Abstract We study the problem of determining maximum size a spherical two-distance set with two fixed angles (one acute and one obtuse) in high dimensions. Let $$N_{\alpha ,\beta }(d)$$ N α , β ( d</m...

Many meshes in computer animation practice are meant to approximate solid objects, but the provided triangular geometry is often unoriented, non-manifold or contains self-intersections, causing inside/outside of objects to be mathematically ill-defined. We describe a robust and efficient automatic approach to define and compute a signed distance field for arbitrary triangular geometry. Starting...

New depth camera technology has potential to make a significant impact on computer systems interaction with 3D objects; yet, it is currently limited due to its poor noise and resolution characteristics. In this thesis we propose to use depth camera’s strongest characteristic, its video rate capture speeds, to overcome these limitations. Previous work to utilize sequences of depth images used 2D...

The signed distance field of a surface can effectively support many geometry processing tasks such as decimation, smoothing, and Boolean operations since it provides efficient access to distance (error) estimates. In this paper we present an algorithm to compute a piecewise linear, not necessarily continuous approximation of the signed distance field for a given object. Our approach is based on...

Consider a binary image containing one or more objects. A signed distance transform assigns to each pixel (voxel, etc.), both inside and outside of any objects, the minimum distance from that pixel to the nearest pixel on the border of an object. By convention, the sign of the assigned distance value indicates whether or not the point is within some object (positive) or outside of all objects (...

In this paper we propose a novel method to construct hierarchical hp-adaptive Signed Distance Fields (SDFs). We discretize the signed distance function of an input mesh using piecewise polynomials on an axis-aligned hexahedral grid. Besides spatial refinement based on octree subdivision to refine the cell size (h), we hierarchically increase each cell’s polynomial degree (p) in order to constru...

We consider the problem of estimating the rearrangement distance in terms of reversals, insertion and deletion between two genomes, G and H with possibly multiple genes from the same gene family. We define a notion of breakpoint distance for this problem, based on matching genes from the same family between G and H. We show that this distance is a good approximation of the edit distance, but NP...

Signed 3D distance fields are used a in a variety of domains. From shape modelling to surface registration. They are typically computed based on sampled point sets. If the input point set contains holes, the behaviour of the zero-level surface of the distance field is not well defined. In this paper, a novel regularisation approach is described. It is based on an energy formulation, where both ...