2,935 research outputs found
A de Casteljau Algorithm for Bernstein type Polynomials based on (p; q)-integers
In this paper, a de Casteljau algorithm to compute (p; q)-Bernstein Bezier curves based on (p; q)- integers are introduced. The nature of degree elevation and degree reduction for (p; q)-Bezier Bernstein functions are studied. The new curves have some properties similar to q-Bezier curves. Moreover, we construct the corresponding tensor product surfaces over the rectangular domain (u; v) in [0; 1] x [0; 1] depending on four parameters. De Casteljau algorithm and degree evaluation properties of the surfaces for these generalization over the rectangular domain are investigated. Furthermore, some fundamental properties for (p; q)-Bernstein Bezier curves are discussed.We get q-Bezier curves and surfaces for (u; v) in [0; 1] x [0; 1] when we set the parameter p1 = p2 = 1: In comparison to q-Bezier curves based on q-Bernstein polynomials, this generalization gives us more flexibility in controlling the shapes of curves
Solution of systems of disjoint Fredholm-Volterra integro-differential equations using Bezier control points
Systems of disjoint Fredholm-Volterra integro-differential equations and the Bezier curves control-point-based algorithm are considered. Systems of two, three and four Fredholm-Volterra integro-differential equations are solved using a developed algorithm. The convergence analysis for the Bezier curves method proves that it is convergent. The examples considered agree with the convergence analysis. The method is more accurate and effective when compared to other existing methods
Query processing of geometric objects with free form boundarie sin spatial databases
The increasing demand for the use of database systems as an integrating
factor in CAD/CAM applications has necessitated the development of database
systems with appropriate modelling and retrieval capabilities. One essential
problem is the treatment of geometric data which has led to the development of
spatial databases. Unfortunately, most proposals only deal with simple geometric
objects like multidimensional points and rectangles. On the other hand, there has
been a rapid development in the field of representing geometric objects with free
form curves or surfaces, initiated by engineering applications such as mechanical
engineering, aviation or astronautics. Therefore, we propose a concept for the realization
of spatial retrieval operations on geometric objects with free form
boundaries, such as B-spline or Bezier curves, which can easily be integrated in
a database management system. The key concept is the encapsulation of geometric
operations in a so-called query processor. First, this enables the definition of
an interface allowing the integration into the data model and the definition of the
query language of a database system for complex objects. Second, the approach
allows the use of an arbitrary representation of the geometric objects. After a
short description of the query processor, we propose some representations for free
form objects determined by B-spline or Bezier curves. The goal of efficient query
processing in a database environment is achieved using a combination of decomposition
techniques and spatial access methods. Finally, we present some experimental
results indicating that the performance of decomposition techniques is
clearly superior to traditional query processing strategies for geometric objects
with free form boundaries
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