RESTORATION OF GRASSMAN GEOMETRICAL BASE OF α~3 CURVES WHEN A SET OF POINTS IS GIVEN AS DATA

摘要

Reconstruction of Grassman geometrical Basis when 8 points of α~3, in certain particular position, are given, is presented and discussed here. It means that there is some freedom in choosing the elements of the Basis. When the restored geometrical Basis is got out of the given 8 points, the ninth point is definite, obtained by performing linear construction on it. All the reconstruction steps are described in details. Some cases of reconstruction of different Bases that produce the same curve are also shown. A proof for existence of additional invariant points, of the α~3 curves, when some elements of the Basis are changed is presented. There are several particular cases for which the change in the order of the appearance of the data points does not affect the resulting curve in spite of getting different Bases.