Gross - 5 
In order to accomplish an estimation of the 3D shape of the beam, rotational symmetry 
was assumed and after extracting one edge and describing it with an interpolating cubic 
B-spline curve b(t) of type 
N 
b(t) = b](t) (1) 
/ = 0 
b?(t) ¡cubic B-spline basis. 
d[. control vertex. 
N: number of knots. 
Once b(t) is given, it is easy to define a NURB-surface of revolution along the z-t axis 
as: 
X&t) = 
x(s, t)' 
y(s, t ) 
'lit) COS0)' 
r{t) sin(s) 
z(s, t ) 
< J 
t 
s,t : parameters 
r(t): radius function derived from b(t). 
( 2 ) 
Equation 2 provides the estimated beam surface and interpolates the detected edges. All 
required postprocessing computations, such as volume and linearity, can be figured out 
from this model. Finally, photorealistic rendering of the 3D beam can be achieved using 
advanced ray-tracers. Figure 3 shows some 3D reconstructions of the copper beam with 
materials and lights adjusted correspondingly. 
Fig. 3 3D photorealistic images rendered using a ray-tracer for NURBS: 
a) Material properties set to copper and incorporation of bumpiness onto the surface. 
b) Different settings, (from [9])