bezier spline 中文意思是什麼
bezier spline
解釋
貝賽爾曲線-
They not only inherit the advantages of bezier curves and b - spline curves, also can be used to represent straight lines precisely and some remarkable transcendental curves precisely, such as circular arc, ellipse, cardioids and twisted pair line etc. especially, the uniform t - b - spline curve of three degrees is smoother than b - spline curve and c - b - spline curve of the same order
此外由於它們還具有三角函數的優點，故既可以精確表示直線段、二次多項式曲線段又可以精確表示圓弧、橢圓弧等二次曲線以及心臟線、雙紐線等超越曲線。特別地， 3次均勻t - b樣條曲線曲面比同階均勻b樣條（ c - b樣條）曲線曲面具有更高的光滑度。 -
Secondly, the various conic arcs and conies are generated by the rational triangular bezier and the b - spline method in polar coordinates system
其次，給出圓錐曲線弧及其補弧的三角有理b zier表示；以及任意角度二次曲線弧的極坐標b樣條表示。 -
During the past decades, some researchers, such as : bezier, kj. versprile, deboor and cox, etc. had made great progress in the filed of constrained b - spline curve and surface fitting. in this article the method of constrained b - spline curve was introduced, which is used to figure out the control vertexes. using this interpolation method we can calculate every points of a uniform b - spline
並且分析了在各種端點情況下，在重節點的情況下，如何反算控制多邊形的頂點；如何在求出控制多邊形頂點之後，插值計算b樣條擬合曲線上的每一點；並通過結合雙尾船的型線，採用visualc + +和autocad2002為平臺，分別編制了相應的軟體，對提供的型值做出繪圖處理，取得了良好的效果。 -
Nurbs surfaces with single interior knots are simple and used widely. the thesis main aims at biuquartic, biquintic, k x fc - degree b - spline surfaces and bicubic nurbs with single interior knots. one of the contributions is to apply knot refinement and the geometric continuous conditions of bezier surfaces to deduce the geometric continuous constraints of nurbs patches and obtain the intrinsic equations of common boundary curves, where the intrinsic equations are the special phenomena of nurbs surfaces
節點向量是內部單節點的nurbs曲面是最簡單也是最常用的，本文重點針對單節點的雙四次、雙五次和雙k次b樣條曲面及雙三次nurbs曲面，運用節點插入技術和b zier曲面的幾何連續理論成果，導出了它們之間的幾何光滑拼接條件，同時得到了公共邊界曲線所必須滿足的本徵方程，其中本徵方程是nurbs曲面所獨有的現象。 -
The details are as follows. the correlative knowledge of basic spline and bernstein basis functions, the theory of basic spline and bezier curves & surface and their rational forms, all these are regarded as the academic background of further research
涉及b樣條基函數及其性質， b樣條曲線曲面和有理b樣條曲線曲面及其性質， bernstein基函數及其性質， b zier曲線曲面和有理b zier曲線曲面及其性質等等。 -
The result shows that the sufficient and necessary condition of the quadratic rational b - spline curve ' s curvature monotony is similar to the quadratic rational bezier curves ", but its condition is some different from the quadratic rational bezier curves " curve ' s rendering algorithm is an important content in computer graphics, cad
曲線的生成演算法是計算機圖形學的重要內容。對於一些基本曲線，如直線，圓，橢圓等，都有快速生成演算法，如畫直線的bresenham演算法， dda演算法，畫圓的bresenham演算法，中點法，正負法， pitterway的橢圓及拋物線繪制演算法等等。 -
Bezier, b - spline, and their rational models play an important role in cad / cam systems. but these models show obvious shortcomings, such as no encompassing transcendent ( i. e., nonalgebraic ) curves, e. g. the circle, the cycloid, the catenary and the hyperbolic helix
B zier ， b -樣條以及它們的有理模型在cad cam系統中有著非常重要的地位，但是這些模型也有著明顯的缺陷，譬如不能精確表示很多非代數曲線，如圓弧，擺線，懸鏈線，雙曲螺線等 -
And then we introduce bezier, b - spline and non - polynomial curves and surfaces modeling, which include l - splines, helix splines, splines in tension and c - curves etc. by analyzing the characters of bezier curves and b - spline curves, we construct trigonometric polynomial curves in the space of trigonometric functions, which assume the characters of b zier curves and b - spline curves
闡述了cagd中參數曲線曲面造型的發展歷史並介紹了bzier方法、 b樣條方法以及非多項式曲線曲面造型方法，後者包括l -樣條、螺旋樣條、張力樣條以及c -曲線等。文章以b zier曲線和b樣條曲線的特點為基礎，在三角函數空間中構造一組具有上述兩類曲線特性的三角函數多項式曲線，稱其為t - b zier曲線和t - b樣條曲線。 -
In fact, rational quadratic bezier curve is just a special form of rational quadratic b - spline curve, the condition of quadratic rational b - spline curve is similar to quadratic rational bezier curve
事實上，二次有理b zier曲線是二次有理b樣條曲線的特例，二次有理b樣條曲線曲率單調的充要條件是否與二次有理b zier曲線相類似 -
We have more important significance studying quadratic rational b - spline curve ' s curvature monotony. this paper derive the curvature monotony condition for the quadratic rational b spline curves by using the skew coordinate system that can reduces the calculation process. and the curvature monotony condition is compared to the quadratic rational bezier curves "
