smooth curvature 中文意思是什麼
smooth curvature
解釋
細切削-
In auto smooth method, we use the curvature and depth analysis to look for " bad point " automatically, and take the latitudinal curve to modify the surface ; referring to the tech of image processing, we import a interactive method to smooth surface based on image smoothing
在自動光順方法中，利用曲率分析及深度分析自動尋找「壞點」並採用緯向曲線重生成的方法予以修正；結合圖像處理的內容，引入了基於圖像平滑的互動式曲面光順方法，取得了滿意的效果。 -
In the third chapter, we introduce geometric expansion of convex planar curves. we discuss the evolution equation using minkowski ' s support function with the speed function of curvature and show that the shapes of curves become round asymptotically when the initial closed curves is smooth and convex
限制曲線在外法向上的演化速度是另一類特殊的曲率函數，研究相應的方程，我們得到了在初始為凸的閉簡單光滑曲線的條件下，曲線的最後形狀是漸近地趨於一個圓。 -
First according to the fact that tangential components of the evolution do not affect the geometric shape of the evolving curves, we introduce the evolution equation of geometric quantities for the general planar curves. then we describe the work of gage - hamilton briefly. last we consider a special curvature flow of curve which evolves with speed function of the principal curvatures along the inner norm and show that convexity of the curve is kept and its length and area are contracted if the initial closed curve is smooth and convex. so the final shape of the curve will be a point in finite time
首先根據曲線在切向分量上發展是不影響曲線的發展形狀，我們引入了曲線的一些幾何變量的發展方程；其次我們簡要地回顧gage - hamilton研究曲線發展的一般步驟；最後我們考慮沿曲線的內法線以曲率的函數為發展速度的一類特殊的曲線族，證明了在初始曲線為凸的閉平面簡單曲線條件下，曲線將保持凸的，並且它的面積和周長將同時收縮，並在有限時間內成為一個點。 -
Secondly, in this part, we will introduce the notation of average geodesic curvature for curves in the hyperbolic plane, and investigate the relationship between the embeddedness of the curve and its average geodesic curvature. finally, we will employ the minkowski ' s support function to construct a new kind of non - circular smooth constant breadth curves in order to attack some open problems on the constant width curves ( for example, whether there is a non - circular polynomial curve of constant width, etc. ) in the second part, we will first follow the ideas of gage - hamilton [ 28 ], gage [ 26 ] and the author ' s dissertation [ 47 ] to present a perimeter - preserving closed convex curve flow in the plane, which is from physical phenomena
其次，對雙曲平面上的曲線引入平均測地曲率的概念，並討論雙曲平面上凸曲線的嵌入性與它的平均測地曲率之間的關系，其目的是為了將雙曲平面上曲線的性質與歐氏平面中曲線的性質作一些對比；最後，我們利用minkowski支撐函數構造了一類新的非圓的光滑常寬曲線，其目的是想回答有關常寬曲線的一些未解決問題（如是否存在非圓的多項式常寬曲線 -
Secondly, the problem of the curve - surface mutual transforming and smooth - finishing have been analyzed farther. for the surface intersecting problem : owing to the introduction of the boundary points, as long as the intersecting points on a certain line, the full intersecting line can be gained. the intersecting line either intersects at the boundary of the triangle surface or forms the loop ; during the course of tracking, the selecting of the pace is restricted by the curvature, the number of the gained intersecting points are not in proportion as the chord - length ; the intersecting points not only record the coordinate and store the parameter
對兩曲面求交問題，當曲面細化足夠小時，曲面求交可近似看成曲面與平面相交問題，引進了邊界點的概念，因此只要知道交線上的任意點，就可以將跨越許多曲面片的整條交線計算出來，所求出的交線或者跨越曲面的邊界，或者形成交線環；從初始點出發跟蹤求解整條交線的過程中，步長的選擇採用了通過曲面片曲率來約束的方法，用該方法求出的交點在不同曲面片上的分佈數目不與弦長成正比；該求交方法包含了各曲面片的邊界線與交線的交點的求解，可獲得邊界交點的坐標值及其參數值。
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