The paper applies algebraic geometry , computational geometry , approximation theory to study the following problems : the nother type theory and the riemann - roch type theory of the piecewise algebraic curve ; the number of real intersection points of piecewise algebraic curves ; the real piecewise algebraic variety and the b - net resultant of polynomials 本文应用代数几何,计算几何,函数逼近论等学科的基本理论,分别就分片代数曲线的n ( ? ) ther型与riemann - roch型定理;分片代数曲线的实交点数;实分片代数簇以及多项式的b -网结式进行研究。
The problem is researched and the algorithm which calculates the intersection points of two graphs created by the same coefficient of the ifs is proposed . the curve described changing of the intersection points number is drawn . the conc lusion is that the curve fluctuates in the tiny range and is smooth when it is seen as a whole 其次,针对同一ifs迭代码两次迭代绘制得到的分形图并非完全相同这一问题展开研究,提出了ifs分形覆盖相交交点变化曲线的概念,给出了覆盖相交交点变化曲线的绘制算法,在此基础上进一步研究了分形覆盖相交交点变化曲线的变化率情况,得到了分形覆盖相交交点变化曲线宏观上比较光滑,但实际上小范围内异常波动的实验结果。
A variable is sampled in a certain increment , and introduced into the equations . there are two sets of any two equations to be solved . the real solutions of the two sets are protracted in spatial coordinate system to obtain two curves , so that the intersection points of the two curves can be found as the solution of the original equations 针对所得三元高次多项式方程组,采用数学分析软件mathematica编制程序,以一定的步长增量,在一定范围内取一个变量的值,并将其代入方程组中,求解其中一个方程分别与另外两个方程联立的方程组的解,将得到的实数解绘制成两条空间曲线,其交点即为原三元方程组的解。
Moreover , based on in - depth research of " the existing scan - line polygon fill algorithm , the author has introduced a new fast method for clipping arbitrary boundary areas algorithm which uses the edge consistency and the scan - line consistency and adopts sorted chain table , i t can reduce the quantity of calculating intersection points and improve the efficiency of algorithm 另外,作者在对已有的扫描线填充算法深入研究的基础上,介绍一种利用裁剪区域的边的连贯性和扫描线的连贯性,从而减少求交计算量、提高算法效率的有序链表的快速裁剪算法。
3 . by using the techniques of an explicit criterion to determine the number of real roots of a univariate polynomial in ( [ 13 ] , [ 73 ] ) ; b - net form of bivariate splines function ; discriminant sequence of polynomial ( cf . [ 13 ] , [ 73 ] ) and the number of sign changes in the sequence of coefficients of the highest degree terms of sturm sequence , this paper determines the number of real intersection points two piecewise algebraic curves whose common points are finite . a lower bound of the number of real intersection points is obtained in terms of method of rotation degree of vector field 大连理工大学博士论义:分片代数价线i片代数簇的若十m穴3 :利用杨路,张景中,侯晓荣在文献v13 , 73 )中关于一元多项式实根的显式判准,以及二元样条函数的b网形式,多项式的判别序列和sturm序列的最高次数项系数序列的变号数,本文给出了两个分片代数曲线的丈交点数(假设公共点是有限的)的计算公式。