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LR B-splines and represetantion of measured shape


Commodity products used in everyday life are produced in factories based on accurate computer generated shape. These many shapes of these shapes are dominated by elementary surfaces (plane, sphere, cylinder, cone, and torus) with some smooth sculptured surfaces. Other products such as molded plastic objects and cars are dominated by smooth sculptured shapes.
Old artifacts, on the other hand, were to a great extent created by hand, and have been exposed to wear and tear over the years. This has modified the shape, smoothing corners and edges scratching and making indentations. These objects are smooth, but with a significantly more local shape variation than modern factory produced objects.
Two decades ago it was expensive to coordinate measure shape, and when measurement was performed the bulk of measured data was small, making point based shape reconstruction on the computer very difficult. Today millions of accurate points can be measured with low costs, producing huge amounts of data. Dependent on the technology used, e.g., 3D cameras, the data points can be assigned color values that allow the point cloud to be used for direct 3D rendering of realistic images of the shape.
Just to render shape, does not give a good impression of the object, gluing image information onto the shape allows very realistic shape visualization, e.g., for web-visualization. However, for shape visualization the quality of the underlying shape description is crucial. Due to the computational cost of textured based rendering, computer graphics has traditionally been focused on shape models based on triangulations. Due to simplicity the model representation in the databases has dominantly been triangulation based. When building triangulations form measured point clouds the triangulation will be as bulky as the original point set. To make the data bulk smaller, the triangulation can be thinned. However, the thinning degrades the shape, and removes fine detail. Thus limiting the future use of shape model.
As the surfaces of old artifacts in general are smooth, the compact smooth representations are in general better suited for their representation than triangulations. Computer Aided Design system (CAD) uses tensor product B-splines as the representation format for designed sculptures. The tensor product B-splines are well suited for designing synthetic shape aimed at modern products, as these have little local shape variation. However, old artifices have more local variations and require a shape representation that supports such variations. Consequently CAD-type B-splines are not feasible.
In 2009 the concept of Locally Refined B-splines [1] (LR B-splines) was first presented inspired by the design oriented T-splines [2]. LR B-splines allow in one surface object, to represent in a very compact way, an overall smooth shape and its finer shape granularity. Modern Graphics Processing Units (GPUs) allows such compact shape representations to be directly rendered on the GPU according to the required visual quality, thus avoiding the traditional problem of the granularity of a triangle representation to limiting the visual quality.
The first test of LR B-spline representations based on aerial laser measurements of landscapes have been performed, and shows great promise. The technology will be further developed in the new integrated project IQmulus (November 2012 – October 2016) IQmulus addresses novel technologies geographical shape processing and representation.
[1] T. Dokken, T. Lyche, K.F. Pettersen, Polynomial Splines over Locally Refined, Box-Partitions, submitted to Computer Aided Geoemtrid Design. Preprint:
[2] T. W. Sederberg, J. Zheng, A. Bakenov., and A. Nasri, T-splines and TNURCCS, ACM Transactions on Graphics (TOG), ACM Trans. Graph., 22 (2003), pp. 477{484.


Academic lecture





  • SINTEF Digital / Mathematics and Cybernetics

Presented at

3D Workshop - 4th International Euro-Mediterranean Conference (EuroMed 2012)




29.10.2012 - 02.11.2012





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