298 COMPUTER AIDED ENGINEERING DESIGN
generation of a set of locally planar surfaces (having tangent plane discontinuity at the boundaries).
The result would be a meshed or faceted surface (e.g., Figure 10.2b) with local sub-regions being
triangular or quadrilateral, primarily former that can be constructed by combining any three neighboring
points in the cloud. In case the point cloud results in sets of two-dimensional slices from MRI or CT
scans, the object boundary at each plane can be modeled as a closed contour (Figure 10.2c). Lofting
or skinning may then be performed using the contours to model the enclosing surface. In a more
general case, we may need to determine connected higher order surface patches (Figure 10.2d) with
or without enforcing smooth continuity. Following sections discuss the aforementioned three modeling
techniques to obtain the bounding surface patches and thus the solid model from the acquired point
cloud data.
Figure 10.2 Geometrical models from point cloud data of a mechanical component: (a) point cloud
acquired, (b) triangulated model, (c) contour model and (d) surface model
10.4 Meshed or Faceted Models
Mesh/faceted models, for example in Figure 10.2 (b), are simpler to construct yielding local planar
facets with barely any intervention of the user. After having obtained a point cloud from any digitizer
(contact or noncontact type), mesh models are generated with faces primarily of triangular topology
though other polygonal faces are also possible. Triangular faceted models are used in graphics,
animation, CAD, CAM as well as prototyping to name a few. A triangular facet data model in STL
format is extensively used in CAD data transfer for downstream applications like tooling for
manufacturing and rapid prototyping. Delaunay triangulation (Appendix 1) is a predominant method
for generating triangular mesh models from point cloud.
A rectangular faceted model is used in Geographical Information System (GIS). Images of
geographical terrains are processed using photographs taken from aircrafts or satellites. A series of
digitized photographs of a region taken from several angles and at different times of the day are
combined and processed to form a digital elevation model (DEM format). This model gives the
terrain surface as a mesh of rectangular grids with each grid point associated with the latitude,
longitude and altitude information.
(a) (b)(c)
(d)