Affine projections

AFFINE PROJECTIONS (EN: affine projections, affine transformation, affine geometry; DE: affine PrAffine projectionsojektionen; FR: projections d'affinage; ES: afinidad geometrica; RU: аффинные проекции) is the three-dimensional image of the object, which has been obtained by the method of the parallel projection of the plane with the figure, which is depicted on this plane, onto another plane, which is positioned under the certain angle. The straight line of intersection of the planes is named the related axis.

Affine projections have the following properties: two related to each other straight lines intersect in the point, which is lying on the related axis; the straight lines of the object plane, which are parallel to this axis, are represented on the image plane without distortion; the ratio of the distances of any pair of the related points from the related axis for the given conditions of projection is the constant value (the factor of conversion). In practice, the most convenient are the rectangular affine projections, when the direction of the projection is at the right angles with the plane of the projection and with the related axis .

They use the affine projections for the compilation of the special plans of the mining works, and for the depiction of the geological structures, if the source data are represented by the horizon-wise geological survey plans (Figure). They perform the construction of the depictions within the affine projections with the analytical, graphic-analytical, and mechanical (by the affinographs) methods.