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

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 Concept For Surface Reconstruction From Digitised Data

Reverse engineering and in particular the reconstruction of surfaces from digitized data is an important task in industry. With the development of new digitizing technologies such as laser or photogrammetry, real objects can be measured or digitized quickly and cost effectively. The result of the digitizing process is a set of discrete 3D sample points. These sample points have to be converted into a mathematical, continuous surface description, which can be further processed in different computer applications. The main goal of this work is to develop a concept for such a computer aided surface generation tool, that supports the new scanning technologies and meets the requirements in industry towards such a product. Therefore first, the requirements to be met by a surface reconstruction tool are determined. This marketing study has been done by analysing different departments of several companies. As a result, a catalogue of requirements is developed. The number of tasks and applications shows the importance of a fast and precise computer aided reconstruction tool in industry. The main result from the analysis is, that many important applications such as stereolithographie, copy milling etc. are based on triangular meshes or they are able to handle these polygonal surfaces. Secondly the digitizer, currently available on the market and used in industry are analysed. Any scanning system has its strength and weaknesses. A typical problem in digitizing is, that some areas of a model cannot be digitized due to occlusion or obstruction. The systems are also different in terms of accuracy, flexibility etc. The analysis of the systems leads to a second catalogue of requirements and tasks, which have to be solved in order to provide a complete and effective software tool. The analysis also shows, that the reconstruction problem cannot be solved fully automatically due to many limitations of the scanning technologies. Based on the two requirements, a concept for a software tool in order to process digitized data is developed and presented. The concept is restricted to the generation of polygonal surfaces. It combines automatic processes, such as the generation of triangular meshes from digitized data, as well as user interactive tools such as the reconstruction of sharp corners or the compensation of the scanning probe radius in tactile measured data. The most difficult problem in this reconstruction process is the automatic generation of a surface from discrete measured sample points. Hence, an algorithm for generating triangular meshes from digitized data has been developed. The algorithm is based on the principle of multiple view combination. The proposed approach is able to handle large numbers of data points (examples with up to 20 million data points were processed). Two pre-processing algorithm for triangle decimation and surface smoothing are also presented and part of the mesh generation process. Several practical examples, which show the effectiveness, robustness and reliability of the algorithm are presented

Conforming restricted Delaunay mesh generation for piecewise smooth complexes

A Frontal-Delaunay refinement algorithm for mesh generation in piecewise smooth domains is described. Built using a restricted Delaunay framework, this new algorithm combines a number of novel features, including: (i) an unweighted, conforming restricted Delaunay representation for domains specified as a (non-manifold) collection of piecewise smooth surface patches and curve segments, (ii) a protection strategy for domains containing curve segments that subtend sharply acute angles, and (iii) a new class of off-centre refinement rules designed to achieve high-quality point-placement along embedded curve features. Experimental comparisons show that the new Frontal-Delaunay algorithm outperforms a classical (statically weighted) restricted Delaunay-refinement technique for a number of three-dimensional benchmark problems.Comment: To appear at the 25th International Meshing Roundtabl

Material flow during the extrusion of simple and complex cross-sections using FEM

This paper deals with the extrusion of rod and shape sections and uses a 3D finite element model analysis (FEM) to predict the effect of die geometry on maximum extrusion load. A description of material flow in the container is considered in more detail for rod and shape sections in order to fully comprehend the transient conditions occurring during the process cycle. A comparison with experiments is made to assess the relative importance of some extrusion parameters in the extrusion process and to ensure that the numerical discretisation yields a realistic simulation of the process. The usefulness and the limitation of FEM are discussed when modelling complex shapes. Results are presented for velocity contours and shear stress distribution during the extrusion process. It is shown that for most of the shapes investigated, the material making up the extrudate cross-sections originates from differing regions of virgin material within the billet. The outside surface of the extrudate originates from the material moving along the dead metal zone (DMZ) and the core of the extrudate from the central deformation zone. The FE program appears to predict all the major characteristics of the flow observed macroscopically

Material flow during the extrusion of simple and complex cross-sections using FEM

This paper deals with the extrusion of rod and shape sections and uses a 3D finite element model analysis (FEM) to predict the effect of die geometry on maximum extrusion load. A description of material flow in the container is considered in more detail for rod and shape sections in order to fully comprehend the transient conditions occurring during the process cycle. A comparison with experiments is made to assess the relative importance of some extrusion parameters in the extrusion process and to ensure that the numerical discretisation yields a realistic simulation of the process. The usefulness and the limitation of FEM are discussed when modelling complex shapes. Results are presented for velocity contours and shear stress distribution during the extrusion process. It is shown that for most of the shapes investigated, the material making up the extrudate cross-sections originates from differing regions of virgin material within the billet. The outside surface of the extrudate originates from the material moving along the dead metal zone (DMZ) and the core of the extrudate from the central deformation zone. The FE program appears to predict all the major characteristics of the flow observed macroscopically

Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation

We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our approach enables to control the error in the computation of the displacement and stress fields around the needle tip and needle shaft by suitably refining the mesh, whilst maintaining a coarser mesh in other parts of the domain. We demonstrate through academic and practical examples that our approach increases the accuracy of the displacement and stress fields around the needle without increasing the computational expense. This enables real-time simulations. The proposed methodology has direct implications to increase the accuracy and control the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anesthesia, or cryotherapy and can be essential to the development of robotic guidance.Comment: 21 pages, 14 figure

Interactive ray shading of FRep objects

In this paper we present a method for interactive rendering general procedurally defined functionally represented (FRep) objects using the acceleration with graphics hardware, namely Graphics Processing Units (GPU). We obtain interactive rates by using GPU acceleration for all computations in rendering algorithm, such as ray-surface intersection, function evaluation and normal computations. We compute primary rays as well as secondary rays for shadows, reflection and refraction for obtaining high quality of the output visualization and further extension to ray-tracing of FRep objects. The algorithm is well-suited for modern GPUs and provides acceptable interactive rates with good quality of the results. A wide range of objects can be rendered including traditional skeletal implicit surfaces, constructive solids, and purely procedural objects such as 3D fractals