This paper present a sufficient and necessary condition of constructing quintic ph curves and analyze the geometric meaning of the control polygon
Firstly explicit algorithm is found that give the unique cubic ph that solves a geometric hermite interpolation problem
Quartic ph curves are studied . their contribution of cusps and inflections are discussed in this paper . a first - order hermite interpolation by quartic ph curves is obtained
If the geometric hermite data is from a smooth function with the arc - length parametric , the cubic ph approximates the smooth function , the error in the approximation of a short segment of length h is found
Pythagorean hodographs exhibit remarkably attractive properties for practical use . for example , their arc length is expressive as a polynomial function of the parameter , and their offsets are rational curves
In the last part of the article applications of space cubic ph to sweep surface modeling and pipe surface modeling are introduced , and sufficient criteria that guarantee that the offset of a sweeping surface are generated by the offset curves of the profile curve is investigated
Nc machining requires " interpolation " algorithms that accurately and efficiently generate sequences of reference position , distributed according to a prescribed feedrate function , along the tool paths . this paper present a systematic derivation of the proper taylor series coefficients for variable feedrate interpolators . when the path is ph curves , detailed formulations for instances are presented where the feedrate v is specified as a constant , the function of the time t , the arc length s and the local curvature k
Based on the extensive studies of subtilisin - like protease ( prl ) of metarhizium anisopliae , extracellullar serine protease is suggested to be a key enzyme involved in the fimgal penetration to invertebrates . the investigation of serine protease in the nematode infected by owvtl may help to understand the mechanism of nematophagous fimgi as biological control agents . a 3l kda serine protease was isolated and purified from the liquid culture of h rhossiliensis owvtl challenged with nematode panagrellus redivivus
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