Thesis

Boundary representation models reverse engineered from three-dimensional range data suffer from various inaccuracies caused by noise in the data and the model building software. Beautification aims to improve such models so that they exhibit exact geometric regularities representing the original, ideal design intent. In this thesis an approach to beautification as a post-processing step solely working with the boundary representation is investigated. Geometric regularities approximately present in the model are detected and a consistent subset of these regularities is imposed on the model. Only models of engineering objects whose surfaces can be represented by planar, spherical, cylindrical, conical and toroidal faces with sharp edges or fixed-radius rolling ball blends are considered. A large number of mechanical parts can be constructed from these surfaces and there are robust reverse engineering methods for them.

A novel approach to approximate geometric regularities is introduced. They are handled as approximate symmetries of discrete properties of boundary representation elements. This leads to new efficient detection methods for different approximate regularity types classified by the underlying symmetry type. Due to the ambiguity present in approximate models many approximate regularities are detected, which are unlikely to be mutually consistent. Hence, a consistent subset of regularities likely to represent the intended design has to be selected. Expressing regularities in terms of geometric constraints and interpreting constraints in a topological context results in a new efficient solvability test for constraint systems based on degrees-of-freedom analysis. In order to select likely, consistent regularities they are added sequentially in order of a priority to a constraint system. A regularity is selected if the expanded constraint system remains solvable. The selected constraint set is solved numerically and an improved model is rebuilt from the solution. Experiments show that this approach can be used to improve reconstructed models.

@PHDTHESIS{Langbein2003,
  author =       {Frank C. Langbein},
  title =        {Beautification of Reverse Engineered Geometric
                  Models},
  school =       {Department of Computer Science, Cardiff University},
  year =         2003,
  month =        {June},
  url =          {http://www.langbein.org/research/solids/borg/thesis/},
  abstract =     {Boundary representation models reverse engineered
                  from three-dimensional range data suffer from
                  various inaccuracies caused by noise in the data and
                  the model building software. Beautification aims to
                  improve such models so that they exhibit exact
                  geometric regularities representing the original,
                  ideal design intent. In this thesis an approach to
                  beautification as a post-processing step solely
                  working with the boundary representation is
                  investigated. Geometric regularities approximately
                  present in the model are detected and a consistent
                  subset of these regularities is imposed on the
                  model. Only models of engineering objects whose
                  surfaces can be represented by planar, spherical,
                  cylindrical, conical and toroidal faces with sharp
                  edges or fixed-radius rolling ball blends are
                  considered. A large number of mechanical parts can
                  be constructed from these surfaces and there are
                  robust reverse engineering methods for them. A novel
                  approach to approximate geometric regularities is
                  introduced. They are handled as approximate
                  symmetries of discrete properties of boundary
                  representation elements. This leads to new efficient
                  detection methods for different approximate
                  regularity types classified by the underlying
                  symmetry type. Due to the ambiguity present in
                  approximate models many approximate regularities are
                  detected, which are unlikely to be mutually
                  consistent. Hence, a consistent subset of
                  regularities likely to represent the intended design
                  has to be selected. Expressing regularities in terms
                  of geometric constraints and interpreting
                  constraints in a topological context results in a
                  new efficient solvability test for constraint
                  systems based on degrees-of-freedom analysis. In
                  order to select likely, consistent regularities they
                  are added sequentially in order of a priority to a
                  constraint system. A regularity is selected if the
                  expanded constraint system remains solvable. The
                  selected constraint set is solved numerically and an
                  improved model is rebuilt from the solution.
                  Experiments show that this approach can be used to
                  improve reconstructed models.},
}

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