[A path to spatial irradiation planning. I. The problem of dose homogeneity within the area of crossing ray beams with different planes of incidence; basic examinations leading to an optimization procedure].

Under certain circumstances, foci within distinct regions of the body are optimally included by irradiation from different directions of the space. In practice, such plannings mostly fail from the difficulty to produce a sufficiently homogenous dose distribution within the target volume. The present considerations disclose the possibility to determine certain parameters or irradiation in an explicit form, based on a vectorial view of the dose distribution, thus obtaining homogeneity of the radiation dose. Part I of this paper is presenting the foundations of a procedure which aims at dose homogeneity in cross-fire techniques with different planes of incidence, utilizing simple mathematical correlations among the vectorial dose quantities.