Abstract: The authors mainly discuss the coordinates transformation technique with which the 3D coordinates in the section of a geological prospecting line and the 2D coordinates in the sectional drawing of the line can be converted reciprocally. A mathematical model of the transformation is given and it is validated through the calculation of real examples. Based on the attributes of the sectional drawing, the intersection point between surface trace of the selected prospecting line section and the vertical plane where the prospecting baseline is located is taken as the reference point (B). The line section is then rotated to the horizontal plane upon the horizontal line (L) which crosses the reference point (B). Upon the reference point(B) the prospecting line section in the horizontal plane is rotated till the horizontal line (L) is in eastwest direction. An expression describing the spatial elements prior and after the rotation is established, with which the 3D coordinates can be transformed into the 2D coordinates. The reverse process from 2D to 3D can also be realized when the 2D coordinates of the transformed sectional drawing of geological prospecting line are given.

Key words: the sectional drawing of geological prospecting line, 3D coordinates, 2D coordinates