1. The barycentric coordinate of the triangle we hit.

2. Based on homogeneous barycentric coordinates, a new geometric variable, sharpness factor, is defined for measuring sharpness of independent vertexes.

3. The advantages of barycentric interpolation formulations in computation are small number of floating point operations(flops) and good numerical stability.

4. The real numbers are called the barycentric coordinates of x.

5. The well arrangement of barycentric position method is a suitable pattern adjustment method in the later period of the development in low permeable oil fields.

6. Chapter 4 uses barycentric subdivision method on arbitrary discrete parametric curves net.

7. With the technique of homogeneous barycentric coordinates and sharpness factor,( ) a new filtering algorithm is developed.

8. The weights respectively equal the ratios of barycentric coordinates elements of the corresponding points of the curves in the four control vertex base before transformation and after.

9. Finally, the pixels of the recovered texture were obtained as a barycentric combination of the colors of the near four pixels.

10. After we put the last step of free-from deformation (which is interpolation of barycentric coordinates) into GPU, we finished a real-time free-form deformation frame work with tetrahedral subdivision.

11. The relativistic geometric time delay of VLBI is derived in the Barycentric Reference System (BRS).

12. The differentiation matrices of unknown function are constructed by using barycentric rational interpolation.

13. It can avoid the oscillation of Lagrange interpolation by using barycentric interpolation formulations and second kind of Chebyshev points as interpolating points.