We demonstrate a method to control the distance between a custom probe and a sample on a μm to nm scale. The method relies on the closed-loop feedback on the angular deflection of an in-contact AFM microcantilever. High performance in stability and accuracy is achieved in this method by taking advantage of the small mechanical feedback path between surface and probe. We describe how internal er...

In this paper we present a new algorithm to compute the Euclidean distance from a point to a quadric surface. In some sense, this algorithm is a generalization of a previous work of V. Hernández, J. Estrada and P. Barrera, where an effective algorithm to compute the Euclidean distance from a point to a plane conic is developed. It provides good approximations of the Euclidean distance from a po...

In instance-based learning, a training set is given to a classifier for classifying new instances. In practice, not all information in the training set is useful for classifiers. Therefore, it is convenient to discard irrelevant instances from the training set. This process is known as instance reduction, which is an important task for classifiers since through this process the time for classif...

For standard subdivision algorithms and generic input data, near an extraordinary point the distance from the limit surface to the control polyhedron after m subdivision steps is shown to decay dominated by the mth power of the subsubdominant eigenvalue. Conversely, for Loop subdivision we exhibit generic input data so that the Hausdorff distance at the mth step is greater or equal to the mth p...

The three-dimensional shapes of tectonic plates that sink into the Earth’s mantle (slabs) are the starting point for a range of geoscience studies, from determining the forces driving the motion of tectonic plates, to potential seismic and tsunami hazards, to the sources of magmas beneath active volcanos. For many of these applications finite element methods are used to model the deformation or...

When we use range finders to observe the shape of an object, many occluded areas may occur. These become holes and gaps in the model and make it undesirable to utilize the model for various applications. We propose a novel method to fill holes and gaps and complement such an incomplete model. We use a signed distance field (SDF) as an intermediate representation, which stores Euclidean signed d...

In this chapter we address the problem of reconstructing the surface geometry, topology, and color map of a 3D scene from a finite set of colored oriented points. These data sets are nowadays obtained using a variety of techniques, including multi-view stereo reconstruction methods from multiple 2D images. We describe a novel variational method which reduces the problem to the solutions of spar...

The Tully-Fisher distance to the galaxy Dwingeloo 1, recently discovered very close to the Galactic Plane, is highly uncertain because of the range of possible foreground extinction values which have been suggested. We show that very high values of A B (10 magnitudes) or low values (4 magnitudes) are unreasonable since the intrinsic surface brightness implied for Dwingeloo 1 would be unrealisti...