翻訳と辞書 Words near each other ・ Slentho ・ SLEP ・ SLEPc ・ Slepcev Storch ・ Slependen ・ Slependen Station ・ Slepi potnik ・ Slepian ・ Slepian's lemma ・ Slepian–Wolf coding ・ Slepotice ・ Slepčany ・ Slepče ・ Slepčević ・ Slepšek ・ Slerp ・ SLES ・ Slesarev Svyatogor ・ Slesinger ・ Slesse Creek ・ Slesse Mountain ・ Slesser ・ Slessor ・ Slessor Glacier ・ Slessor Peak ・ Slesvig ・ Slesvigske musikkorps ・ Slet, Aarhus ・ Sletnicu River ・ Sletringen Lighthouse Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Slerp ： ウィキペディア英語版 Slerp In computer graphics, Slerp is shorthand for spherical linear interpolation, introduced by Ken Shoemake in the context of quaternion interpolation for the purpose of animating 3D rotation. It refers to constant-speed motion along a unit-radius great circle arc, given the ends and an interpolation parameter between 0 and 1. ==Geometric Slerp== Slerp has a geometric formula independent of quaternions, and independent of the dimension of the space in which the arc is embedded. This formula, a symmetric weighted sum credited to Glenn Davis, is based on the fact that any point on the curve must be a linear combination of the ends. Let ''p''0 and ''p''1 be the first and last points of the arc, and let ''t'' be the parameter, 0 ≤ ''t'' ≤ 1. Compute Ω as the angle subtended by the arc, so that , the ''n''-dimensional dot product of the unit vectors from the origin to the ends. The geometric formula is then :$\backslash mathrm(p\_0,p\_1;\; t)\; =\; \backslash frac">)\}\; p\_0\; +\; \backslash frac\; p\_1.$ The symmetry can be seen in the fact that = . In the limit as Ω → 0, this formula reduces to the corresponding symmetric formula for linear interpolation, :$\backslash mathrm(p\_0,p\_1;\; t)\; =\; (1-t)\; p\_0\; +\; t\; p\_1.\backslash ,\backslash !$ A Slerp path is, in fact, the spherical geometry equivalent of a path along a line segment in the plane; a great circle is a spherical geodesic. More familiar than the general Slerp formula is the case when the end vectors are perpendicular, in which case the formula is . Letting , and applying the trigonometric identity , this becomes the Slerp formula. The factor of in the general formula is a normalization, since a vector ''p''1 at an angle of Ω to ''p''0 projects onto the perpendicular ⊥''p''0 with a length of only . Some special cases of Slerp admit more efficient calculation. When a circular arc is to be drawn into a raster image, the preferred method is some variation of Bresenham's circle algorithm. Evaluation at the special parameter values 0 and 1 trivially yields ''p''0 and ''p''1, respectively; and bisection, evaluation at ½, simplifies to , normalized. Another special case, common in animation, is evaluation with fixed ends and equal parametric steps. If ''p''''k''−1 and ''p''''k'' are two consecutive values, and if ''c'' is twice their dot product (constant for all steps), then the next value, ''p''''k''+1, is the reflection . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Slerp」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.