Distance ranked connectivity compression of triangle meshes

We present a new, single-rate method for compressing the connectivity information of a 2-manifold triangle mesh with or without boundary. Traditional compression schemes interleave geometry and connectivity coding, and are thus unable to utilise information from vertices (mesh regions) they have not yet processed. With the advent of competitive point cloud compression schemes, it has become feasible to develop separate connectivity encoding schemes which can exploit complete, global vertex position information to improve performance. Our scheme demonstrates the utility of this separation of vertex and connectivity coding. By traversing the mesh edges in a consistent breadth-first fashion, and using global vertex information, we can predict the position of the vertex which completes the unprocessed triangle attached to a given edge. We then rank the vertices in the neighbourhood of this predicted position by their Euclidean distance. The distance rank of the correct closing vertex is stored. Typically, these rank values are small, and the sequence of rank values thus possesses low entropy and compresses very well. The paper details the algorithm as well as the predictors we have tested. Results indicate improvement on the current best valence-based schemes for many common mesh classes

Fast in-place binning of laser range-scanned point sets

Laser range scanning is commonly used in cultural heritage to create digital models of real-world artefacts. A large scanning campaign can produce billions of point samples — too many to be manipulated in memory on most computers. It is thus necessary to spatially partition the data so that it can be processed in bins or slices. We introduce a novel compression mechanism that exploits spatial coherence in the data to allow the bins to be computed with only 1.01 bytes of I/O traffic for each byte of input, compared to 2 or more for previous schemes. Additionally, the bins are loaded from the original files for processing rather than from a sorted copy, thus minimising disk space requirements. We demonstrate that our method yields performance improvements in a typical point-processing task, while also using little memory and guaranteeing an upper bound on the number of samples held in-core

Moving Least-Squares Reconstruction of Large Models with GPUs

Modern laser range scanning campaigns produce extremely large point clouds, and reconstructing a triangulated surface thus requires both out-of-core techniques and significant computational power. We present a GPU-accelerated implementation of the Moving Least Squares (MLS) surface reconstruction technique. While several previous out-of-core approaches use a sweep-plane approach, we subdivide the space into cubic regions that are processed independently. This independence allows the algorithm to be parallelized using multiple GPUs, either in a single machine or a cluster. It also allows data sets with billions of point samples to be processed on a standard desktop PC. We show that our implementation is an order of magnitude faster than a CPU-based implementation when using a single GPU, and scales well to 8 GPUs

Compression of Dense and Regular Point Clouds

We present a simple technique for single-rate compression of point clouds sampled from a surface, based on a spanning tree of the points. Unlike previous methods, we predict future vertices using both a linear predictor, which uses the previous edge as a predictor for the current edge, and lateral predictors that rotate the previous edge 90 degrees left or right about an estimated normal. By careful construction of the spanning tree and choice of prediction rules, our method improves upon existing compression rates when applied to regularly sampled point sets, such as those produced by laser range scanning or uniform tesselation of higherorder surfaces. For less regular sets of points, the compression rate is still generally within 1.5 bits per point of other compression algorithms

Animation space: a truly linear framework for character animation

Skeletal subspace deformation (SSD), a simple method of character animation used in many applications, has several shortcomings; the best-known being that joints tend to collapse when bent. We present animation space, a generalization of SSD that greatly reduces these effects and effectively eliminates them for joints that do not have an unusually large range of motion.While other, more expensive generalizations exist, ours is unique in expressing the animation process as a simple linear transformation of the input coordinates. We show that linearity can be used to derive a measure of average distance (across the space of poses), and apply this to improving parametrizations.Linearity also makes it possible to fit a model to a set of examples using least-squares methods. The extra generality in animation space allows for a good fit to realistic data, and overfitting can be controlled to allow fitted models to generalize to new poses. Despite the extra vertex attributes, it is possible to render these animation-space models in hardware with no loss of performance relative to SSD

Correct normal transformations for articulated models

It is well-established that when a matrix is used to transform a rigid object, the normals should be transformed by the inverse transpose of that matrix. However, this is only valid where the transformation matrix is locally constant. This is not the case for models animated with skeletal subspace deformation (SSD), where the transformation matrix is computed for each vertex. We derive a formula for correctly transforming normals on SSD models

Terrain Sketching

Procedural methods for terrain synthesis are capable of creating realistic depictions of heightfield terrains with little user intervention. However, users often do wish to intervene in controlling the placement and shape of landforms, but without sacrificing realism. In this paper, we present a sketching interface to procedural terrain generation. This system enables users to draw the silhouette, spine and bounding curves of both extruding (hills and mountains) and embedding landforms (river courses and canyons). Terrain is interactively generated to match the sketched constraints using multiresolution surface deformation. In addition, the wavelet noise characteristics of silhouette strokes are propagated to the surrounding terrain. With terrain sketching users can interactively create or modify landscapes incorporating varied and complex landforms

Accelerating kd-tree searches for all k-nearest neighbours

Finding the k nearest neighbours of each point in a point cloud forms an integral part of many point-cloud processing tasks. One common approach is to build a kd-tree over the points and then iteratively query the k nearest neighbors of each point. We introduce a simple modification to these queries to exploit the coherence between successive points; no changes are required to the kd-tree data structure. The path from the root to the appropriate leaf is updated incrementally, and backtracking is done bottom-up. We show that this can reduce the time to compute the neighbourhood graph of a 3D point cloud by over 10%, and by up to 24% when k = 1. The gains scale with the depth of the kd-tree, and the method is suitable for parallel implementation

Proof of Field D*'s Case Separation for Arbitrary Simplices

In their development of the Field D* algorithm, Ferguson et. al. prove that a path through a unit length right-angled triangle originating from an interpolated edge, and travelling to the opposite vertex must either be a direct or indirect case. A combination of the two is not optimal. Later work, proves this for arbitrary, but non-degenerate triangles. In this technical report, we prove the same for non-degenerate simplices, which are generalisations of triangles to higher dimensions

Large-Scale Structure in the Universe

Cosmologists are currently researching the theory of large-scale structures, which are in essence groups of neighbouring galaxies. Recent “galaxy-hunts” have resulted in data for hundreds of thousands of galaxies being made publicly available, and it has become infeasible to isolate large-scale structures by hand from this data. Furthermore, it is difficult for cosmologists to visualise such structures by simply observing the galaxies that comprise the structure; they need a graphically rendered system in which they can change their viewpoint and observe the structure from any position desired. We present a system that identifies large-scale structures from datasets of galaxy information, and then displays the data using OpenGL in such a way that the user can “fly” through space in realtime, observing not only a single structure but the entire dataset and how structures are positioned relative to each other