Geoscience Reference
In-Depth Information
Fig. 7
Healing of the ground
and WallSurface
Another option is to triangulate the polygon and split it into multiple triangular
polygons. There exist usually more than one triangulation possibilities which make
it impossible to decide which one would be the best solution. The third option is a
general adjustment of the whole building with planar polygons as a constraint.
The healing of non-planar surfaces of a building with the first method is
divided in three phases:
Healing of the
GroundSurface
We are identifying the
GroundSurface
as the surface with the smallest z-coordi-
nate and the least deviation with respect to the direction of the normal vector
n
z
of the xy-plane P
xy
. All points belonging to the linear ring of the
GroundSurface
are projected onto a plane parallel to P
xy
and passing through the minimal z-value
of the
LinearRing
. The blue, non-planar polygon is being projected on the green,
planar one (Fig.
7
).
Healing of
WallSurfaces
We assume that each
WallSurface
shares a common edge with the
GroundSurface.
Each Surface of an LoD1 geometry, adjacent to the base surface of the geometry,
is handled accordingly. Let wi
i
be the ith WallSurface, ei
i
the common edge with
the GroundSurface and
n
wi
the normal vector of the least squares plane through
all points of the linear ring of wi. If
<
ε
, with
ε
being a user-
defined tolerance value., then all points of the
LinearRing
are projected onto the
plane spanned by the directional vector of ei
i
and
n
z
. With this approach we omit
walls with a given slope angle (Fig.
7
).
‖
∠(
n
z
,
n
wi
)
−
90°
‖
Healing of
RoofSurfaces
The first approach handles LoD1 roofs and LoD2 flat roofs. The top surface of an
