Abstract: Geometric modeling plays an important role in the
constructions and manufacturing of curve, surface and solid
modeling. Their algorithms are critically important not only in
the automobile, ship and aircraft manufacturing business, but are
also absolutely necessary in a wide variety of modern applications,
e.g., robotics, optimization, computer vision, data analytics and
visualization. The calculation and display of geometric objects
can be accomplished by these six techniques: Polynomial basis,
Recursive, Iterative, Coefficient matrix, Polar form approach and
Pyramidal algorithms. In this research, the coefficient matrix (simply
called monomial form approach) will be used to model polynomial
rectangular patches, i.e., Said-Ball, Wang-Ball, DP, Dejdumrong and
NB1 surfaces. Some examples of the monomial forms for these
surface modeling are illustrated in many aspects, e.g., construction,
derivatives, model transformation, degree elevation and degress
reduction.