A plane surface can be represented by this following equation:
where
is unit normal vector to the plane and
d
is the distance to the origin. For each plane surface we consider a
local frame centered on a point belonging to the plane (in practice this
point is taken as the center of gravity of the measurement points), so
the plane equation can be written as
Let's consider N planes, where the angles between planes' normals are known. The orientation relationship between the different planes are defined by the following constraints:
Each plane normal has also to satisfy the unity constraint
The constraint functions are squared in order to have convex functions. The constraints ( 15 ) and ( 16 ) can be written under a matrix formulation:
where
,
and
are
block matrices defined by:
and
is the
identity matrix.
Naoufel Werghi
