This paper presents various triangle tessellation algorithms of NURBS surfaces. The surfaces required for understanding algorithms are precisely defined – the Bézier, B-spline and NURBS surface. It is explained that NURBS surface tessellation algorithms require the NURBS surface to be displayed using Bézier surfaces. The terms uniform, adaptive and fully adaptive tessellation are explained, as well as the corresponding tessellation accuracy tests. Furthermore, OpenGL, the graphical applications programming interface is presented. The graphical tessellation structure in OpenGL is explained, and special emphasis is placed on the phases responsible for tessellation. The level of tessellation is defined, and the difference between inner and outer tessellation is explained. The paper also demonstrates how the level of tessellation affects the tessellation of an individual triangle. Finally, the implementation of a solution which uses a special form of the Bézier surface – the Bézier triangle is described. The algorithm steps are described, and the results for three objects are provided. Images of the object before and after the tessellation are provided, with various tessellation levels. The higher tessellation levels yield better results.