`%0 Conference Proceedings`

`%4 sid.inpe.br/sibgrapi/2015/08.02.13.19`

`%2 sid.inpe.br/sibgrapi/2015/08.02.13.19.40`

`%T Estimating affine normal vectors in discrete surfaces`

`%D 2015`

`%A Freitas, Nayane Carvalho,`

`%A Morera, Dimas Martínez,`

`%A Silva, Maria de Andrade Costa e,`

`%@affiliation Universidade Federal de Alagoas`

`%@affiliation Universidade Federal de Alagoas`

`%@affiliation Universidade Federal de Alagoas`

`%E Segundo, Maurício Pamplona,`

`%E Faria, Fabio Augusto,`

`%B Conference on Graphics, Patterns and Images, 28 (SIBGRAPI)`

`%C Salvador`

`%8 Aug. 26-29, 2015`

`%I Sociedade Brasileira de Computação`

`%J Porto Alegre`

`%S Proceedings`

`%K Discrete Surface, Triangular Bézier Patch, Affine Normal Vector.`

`%X The invariance of geometric properties is a crucial factor in many areas of Mathematics, particularly in Computer Graphics. The affine geometry has occupied a significant place in this field of application, having an intermediate position between euclidean and projective geometries. The affine geometry is a generalization of the euclidean geometry, but it is simpler than projective geometry, both from the analytical and computational point of view. It can be used to describe many common operations in Computer Graphics. However, we did not find in literature estimators for affine geometric properties in discrete surfaces. The proposal of this work is to search for affine invariants in these surfaces, beginning with an estimate of the affine normal vector. This estimate was obtained from a discrete representation of the surface using as elements pieces of paraboloids instead of planes.`

`%@language en`

`%3 affine.pdf`