本論文通過建立斜坐標系，簡化了計算過程，推導出了二次有理b樣條曲線曲率單調充要條件，並與二次有理b zier曲線的曲率單調條件相比較，結果表明：二次有理b樣條曲線曲率單調的充要條件與二次有理b zier樣條曲線相類似，但其條件又有不同。 -
To fulfill the need of the application of rp technique in medical domain, reverse cad modeling from medical cross sections is systematically studied in this dissertation. firstly, some algorithms related to the research of this dissertation are studied. new algorithms for orientation and inclusion test for simple polygon, an error constrained automatic faring algorithm for b - spline curve and a theorem regarding the termination criterion for subdivision of triangular bezier patch are proposed
本文針對rp技術在醫學領域應用的需要，系統研究了基於醫學斷層輪廓數據的反求cad建模理論和方法： （ 1 ）在基礎演算法研究部分，提出了簡單多邊形方向及點在多邊形內外判斷的新方法、三角b zier曲面片離散的誤差控制定理和一種帶誤差約束的b樣條曲線的自動光順方法； （ 2 ）提出了一種基於相鄰層輪廓相似性的醫學斷層輪廓數據曲面重構方法； （ 3 ）提出了一種稱為「虛擬測量」的曲面模型處理方法。 -
Paper [ 76 ] provides a integer algorithm for rasterizing free curves, we need change the curve form to implicit function form, then use curve ' s positive - negative property to draw, but we ca n ' t use this algorithm when curve ' s degree is higher than 3 and this algorithm ca n ' t avoid using multiplication ; paper [ 77 ] provides a new generating algorithm, this algorithm can draw bezier very well, but for b - spline curve, we need use convert them into bernstein base form. because this process spends a lot of time, this algorithm has not a good speed and effect for rendering rational b - spline curve
現在經常採用的演算法也是基於幾何的演算法（即線式生成演算法）和基於像素的演算法（點式生成演算法） ;文獻78 ]提供了一種有理參數曲線的快速逐點生成演算法，該演算法對有理b吮ier曲線的繪制，能起到很好的作用，但是對于有理b樣條曲線，必須先通過多項式的代數基與bemstein基間的變換矩陣，把原式用bemstein基表示，這一過程由於計算量大，降低了曲線生成的速度和效率 -
Another approach of this thesis is to demonstrate that the lowest degree is 5 in order to make the b - spline patches hold the property of local adjustment if no specific 111 abstract restriction to the partition. most existed surfaces reconstruction methods adopt bezier tool and demand particular partition. the local scheme addressed in this thesis does n ' t restrict the partitions of fitted surfaces, and the fitting tools is biquartic b - spline surfaces with double interior knots and biquintic b - spline surface with single interior knots
本文論述的「局部格式」調整方法不對剖分區域施加任何限制，主要採用內部具有二重節點的雙四次b樣條曲面和單節點的雙五次b樣條曲面做為擬合工具，給出了「局部」調整的方法，該方法能很好的保持拼接曲面的幾何特徵，克服了許多已有的重構方法僅採用簡單共線法處理幾何光滑性的弊端。 -
We often adjust the shape of curves or change the site of curves. this thesis mainly discusses the question of local modifications of the bezier spline curves in computer aided geometry design. it is composed of four chapters
在cagd中，往往要調整曲線的形狀或改變曲線的位置，本文主要討論了b zier樣條曲線的局部修改問題，全文共分四章。 -
This paper summaries the researches on the new schemes of parameter curves and surfaces modeling - curves and surfaces modeling of trigonometric polynomial, which includes curves and surfaces of t - bezier, t - b - spline, tc - bezier and tc - b - spline. hc - b zier curves and surfaces are also discussed in the space of hyperbolic functions in the end
本文主要對參數曲線曲面造型的一種新方法? ?三角多項式曲線曲面進行了深入研究，其內容主要包括t - b zier曲線曲面、 t - b樣條曲線曲面、 tc - b zier曲線曲面和tc - b樣條曲線曲面。 -
Their representatives are simple and direct. we call them as t - bezier curves and t - b - spline curves
它們繼承了b zier曲線和b樣條曲線的特點，曲線表示簡單、直觀。 -
The first one focuses on the notations and properties of basic spline and bernstein basis functions. at the same time, the theory of basic spline and bezier curves and surfaces are reviewed as the premise of further research. the second one emphasizes in the theory of bsc curves and surfaces
主要是b樣條函數和bernstein基函數的概念和性質， b樣條曲線曲面和b zier曲線曲面的基礎知識，作為研究的理論前提；第二部分為bsc曲線曲面的理論。 -
The author acquires three main results, i. e. an approach of constructing polynomial curves with some shape parameters, c2 - continuous spline curves of degree 4 with some shape parameter, and planar piecewise bezier curve of 3 4th and 6th degree with given control polygon and the curve segments are joined together with c1 c2 and c3 - continuity
作者在後三章得到了本文的三個主要結果： （ 1 ）構造了一種帶形狀參數的多項式曲線； （ 2 ）構造了一類c ~ -連續帶形狀參數的四次樣條逼近曲線； （ 3 ）構造了與給定多邊形相切的可調控保形分段c ~ 1三次、 c ~ 3六次b zier樣條曲線。 -
There are two mainly method for surface rebuild, one is based on three angular bezier surface, the other is b - spline or nurbs surface. the property of b - spline and nurbs curve is introduced and how to generate curve and surface with interpolation is studied
對基於三角bezier曲面和b樣條或nurbs曲面的曲面重構進行了論述，介紹了b樣條和nurbs曲線曲面特點並對用插值法生成曲線曲面進行了研究。
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