\r\nconstructions and manufacturing of curve, surface and solid

\r\nmodeling. Their algorithms are critically important not only in

\r\nthe automobile, ship and aircraft manufacturing business, but are

\r\nalso absolutely necessary in a wide variety of modern applications,

\r\ne.g., robotics, optimization, computer vision, data analytics and

\r\nvisualization. The calculation and display of geometric objects

\r\ncan be accomplished by these six techniques: Polynomial basis,

\r\nRecursive, Iterative, Coefficient matrix, Polar form approach and

\r\nPyramidal algorithms. In this research, the coefficient matrix (simply

\r\ncalled monomial form approach) will be used to model polynomial

\r\nrectangular patches, i.e., Said-Ball, Wang-Ball, DP, Dejdumrong and

\r\nNB1 surfaces. Some examples of the monomial forms for these

\r\nsurface modeling are illustrated in many aspects, e.g., construction,

\r\nderivatives, model transformation, degree elevation and degress

\r\nreduction.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 152, 2019"}