Studying on azimuthal projection

Azimuthal projection is a kind of projection technology with long history, and has been widely used in map-making of uranium geological exploration and reserves calculation. In recent years, new demands are needed urgently on mathematics fundament of geological map with the application of global positioning system (GPS) in uranium geological exploration. Based on perspective azimuthal projection, a synoptical formula has been set forth in this report by using concluding methods. Applying this formula, almost all problems of present azimuthal projections could be covered and this formula may be applied to get arbitrary kind azimuthal projection as well. Moreover, it is more important that the formula is a very convenient tool for calculating various azimuthal projections and for coordinates converting between different kind azimuthal projections. Meanwhile, having studied characters of gnomonic projection it has been gotten that any great circle of spherical surface will be projected into straight line in gnomonic projection. Cofocal hyperbola of spherical surface will also be projected into cofocal hyperbola in gnomonic projection. The cofocal ellipse and hyperbola of spherical surface will also be projected into the cofocal ellipse and hyperbola in gnomonic projection. Therefore, the geometrical problems of calculating great circle, ellipse and hyperbola of spherical surface could be come down to calculate straight line, ellipse and hyperbola of plane accordingly, which makes actual application be more simplification. (authors)