On The Some Special Biquadratic Bezier Surfaces in E^3

In this study, biquadratic Bezier surfaces were investigated. These surfaces have a very important place in the scientific world. The importance of biquadratic Bézier surfaces lies in their ability to provide a smooth, flexible, and computationally efficient method for modeling surfaces. They fill the gap between simpler bilinear surfaces and more complex bicubic surfaces, offering a great solution in areas where both simplicity and precision are needed. While not as commonly used in high-end 3D modeling as their higher-order counterparts, they remain a useful tool for surface design, particularly when the trade-off between quality and computational efficiency is critical. In this study, firstly the matrix representations of biquadratic Bezier surfaces are given. Then, it is stated how to find the control points of some special surface types given as biquadratic Bezier surfaces, and the control points of parabolic cylinder, elliptic paraboloid and hyperbolic paraboloid surfaces are calculated.