Keywords: computer aided design, surface re-construction, segmentation, middle axes of triangle meshes, freeform surfaces.

Many industrial products are originally designed using physical clay models before a computer aided design model is generated. In the process of surface reconstruction clouds of three dimensional measurement points gained by laser scanning are transformed into a freeform surface representation. Many methods of surface reconstruction are implemented within commercial software tools. The category of "quick & dirty" reconstruction methods suffers from insufficient surface quality. On the other hand, the "slow & clean" methods imply the disadvantage of time consuming editing effort.

In this contribution a novel approach of surface reconstruction is presented, which avoids the above mentioned shortcomings. The key idea is to generate freeform surfaces which overlap their original boundary and which have to be trimmed and filleted subsequently within any conventional computer aided design system. This approach claims to fit the re-constructed surfaces to the original design intent. Basic phases of this reconstruction process are

• the segmentation of the triangulated point scans,
• the generation of regular basis grids and
• the generation of approximating freeform surfaces.

In the first phase, the initial triangle mesh is decomposed into segments with similar surface characteristics. This decomposition is based on the graph of the mesh of triangles in combination with logical conditions defining the connectivity of adjacent triangles. Based on the methods of graph theory connective components are estimated. These connective components are segments of the original mesh of triangles, which will separately be represented by a free form surface.

Within the second phase, a regular basis grid is generated for each segment. Therefore, the triangles of a segment are mapped onto a middle axis representing the center line of the segment. Secondary axes are defined equidistant and perpendicular to the middle axis. The middle axis as well as the secondary axes lie on the triangles of the actual segment. The regular basis grid is based on middle and secondary axes while the interior characteristics of the segment are pursued over the original segment boarder.

In the third phase, an initial control point grid of the freeform surface is created based on the regular basis grid. The initial control points lie on the basis grid and consequently, the resulting Bezier freeform surface does not contact the original triangles of the segment. The dragging algorithm, valid for geodetic surfaces, is adopted for general three dimensional surfaces.

The approach of design intent orientated surface reconstruction is showcased with an illustrative example from the field of car body design.

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