Computer Aided Engineering Design

302 COMPUTER AIDED ENGINEERING DESIGN

Figure 10.8 (a) A bad linear parameter correspondence leading to twisting and (b) parameter correspondence
determined by angular spacing (viewing into the z direction)

(a)

y

x

ui = ui+1 = 0.0

ui= 0.9

ui+1 = 0.83

ui= 0.8

ui+1 = 0.78 ui= 0.7

ui+1 = 0.72

ui= 0.6

ui+1 = 0.67

ui= 0.5

ui+1 = 0.6

ui= 0.4

ui+1 = 0.52

ui= 0.3

ui+1 = 0.41

ui= 0.2

ui+1 = 0.3

ui= 0.1

ui+1 = 0.18

patches and the continuity across boundaries vary depending on the nature of the object and hence its
point cloud. Point cloud of prismatic objects can generally be modeled using quadric surfaces, e.g.,
planes with C^0 (position) continuity, or in some cases conics with C^1 (slope) continuity. When
designing the exterior of automobiles, household appliances, cellular phones and aerospace components,
free form patches (e.g., Bézier or B-spline) are usually employed to enhance the design features and
functionality.
A broad classification of bounding surface types used is presented in Figure 10.9. Hierarchy of
patches (planes, quadrics, sweep surfaces, B-splines) that are in the order of geometric complexity
has to be defined at this stage, which a user can recognize and specify to the computer to determine
the final model. Free form surface reconstruction from point cloud requires to perform the following:

• Segmentation: To divide the original point cloud into subsets of points, one for each natural^1
  surface, so that each subset contains just those points sampled from a particular natural surface.


• Classification: To determine the type of surface each subset of points may belong to.


• Fitting: To find the surface of the chosen type, as the best fit through the points in a given subset.

(^1) A surface patch (planar, cylindrical, conical and spherical) that can be easily identified by a user by inspection.
Bounding surfaces
Primary geometry Secondary geometry
Simple surfaces Regular swept surfaces General free form surfaces Vertex blends
Edge blends
Planes
Natural quadrics
Tori
Translational sweeps
Rotational sweeps
Rectangular boundary
Irregular boundary
Figure 10.9 Broad classification of bounding surfaces
Note that the segmentation and classification of the point cloud above are not sequential but parallel.