Geometry for digital recontruction

• There are two general approaches to capturing physical form.
• One is the use of a tracking arm, especially suitable for capturing strings of point data from selected feature curves. 捕获挑选的特征曲线上的点云
• The other method uses a laser range scanner and results in a large number of more or less regularly distributed measurement points from the surface of the given physical model. 从曲面上获取近乎正则分散的点云
• Finally, all of these point clouds have to be merged into a single combined point cloud represented in the same coordinate system. This procedure is called registration.

Data acquisition and registration 数据获取和匹配

• Digitizer arms. The method is very well suited to capturing particular selected features of a model.
• Optical scanning devices: Near-range scanners, measure objects of a size less than a few meters.
• Medium- and long-range scanners, when the distance between scanner and object exceeds 2 meters.
• Outlier removal and noise reduction.
• Fully automatic registration and surface matching.

The polygon phase 多边形阶段

• Voronoi diagrams in the plane.
• Two-dimensional Delaunay triangulation.
• The Delaunay triangulation joins exactly those points from the input set p1, p2, …, pN by an edge whose Voronoi cells share a common edge.
• Voronoi diagrams in three dimensions.
• Surface triangulations.
• Interactive improvements.
  Hole filling requires the specification of part of the triangulation around the detected hole.
• Relaxation and smoothing.
• Mesh decimation.

Segmentation 分割

• A feature region is defined as one with a significant difference in the principal curvatures (i.e., with a small principal curvature in feature direction and a high one across the feature).

Surface fitting 曲面拟合

• plane, sphere, cone, and cylinder exhibit only simple surfaces. These shapes are not only rather easy to detect automatically but approximations of them are not difficult to compute within the detected surface class
• Freeform surface fitting.

The surfaces need to be build 需被建造的曲面

• for applications in architecture it may be better to sacrifice some accuracy and try to approximate the measurement data by a union of surface patches that can “easily” be built.
• These surfaces include ruled surfaces, developable surfaces, and other kinematically generated surfaces.
• Approximation with ruled surfaces.
• Developable surfaces.

References and further reading