NURBS surfaces are among the most commonly used parametric surfaces in CAGD and Computer Graphics. This paper investigates shape modification of NURBS surfaces with geometric constraints, such as point, normal vector, and curve constraints. Two new methods are presented by constrained optimization and energy minimization. The former is based on minimizing changes in control net of surfaces, whereas the latter is based on strain energy minimization. By these two methods, we change control points and weights of an original surface, such that the modified surface satisfies the given constraints. Comparison results and practical examples are also given.

We present an algorithm for recognition and reconstruction of scanned 3D indoor scenes. 3D indoor reconstruction is particularly challenging due to object interferences, occlusions and overlapping which yield incomplete yet very complex scene arrangements. Since it is hard to assemble scanned segments into complete models, traditional methods for object recognition and reconstruction would be inefficient. We present a search-classify approach which interleaves segmentation and classification in an iterative manner. Using a robust classifier we traverse the scene and gradually propagate classification information. We reinforce classification by a template fitting step which yields a scene reconstruction. We deform-to-fit templates to classified objects to resolve classification ambiguities. The resulting reconstruction is an approximation which captures the general scene arrangement. Our results demonstrate successful classification and reconstruction of cluttered indoor scenes, captured in just few minutes.

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