• Korean Journal of Computational Design and Engineering
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• v.4 no.4
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• pp.312-317
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• 1999

An inflection point on a curve is a point where the curvature vanishes. An inflection point is useful for various geometric operations such as the approximation of curves and intersection points between curves or curve approximations. An inflection point on planar Bezier curves can be easily detected using a hodograph and a derivative of hodograph, since the closed from of hodograph is known. In the case of rational Bezier curves, for the detection of inflection point, it is needed to use the first and the second derivatives have higher degree and are more complex than those of non-rational Bezier curvet. This paper presents three methods to detect inflection points of rational Bezier curves. Since the algorithms avoid explicit derivations of the first and the second derivatives of rational Bezier curve to generate polynomial of relatively lower degree, they turn out to be rather efficient. Presented also in this paper is the theoretical analysis of the performances of the algorithms as well as the experimental result.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.4
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• pp.562-565
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• 2013

A new variable rate speech coding technique is proposed. The method is based on the observation that the speech signal approximately looks linear for a very short period of time. The information transmitted is the location and data value of inflection points. If the distance between the inflection points is large, the mid point location and its data value are also delivered. Thus, the encoder transmits both the location and the data value for the inflection samples, but the location only for the non-inflection points. The location information is expressed using one bit for each sample, 0 for non-inflection and 1 for inflection point. At the receiver, using the interpolation, the decoder estimates the untransmitted sample values for non-inflection locations from the received sample values for the inflection samples. With 50 % of computational cost of the existing CVSD delta modulation, the proposed method is expected to achieve the data rate of 36 to 38 kbps and the SNR of 10 to 13 dB.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.353-368
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• 2022

In the previous paper [4], we classified the Weierstrass semigroups at a pair of inflection points of multiplicities d and d - 1 on a smooth plane curve of degree d. In this paper, as a continuation of those results, we classify all semigroups each of which arises as a Weierstrass semigroup at a pair of inflection points of multiplicities d, d - 1 and d - 2 on a smooth plane curve of degree d.

• Computers and Concrete
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• v.1 no.1
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• pp.99-113
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• 2004

The article reports data on, and numerical modelling of, beams exhibiting points of inflection and subjected to sequential loading. Both tests and analysis point to inadequacies in current codes of practice. An alternative design methodology, which is strongly associated with the notion that contraflexure points should be designed as "internal supports", is shown to produce superior performance even though it requires significantly less secondary reinforcement than that advocated by codes.

• Journal of IKEEE
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• v.25 no.4
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• pp.710-715
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• 2021

Power line signal can show disturbances due to various causes. Typical anomalies are temporary sag/swell of the amplitude, flat topped signal, and harmonic distortions. The disturbances need to be detected and treated properly for the quality of the power signal. In this study, the power disturbances are detected using the inflection points (IP). The inflection points are defined as points where local maxima/minima or the slope changes occur. The power line signal has a fixed IP pattern since it is basically sinusoidal, and it may have additional inflection points if there is any disturbance. The disturbance is detected by comparing the IP patterns between the normal signal and distorted signal. In addition, by defining a cost function, the time instant where the disturbance happens can be decided. The computer simulation shows that the proposed method is useful for the detection of various disturbances. The simple sag or swell signal only shows the amplitude changes at the detected inflection points. However, the flat top signal and harmonically distorted signal produce additional inflection points and large values in the cost function. These results can be exploited for the further processing of disturbance classification.

• Journal of IKEEE
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• v.27 no.4
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• pp.472-476
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• 2023

Fundamental frequency/pitch period are major characteristics of speech signals. They are used in many speech applications like speech coding, speech recognition, speaker identification, and so on. In this paper, some of inflection points are used to estimate the pitch which is the inverse of the fundamental frequency. The inflection points are defined as points where local maxima, local minima or the slope changes occur. The speech signal is preprocessed to remove unnecessary inflection points due to the high frequency components using a low pass filter. Only the inflection points from local maxima are used to get the pitch period. While the existing pitch estimation methods process speech signals in blockwise, the proposed method detects the inflection points in sample and produces the pitch period/fundamental frequency estimates along the time. Computer simulation shows the usefulness of the proposed method as a fundamental frequency estimator.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.11
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• pp.166-170
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• 2003

Contouring errors are important especially for high speed and precision machining. In this study, contouring errors along contours having inflection points are studied. When a table of a machine tool moves along a circular path, acceleration acts toward the center of the circle. Thus, at inflection points, acceleration as well as inertia force changes its direction abruptly. The effect of inertia force on the contouring error is investigated in this study. It is found that the contouring error at an inflection point is proportional to the acceleration. This result can be useful in determining contouring errors along general paths.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.369-378
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• 2007

We classify all semigroups each of which arises as a Weierstrass semigroup at a pair of inflection points of multiplicities d or d-1 on a smooth plane curve of degree d.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.12
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• pp.1750-1754
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• 2013

A variable bit rate speech coder is presented. The coder is based on the observation that a speech signal can be viewed as a combination of piecewise linear signals in a short time period. The encoder detects the sample points where the slope of the signal changes, which are called the inflection points in this paper. The coder transmits the location and value for the detected inflection sample, but only the location information for the noninflection samples. In the decoder, the noninflection samples are estimated with interpolation of the received information. Several factors affecting the performance of the coder have been tested through simulation. Simulation results show that the linear interpolation produces 1 ~ 5 dB improvement over the cubic spline interpolation. And the -law companding does not provide any benefit when it is applied before the inflection detection. With low threshold values in the inflection point detection, the coder shows better MOS and more than 16 dB improvement in SNR compared to the continuously variable slope delta modulation (CVSDM).

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2011.11a
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• pp.237-240
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• 2011

Numerical simulation was carried out to investigate the effect of pintle inflection point on the performance of the SNECMA modulatable thrust devices. Results show that the effect of inflection points in the pintle is to decrease aerodynamic load while maintaining required thrust level.