The algorithm of three dimensional stratum (3D stratum) incision is the essential basis of the visualization of 3D-stratum and the calculation of excavated earth volume. For the moment

there is short of practical arithmetic in the cutting of stratum. Firstly

the 3D stratum is constructed by the method of modeling of triangular prisms

and then

by discussing all the cases of incised triangular prisms with an oblique plane

the incision algorithm for the stratum

which is composed by triangular prisms

are obtained. Thus

by taking the incision plane as an interface

a useful way to divide one triangle prism into several smaller ones is brought forward. The main principle is that

divide the top surface

bottom surface and the intersection of a triangle prism into several triangles according to a certain rule; and make the projections of these triangles in the horizontal plane coincided with each other; Constitute the three layered triangles into two layered small triangular prisms

which take the incision plane as an interface; thereby

the incision is finished. Further more

the calculation method of excavated earth volume is put forward too; i.e.

given the boundary controlled equation for the excavated body; according to the inside boundary (which is limited by the equation)

the excavated area can be easily obtained. By combining the excavated equation with the incision algorithm

incising triangular prisms with the planes that contain the excavated surfaces

aggregating all the triangle prisms that locate in the excavated volume

thus

the total volume of these triangular prisms will be equal to the excavated earth volume. Finally

by applying these two methods about triangular prism division and earth volume calculation to a certain major water supply project in Guangdong area

South China

the simulation of excavation for a foundation pit and its volume estimation is successfully realized.