Estimativa do vetor normal afim em superfícies discretas

Abstract

The invariance of geometric properties is an important factor in many areas of Mathematics, particularly in Computer Graphics. Accordingly, the affine geometry has occupied a significant place in this field of application, since it has an intermediate position between euclidean and projective geometries. Affine geometry is a generalization of euclidean, but working with it is simpler than working with projective geometry, both analytically and compucionally, and allows to describe much of the operations used in Computer Graphics. However, we have not found in literature estimators of affine geometrical properties for discrete surfaces. Therefore, the aim of this work is to take the first step in the study of affine invariants in these surfaces, presenting here an estimate of the affine normal vector. This estimate is obtained from a discrete representation of the surface using paraboloids instead of planes.