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利用拼接的圓漸開線實現對平面上的數據點及其切向的插值.用英語怎么說？

利用拼接的圓漸開線實現對平面上的數據點及其切向的插值.

Aspline curve is presented which interpolates given points and tangent directions with piecewise involute of circle.

curve

n. 弧線，曲線，曲線狀物，彎曲物，[棒]曲線板；vt. 使彎曲，使成曲線，使成弧形；vi. 彎曲，彎成曲線，彎成弧形，沿曲線行進；adj. 彎曲的，曲線形的；

例句
...the curve of his lips.
他嘴唇的曲線

is

vt.& vi. 是（be的三單形式；n. 存在；

例句
Bollinger 'RD' is a rare, highly prized wine.
博林格RD香檳是一種名貴的備受推崇的葡萄酒。

presented

vt.& vi. （動詞present的過去式及過去分詞形式），表示"展示，展現，出示"；v. 舉向( present的過去式和過去分詞 )，面向，舉槍瞄準，（分娩時嬰兒）露出；

例句
...the gifts presented to them in appreciation of their work.
為感謝他們所做的工作而贈與他們的禮物

which

pron. 哪一個，哪一些，哪個，那，指前面提到的事物；adj. 哪一個，哪一些；

例句
...the latest date at which a foetus can be aborted.
能夠打胎的最遲日期

interpolates

v. 插入，插（話）( interpolate的第三人稱單數 )，篡改；

例句
Aspline curve is presented which interpolates given points and tangent directions with piecewise involute of circle.
利用拼接的圓漸開線實現對平面上的數據點及其切向的插值.

given

adj. 指定的，確定的，假設的，假定的，有…傾向的，贈送的；prep. （表示原因）考慮到，（表示假設）倘若，假定；n. 假設；v. 給予，贈送( give的過去分詞)；

例句
Outsiders who wed islanders are given only three years' right of abode at first.
島外的人和島民結婚之初只能獲得三年的居住權。

points

n. <英>（鐵道的）道岔，轉轍器，點( point的名詞復數 )，要點，特點，重點；

例句
Aberdeen are nine points adrift of Rangers at the top of the Scottish League.
在蘇格蘭足球聯賽中，亞伯丁隊比排在首位的流浪者隊落后9分。

and

conj. 和，與，而且，于是，然后，因此；

例句
I spend a lot on expensive jewelry and clothing...
我花很多錢購買昂貴的首飾和衣服。

tangent

例句
Construct an animation showing the tangent sweeping out the interior of astroid.
建構一動態繪圖:展示星狀線的切線所有掃掠過的內部軌跡.

directions

n. direction的復數形式，方面( direction的名詞復數 )，方向，指南，（電影導演的）指點；

例句
I should know by now not to throw away the directions until we've finished cooking...
現在我知道了不該在飯沒做完之前就扔掉烹飪說明。

with

prep. 和，跟，隨著，關于，和…一致；

例句
A waiter entered with a tray...
侍者端著托盤進來了。

involute

adj. 紛亂的，復雜的；n. 漸開線；vi. 恢復原狀，消失；

例句
The surface obtained when every point on the edge generates an involute is called helicoid.
表面獲得了在邊緣的每點什么時候引起一斷開線叫斷開線螺旋面.

of

prep. 關于，屬于…的，由…制成；aux. 助動詞 [非標準用語、方言] =have [主用于虛擬語氣]；

例句
He did have a real knowledge of the country...
他對該國的確知之甚多。

circle

n. 圓，圓狀物，一圈，圈子；vt. 圈出，包圍，繞…運轉；vi. 環繞，盤旋；

例句
I have a large circle of friends and acquaintances engaged in photography.
我在攝影界交游甚廣。

...the spiralling vortex airflow that slows the plane.
使飛機減速的螺旋形氣流渦旋

You just go on ahead. I'll come by later...
你只管先往前走。我隨后就來。

He who spares his rod hates his son, But he who loves him chastens him early.
24不忍用杖打兒子的,是恨惡他;疼愛兒子的, 趁早管教.

For further information, please contact 414 3925, extension 2253.
詳情請致電414 3925,轉分機2253。

He sat there while I made the case for his dismissal...
他坐在那兒，聽我陳述解雇他的理由。

Baroness Thatcher's claims seem credible to many.
撒切爾女男爵的主張在很多人看來是可信的。

Nothing to be got without pains but poverty.
一份耕耘，一份收獲。

This decree obliges unions to delay strikes.
該法令迫使工會推遲罷工。

The right to demand payment from the endorser of a commercial paper when the first party liable fails to pay.
追索權當有支付義務的第一方不能支付時，可以向商業票據的背書人要求支付的權力。

The forward left the club to join Blackburn Rovers in 1994.
這位前鋒1994年加入了布萊克本.

Police said they suspected that Sobhraj had accomplices who are drug smugglers.
警方說他們懷疑索布拉還有一些走私毒品的同伙.

The relations of friendly cooperation between our two countries are developing satisfactorily.
我們兩國的友好合作關系正在令人滿意地發展著.

Objective To observe the effect of Luvos on blood picture and organ histomorphology in rats.
目的觀察樂福至長期用藥后對大鼠血象及重要器官組織形態學的影響.

Her favourite saying was: 'There are a lot of people far worse off than me.'
她最喜歡的諺語是：“比上不足，比下有余。”

...a frilled shirt and floppy cravat.
帶褶邊的襯衣和耷拉的領結

an overcrowded room
過度擁擠的房間

The club is under investigation by the fraud squad.
反詐騙調查組正在對該俱樂部進行調查。

It must be terribly frustrating to lobby and get absolutely nowhere.
游說未取得一點結果，一定讓人非常沮喪。