The theory of polar forms can be applied on parametric continuity of surfaces. Therefore, if we want to find out a vallue of a derivative of a polynomial we don't need to derive but it is enough to look at a certain value of its blossom. From the previous theorem we get conditions for parametric continuity of two patches. Let's investigate a continuity of these two patches along the common edge t 1 t 2 . So that it is enough to find only one more direction which is lineary independent with e 1 with respect to which the maps F,G poses the same derivative.
E d are maps.
But F has to be derivated as a compound function. Similary let F ' is the matrix of first derrivatives of F , F '' is the matrix of its second derivatives and so on. We observe that the relations for the geometric continuity of surfaces are very similar to the ones for the geometric continuity of curves. But as a shape parameters there are matrixes W ij instead of real numbers. In the beginning we require geometric continuity of the first order of the patches F and G along the common boundary t 1 t 2 .