Progressive refinement rendering of implicit surfaces

The visualisation of implicit surfaces can be an inefficient task when such surfaces are complex and highly detailed. Visualising a surface by first converting it to a polygon mesh may lead to an excessive polygon count. Visualising a surface by direct ray casting is often a slow procedure. In this paper we present a progressive refinement renderer for implicit surfaces that are Lipschitz continuous. The renderer first displays a low resolution estimate of what the final image is going to be and, as the computation progresses, increases the quality of this estimate at an interactive frame rate. This renderer provides a quick previewing facility that significantly reduces the design cycle of a new and complex implicit surface. The renderer is also capable of completing an image faster than a conventional implicit surface rendering algorithm based on ray casting

A progressive refinement approach for the visualisation of implicit surfaces

Visualising implicit surfaces with the ray casting method is a slow procedure. The design cycle of a new implicit surface is, therefore, fraught with long latency times as a user must wait for the surface to be rendered before being able to decide what changes should be introduced in the next iteration. In this paper, we present an attempt at reducing the design cycle of an implicit surface modeler by introducing a progressive refinement rendering approach to the visualisation of implicit surfaces. This progressive refinement renderer provides a quick previewing facility. It first displays a low quality estimate of what the final rendering is going to be and, as the computation progresses, increases the quality of this estimate at a steady rate. The progressive refinement algorithm is based on the adaptive subdivision of the viewing frustrum into smaller cells. An estimate for the variation of the implicit function inside each cell is obtained with an affine arithmetic range estimation technique. Overall, we show that our progressive refinement approach not only provides the user with visual feedback as the rendering advances but is also capable of completing the image faster than a conventional implicit surface rendering algorithm based on ray casting

Incorporating interactive 3-dimensional graphics in astronomy research papers

Most research data collections created or used by astronomers are intrinsically multi-dimensional. In contrast, all visual representations of data presented within research papers are exclusively 2-dimensional. We present a resolution of this dichotomy that uses a novel technique for embedding 3-dimensional (3-d) visualisations of astronomy data sets in electronic-format research papers. Our technique uses the latest Adobe Portable Document Format extensions together with a new version of the S2PLOT programming library. The 3-d models can be easily rotated and explored by the reader and, in some cases, modified. We demonstrate example applications of this technique including: 3-d figures exhibiting subtle structure in redshift catalogues, colour-magnitude diagrams and halo merger trees; 3-d isosurface and volume renderings of cosmological simulations; and 3-d models of instructional diagrams and instrument designs.Comment: 18 pages, 7 figures, submitted to New Astronomy. For paper with 3-dimensional embedded figures, see http://astronomy.swin.edu.au/s2plot/3dpd

Incorporating interactive 3-dimensional graphics in astronomy research papers

Most research data collections created or used by astronomers are intrinsically multi-dimensional. In contrast, all visual representations of data presented within research papers are exclusively 2-dimensional. We present a resolution of this dichotomy that uses a novel technique for embedding 3-dimensional (3-d) visualisations of astronomy data sets in electronic-format research papers. Our technique uses the latest Adobe Portable Document Format extensions together with a new version of the S2PLOT programming library. The 3-d models can be easily rotated and explored by the reader and, in some cases, modified. We demonstrate example applications of this technique including: 3-d figures exhibiting subtle structure in redshift catalogues, colour-magnitude diagrams and halo merger trees; 3-d isosurface and volume renderings of cosmological simulations; and 3-d models of instructional diagrams and instrument designs.Comment: 18 pages, 7 figures, submitted to New Astronomy. For paper with 3-dimensional embedded figures, see http://astronomy.swin.edu.au/s2plot/3dpd

Map Calculus in GIS: a proposal and demonstration

This paper provides a new representation for fields (continuous surfaces) in Geographical Information Systems (GIS), based on the notion of spatial functions and their combinations. Following Tomlin's (1990) Map Algebra, the term 'Map Calculus' is used for this new representation. In Map Calculus, GIS layers are stored as functions, and new layers can be created by combinations of other functions. This paper explains the principles of Map Calculus and demonstrates the creation of function-based layers and their supporting management mechanism. The proposal is based on Church's (1941) Lambda Calculus and elements of functional computer languages (such as Lisp or Scheme)

Topological correction of hypertextured implicit surfaces for ray casting

Hypertextures are a useful modelling tool in that they can add three-dimensional detail to the surface of otherwise smooth objects. Hypertextures can be rendered as implicit surfaces, resulting in objects with a complex but well defined boundary. However, representing a hypertexture as an implicit surface often results in many small parts being detached from the main surface, turning an object into a disconnected set. Depending on the context, this can detract from the realism in a scene where one usually does not expect a solid object to have clouds of smaller objects floating around it. We present a topology correction technique, integrated in a ray casting algorithm for hypertextured implicit surfaces, that detects and removes all the surface components that have become disconnected from the main surface. Our method works with implicit surfaces that are C2 continuous and uses Morse theory to find the critical points of the surface. The method follows the separatrix lines joining the critical points to isolate disconnected components

Study of hybrid air vehicles stability using computational fluid dynamics

This paper uses Computational Fluid Dynamics to predict aerodynamic damping of airships or hybrid air vehicles. This class of aircraft is characterised by large lifting bodies combining buoyancy and circulatory lift. Damping is investigated via forced oscillations of the vehicle in pitch and yaw. The employed method is verified using data for lighter than air vehicles. The use of fins and stabilisers was found to be beneficial. The rear part of the body was dominated by separated flow that containedmore frequencies than the forcing frequency imposed on the body. The final design is seen to be dynamically stable across a range of conditions for small pitch angles

3D freeform surfaces from planar sketches using neural networks

A novel intelligent approach into 3D freeform surface reconstruction from planar sketches is proposed. A multilayer perceptron (MLP) neural network is employed to induce 3D freeform surfaces from planar freehand curves. Planar curves were used to represent the boundaries of a freeform surface patch. The curves were varied iteratively and sampled to produce training data to train and test the neural network. The obtained results demonstrate that the network successfully learned the inverse-projection map and correctly inferred the respective surfaces from fresh curves