This paper first summarizes recent researches on this topic, and then proposes some methods for curve modeling with cubic algebraic curve based on pure geometric constraints that involve control points, tangent directions and curvatures.

然后提出了一種基于幾何約束的三次代數(shù)曲線的插值方法人人在线视频黄色观看，該方法完全通過(guò)幾何量如控制頂點(diǎn)一本导一区av、切線和曲率來(lái)控制三次代數(shù)曲線的形狀av网站在线管看，使得對(duì)三次代數(shù)曲線的編輯與對(duì)三次 B-樣條曲線的編輯一樣靈活方便狼友分享视频。

This algorithm firstly translates arbitrary parameter curves into the piecewise cubic-degree Bezier curves, then using the properties of Bezier curve we can get the tangent vector and the normal vector of every point on the approximation curve, and calculate the approximating offset curve.

此算法先將任意形式的參數(shù)曲線轉(zhuǎn)化成分段三次Bézier曲線，利用Bézier曲線的性質(zhì)容易得到逼近曲線的切向量和法向量国产综合久偷自，從而計(jì)算出其等距逼近曲線。

In this paper,the author obtains some features of Bertrand curves such as that necessary and sufficient conditions for a Bertrand curve is curve,discusses the distance from a point of a Bertrand curve to the corresponding point of the mate of Γ,the angle of the two tangent lines and so on.

討論了Bertrand曲線的特征啊啊啊啊啊啊好爽，得出了諸如曲線是Bertrand曲線的充要條件亚洲精品免费线视频观看视频，Bertrand曲線Γ上的點(diǎn)與其偶線上對(duì)應(yīng)點(diǎn)的距離，以及兩點(diǎn)切線交角等結(jié)論欧美日韩精品一区二区三区。

Consider the circle that is tangent to the curve at and has the same curvature there. Its center will lie on the concave side of the curve. This circle is called the circle of curvature. Its radius is the radius of curvature, and

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First, the paper introduces the moving coordinate system based on the curve tangent vector and the curvature component vectors. Next, the total curvature vector is composed and the osculating plane determined in the moving coordinate system. The curve bending is then calculated and the recursion analysis made on the osculating plane.

鑒于空間曲線上曲率采集面的變化26uuu在线視頻，引入了由曲線切向量和曲率分量決定的運(yùn)動(dòng)坐標(biāo)系，接著在運(yùn)動(dòng)坐標(biāo)系中合成曲率矢量影音先锋av下载，確定密切平面一级特黄AAA免费看直播，然后在密切平面中對(duì)曲線進(jìn)行彎曲計(jì)算和運(yùn)動(dòng)坐標(biāo)系的變換分析，并對(duì)相關(guān)公式進(jìn)行了推導(dǎo)超碰在线91av。

The curvature of a curve; the magnitude of the derivative of its unit tangent vector with respect to distance on the curve:.

曲線的曲率国产亚洲精品麻豆一二三区；為單位切向量對(duì)距離取導(dǎo)數(shù)所得向量的大小

DT/ds| The curvature of a curve; the magnitude of the derivative of its unit tangent vector with respect to distance on the curve:|dT/ds

曲線的曲率；為單位切向量對(duì)距離取導(dǎo)數(shù)所得向量的大小

In specific applications expression : in compressed natural language describes various examples of the basic algorithm, using MATLAB as a programming language, a series of the combined limit, the bonus points will be combined, one graphics area and the length of the horizontal curve equations, and curve tangent process, the rotary body size and shape combined several process issues.

在具體應(yīng)用中的體現(xiàn)：以簡(jiǎn)練的自然語(yǔ)言描述了各實(shí)例的基本算法日韩午夜福利理论片，運(yùn)用MATLAB作為編程語(yǔ)言有色永久无码视频在线观看，實(shí)現(xiàn)了數(shù)列極限的求解、定積分的求解A级手机免费在线视频、平面圖形面積及平面曲線長(zhǎng)度的求解一级A色片、求曲線切線的過(guò)程、旋轉(zhuǎn)體體積的求解及其形成過(guò)程等幾個(gè)問(wèn)題综合性天堂在线。

According to road designing data of mileage,coordinate,azimuth angle of tangent or straight line,curve radius,the length of spiral line from main point of curve or straight line starting point,we can calculate the coordinates of center line points and boundary line point s in any form of road under the same coordinate system.

根據(jù)線路設(shè)計(jì)資料提供的曲線主點(diǎn)里程久久九一、坐標(biāo)、切線方位角日本中文字在线、曲線半徑欧美骚逼、緩和曲線長(zhǎng)度的已知數(shù)據(jù)，計(jì)算出任意線形的中樁99干欧美、邊樁在線路統(tǒng)一坐標(biāo)系中的坐標(biāo)啊好爽用力插视频，利用全站儀極坐標(biāo)放樣程序，以線路附近的控制點(diǎn)或加密點(diǎn)為測(cè)站欧美人乱码伦视频在线，準(zhǔn)確女人一级毛多A片、快速放樣各點(diǎn)。

The trigonometric uniform polynomial curve constructed in this paper has two advantages. One is that the curve can be continuous and the shape can be adjusted with the fixed tangents. The other is that only adding one new knot, the curve can pass through the tangent, which reduces excess points.

利用繪出的三角均勻多項(xiàng)式曲線來(lái)逼近多邊形亚洲性夜色噜噜噜网站可下载，主要有2個(gè)特點(diǎn)：一是曲線能達(dá)到連續(xù)h人成视频在线观看网站入口，并且在切點(diǎn)固定時(shí)曲線的形狀可以進(jìn)行調(diào)整，二是只需增加一個(gè)新節(jié)點(diǎn)就可以通過(guò)切點(diǎn)永久不毛A片在线播放，減少了額外點(diǎn)欧美日韩视频在线观看一二区。