| Given a parametric rational curve or surface, the procedure of finding its implicit equation is called implicitization of the rational curve or surface. The problem of implicitizing rational curves and surfaces has much important theoretic meanings in Computer Aided Geometric Design and Computer Graphics, and much work has been done in this area. But the practical usefulness of implicitization is hampered by the complex representation of the implicit equations of high degree rational curves and surfaces. The work done by this paper is to apply traditional method according to three times Bezier curve discussion mainly with Wu method come to realize parameter equation implicitization of the rational curves, discuss mainly Wu method in parameter equation implicitization of the rational in the realization of application and related program. Wu method[9]:Judge with the method of Wu a sets question, to divide three proceedings. The square one is to orders a public zero for to setting question changing into algebra form, and judging a polynomial gather whether is included to order the problem that gather in another the zero of the polynomial. The second step is whole preface , setting question to depict namely the conditional polynomial a HS was changed into by whole preface to rise the row AS. The third step is a polynomial to remaining, will soon depict to set question the conclusion g to rise the row AS invite to turn to beg to take the remaining type R. If R equal 0, can immediately break to settle to set question at deteriorate the term notI1I2 … Ik ≠0Under establish, or say that set question to establish generally. Among them I1, I2, … Ik is an early type to rise row AS each polynomial of inside. If R is not equal 0, then being AS as can't invite to rise the row, can break to settle to set question not really.Remaining type formula (pseudodivision) [9]: establish on rising the row A: A1, A2, … , At with a polynomial g, invite to turn to the A the g, do the division one by one in order namely:Istg=QA+Rt-1, Ist-1Rt-1=Qt-1At-1+Rt-2,…………Is2R2=Q2A2+R1, Is1R1=Q1A1+R0, The among them every division all sees each polynomial with the Ai lord main unitary is unitary polynomial to changes the unitary. The R0 of getting is certain with the unique from the g, combining to call R0 as the g to the remaining type that rise the row A. But the Ij is an Aj early type, the sj is some not negative integrals. Then enough type formula: Is1Is2 … Istg= P1A1+ P2A2+ … + PtAt+ Ro among them R1, … , Rt is some polynomials. From remaining type formula therefore, be the Ro ≡ 0, the A any zero orders if is not zero that I1 I2 … It of the zero orders, then ordering for the g necessarily. The method of Wu is in three times Bezier curve conversion between parametric and implicit process of basic thought is: See the square distance in curvilinear parameter to make square distance in polynomial set, among them the changing of square distance in the type of implicit inside deal sees to make the constant handles, making use of the false division to toss about to the square distance in polynomial an usage mutually division, lower every proceed the rank of the square distance in parameter in once false division number, end expurgation parameter, the square distance in type in remaining in income turns to mean the form for the type of implicit of the square distance in parameter namely. Realizes in a specific way process is as follows:Square one: Be inputted by keyboard four controls top;The second step: Compute three Times Square distance in curvilinear parameter in Bezier;The third step: See the square distance in curvilinear parameter in Bezier polynomial, make use of the high a polynomial the pseudodivision by the low a polynomial according to the method of Wu, square distance in parameter in expunction a tallest a parameter for, making remaining type 1 smaller divisor in number of times in tallest a parameter number of times;The fourth step: Making use of the third step falls into trap to cal...
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