We present in this paper a new curve and surface implicit model. This
implicit model is based on hyperquadrics and allows a local and global
control of the shape and a wide variety of allowable shapes. We defin
e a hybrid hyperquadric model by introducing implicitly some local pro
perties on a global shape model. The advantage of our model is that it
describes global and local properties through a unique implicit equat
ion, yielding a representation of the shape by means of its parameters
, independently of the chosen numerical resolution. The data fitting i
s obtained through the minimization of energy, modeling the attraction
to data independently of the implicit description of the shape, After
studying the geometry of hyperquadrics and how the shape deforms when
we modify slightly its implicit equation, we are able to define an al
gorithm for automatic refining of the fit by adding an adequate term t
o the implicit representation, This geometric approach malt:es possibl
e an efficient description of the data points and an automatic tuning
of the fit according to the desired accuracy. (C) 1996 Academic Press,
Inc.