سوال ۲۹ کنکور ارشد علوم کامپیوتر ۱۳۹۹

Read the following passage and answer the question.

PASSAGE 3:

In our study of geometric modeling, we will make extensive use of several important mathematical techniques. The most important are linear algebra, vectors, matrix methods, determinants, set theory, polynomial interpolation, and numerical approximation. Let us briefly review some of these.

Vectors offer a distinct advantage over classic analytic geometry by minimizing our dependence on a specific coordinate system. In addition, vectors carry inherent geometric meaning, such as length and direction. Vector operations allow us to readily determine perpendicularity or parallelism.

Next we turn to matrix methods. The array of numbers that makes up a matrix can represent simply an orderly way of storing numbers or perhaps a set of polynomial equation coefficients. Another use of a matrix is as an operator. Here, the matrix performs a geometric transformation on a set of points by operating on the position vectors that define these points. This interpretation of a matrix as a geometric operator is the foundation of most geometric-modeling computations.

Now let us look at polynomial interpolation. A great deal of practical numerical analysis depends on techniques called numerical interpolation. Here, we discover the powerful but simple theorem that a straight line can be defined by, and passed through, two points, a conic curve through three points, and so on. We use polynomials for interpolation, because they can be evaluated, differentiated, and integrated easily and in a finite number of steps by using just the basic arithmetic operations of addition, subtraction, and multiplication.

Question: Piecewise interpolating polynomials are used to -----------.