Ermes, Pierre 
  
2 CONSTRAINTS IN THE CONSTRUCTION AND RECONSTRUCTION OF INDUSTRIAL 
INSTALLATIONS 
Geometric constraints in CAD applications have been subject to extensive research. Bouma et al. (2000) sees two basic 
strategies for constraint solving methods; instance solvers and generic solvers. Instance solvers use the explicit values of 
the parameters and constraints while generic solvers determine whether constraint configurations can be satisfied, 
independent of the values of the parameters. In their turn, instance solvers can be subdivided into analytical approaches 
and numerical approaches. An analytical instance solver formulates the constraints as a system of algebraic equations 
and uses general symbolic computations to find the solution(s). A numerical instance solver uses an iterative technique 
to compute a solution of the system of algebraic equations. 
The use of geometric constraints in geodetic and photogrammetric applications is well known (Mikhail 1976). 
Constraints that are included in an iterative least-squares adjustment fall into the class of numerical instance solvers. 
Constraints in a least-squares adjustment can be implemented as either hard constraints or soft constraints. A hard 
constraint maintains a geometric relation *at all costs" while the residual of a soft constraint, in combination with a 
weight, is minimized in the least-squares adjustment. 
The main difference between constraints in CAD applications and constraints in photogrammetric applications comes 
from the difference in use of the two types of applications; CAD is used in the construction phase of an object while 
photogrammetry is applicable to the reconstruction of an object. In the design phase, product features need to fulfill 
certain requirements e.g. to be parallel or perpendicular or to have a specific value, whereas during reconstruction the 
measured dimensions might show a slight difference from the intended values. To allow small imperfections in the 
constraint specification we choose to use soft constraints in our mathematical model (also known as the unified 
approach). 
3 OVERVIEW OF PIPER 
A model-oriented photogrammetric system (Piper) has been developed which allows the interactive measurement of 
CSG models in images. CSG models are constructed from one or more primitive shapes (such as a cylinder, a box, a 
sphere, etc.) that are combined using the volumetric Boolean operations union, intersection and subtraction, to construct 
more complex shapes. An operator selects the CSG model he/she wants to measure from a database of template 
models. The model is projected into the images with a so-called hidden-line projection. The hidden-line projection 
computes contours of curved surfaces and determines which edges, or parts of edges, are visible from the given 
viewpoint. The interior and exterior orientations of the images are known, or at least have approximate values. 
The operator can interactively drag an edge from the hidden-line projection to the corresponding position in the image 
and thus perform a measurement. An observation equation is set up that directly relates the parameters of the model to 
the measured position. For a more detailed description of the measurement method, see Ermes et al. (1999). When a 
CSG model is constructed from several primitives, geometric relations often can be identified between the primitives 
(internal constraints). See, for example, Figure 1: a T-junction. The radii of both cylinders are equal, the cylinders are 
perpendicular to each other, and the beginning of the horizontal cylinder is positioned in the middle of the vertical 
cylinder. Integration of these relations in the interactive measurement method reduces the degrees of freedom of the two 
cylinders and thus facilitates the measurements. When measuring standardized components in an industrial installation, 
extra benefits arise because of the known dimensions of the parts. 
  
Figure 1. A hidden-line projection of a T-junction. 
Not only constraints within CAD models are relevant for the reconstruction of an installation, but also geometric 
relations between models (external constraints) play an important role; e.g. parts can be parallel to each other, or piping 
  
216 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 
  
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