Based on the experience obtained in recent construction,a new method is proposed to measure the central coordinate by combining the non-prism total station with the mathematical theory of three-point-determining-one-circle,which is simple and practical.

The barycentric coordinates of the plane view projection of a coal face are solved with a formula of geometric gravity centre.

At first the original data points are resampled using barycentric coordinates,followed by fitting the resampled data points.

From some identities and the embedding inequality in the triangle,by using the substitution of the barycentric coordinates and method of completing the square,a ratio type inequality involving the distances from an arbitrary point to three vertexes and sides of the triangle is proved,some new results are obtained.

Then applying barycentric coordinate equation on the gotten GBD points,the mapping results were calculated.

During the point location, the barycentric coordinates are used to extract local heuristic information about the location of p so as.

By means of analyzing all directional derivatives of barycentric coordinate form of Be zier curves,an efficient evaluation method for this form has been furnished,and all the storage quantity and multiplication number are equivalent to that of de Castelisu algorithm.

A simple calculation expression of the shearing flow and the coordinates of bending center is introduced for the thin-walled beam with open section.