Projective Reparameterization of Rational B Ezier Simplices
نویسنده
چکیده
A group-theoretic analysis is applied to nd the transformation of the homogeneous control points of k-dimensional B ezier simplices (such as two dimensional triangles and three dimensional tetrahedra) under a k-dimensional projective reparameterization. This transformation has applications in the perspective projection of textures represented as triangular spline intensity surfaces , in arbitrary B ezier simplicial subdivision, and in weight normalization. The theoretical results contained in this exposition are generalizations of similar results for 1-dimensional B ezier curves, reported by Richard R. Patterson in 1985. R ESUM E Une analyse en th eorie des groupes est faite pour trou-ver la transformation des points de contr^ ole homog enes pour un simplexe B ezier de dimension k, en faisant une r eparam eterisation projectif de dimension k. On peut utiliser cette transformation pour la projection en perspective des textures faites avec les surfaces splines d'intensit e, pour la sous-division des simplexes B eziers, et pour r egulariser les poids pour la normalisation. Les r esultats th eoretiques qu'on pr esente dans cet ex-pos e sont des g en eralisations des r esultats que Richard R. Patterson a pr esent e en 1985 pour des courbes B eziers ayant une seule dimension.
منابع مشابه
Rational Bezier Simplices
A gr'oup-theor'etic analysis is applied to find th e transf01'11wtion of the homogeneous control points of kdim ensional B ezier simplices {such as two dim ensional triangles and three dim ensional tetrah edra} under' a kdim ensional projec tive reparam eterization, This transf ormation has applications in the perspec tive projec ti on of textur'es represented as triangular spline intensity sur...
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