled 2,000 frames, the rate of success is over 90%.t text here.