2006 | OriginalPaper | Buchkapitel
Computation of Normals for Stationary Subdivision Surfaces
verfasst von : Hiroshi Kawaharada, Kokichi Sugihara
Erschienen in: Geometric Modeling and Processing - GMP 2006
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
This paper proposes a method for computing of normals for stationary subdivision surfaces.
In [1, 2], we derived a new necessary and sufficient condition for
C
k
-continuity of stationary subdivision schemes. First, we showed that tangent plane continuity is equivalent to the convergence of difference vectors. Thus, using “normal subdivision matrix” [3], we derived a necessary and sufficient condition of tangent plane continuity for stationary subdivision at extraordinary points (including degree 6). Moreover, we derived a necessary and sufficient condition for
C
1
-continuity.
Using the analysis, we show that at general points on stationary subdivision surfaces, the computation of the exact normal is an infinite sum of linear combinations of cross products of difference vectors even if the surfaces are
C
1
-continuous. So, it is not computable. However, we can compute the exact normal of subdivision surfaces at the limit position of a vertex of original mesh or of
j
-th subdivided mesh for any finite
j
even if the surfaces are not regular.