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

Surface Reconstruction from Constructive Solid Geometry for Interactive Visualization

A method is presented for constructing a set of triangles that closely approximates the surface of a constructive solid geometry model. The method subdivides an initial triangulation of the model’s primitives into triangles that can be classified accurately as either on or off of the surface of the whole model, and then recombines these small triangles into larger ones that are still either entirely on or entirely off the surface. Subdivision and recombination can be done in a preprocessing step, allowing later rendering of the triangles on the surface (i.e., the triangles visible from outside the model) to proceed at interactive rates. Performance measurements confirm that this method achieves interactive rendering speeds. This approach has been used with good results in an interactive scientific visualization program

A Note on Some Applications of Interval Arithmetic in Hierarchical Solid Modeling

Techniques of reliable computing like interval arithmetic can be used to guarantee a reliable solution even in the presence of numerical round-off errors. The need to trace bounds for the error function separately can be eliminated using these techniques. In this talk, we focus on some demonstrations how the techniques and algorithms of reliable computing can be applied to the construction and further processing of hierarchical solid representations using the octree model as an example. An octree is a common hierarchical data structure to represent 3D geometrical objects in solid modeling systems or to reconstruct a real scene. The solid representation is based on recursive cell decompositions of the space. Unfortunately, the data structure may require a large amount of memory when it uses a set of very small cubic nodes to approximate a solid. In this talk, we present a novel generalization of the octree model created from a CSG object that uses interval arithmetic and allows us to extend the tests for classifying points in space as inside, on the boundary or outside the object to handle whole sections of the space at once. Tree nodes with additional information about relevant parts of the CSG object are introduced in order to reduce the depth of the required subdivision. Furthermore, this talk is concerned with interval-based algorithms for reliable proximity queries between the extended octrees and with further processing of the structure. We conclude the talk with some examples of implementations

Ray tracing for constructive solid modeling

This thesis describes a system for the creation and realistic depiction of non-geometric, complex, three dimensional solid models by utilizing a ray tracing algorithm and a graphics relational database. Geometric primitives such as a sphere, cylinder, block, and cone are combined together by using the Boolean set operations of union (+), intersection (&), and difference (-). The three dimensional solid models are built based on the concept of constructive solid geometric modeling. The database provides functions for the creation, transformation, and deletion of the primitives and models. A model may be displayed as a wireframe for a fast display or as a shaded solid for a realistic display

A Method of Rendering CSG-Type Solids Using a Hybrid of Conventional Rendering Methods and Ray Tracing Techniques

This thesis describes a fast, efficient and innovative algorithm for producing shaded, still images of complex objects, built using constructive solid geometry ( CSG ) techniques. The algorithm uses a hybrid of conventional rendering methods and ray tracing techniques. A description of existing modelling and rendering methods is given in chapters 1, 2 and 3, with emphasis on the data structures and rendering techniques selected for incorporation in the hybrid method. Chapter 4 gives a general description of the hybrid method. This method processes data in the screen coordinate system and generates images in scan-line order. Scan lines are divided into spans (or segments) using the bounding rectangles of primitives calculated in screen coordinates. Conventional rendering methods and ray tracing techniques are used interchangeably along each scan-line. The method used is detennined by the number of primitives associated with a particular span. Conventional rendering methods are used when only one primitive is associated with a span, ray tracing techniques are used for hidden surface removal when two or more primitives are involved. In the latter case each pixel in the span is evaluated by accessing the polygon that is visible within each primitive associated with the span. The depth values (i. e. z-coordinates derived from the 3-dimensional definition) of the polygons involved are deduced for the pixel's position using linear interpolation. These values are used to determine the visible polygon. The CSG tree is accessed from the bottom upwards via an ordered index that enables the 'visible' primitives on any particular scan-line to be efficiently located. Within each primitive an ordered path through the data structure provides the polygons potentially visible on a particular scan-line. Lists of the active primitives and paths to potentially visible polygons are maintained throughout the rendering step and enable span coherence and scan-line coherence to be fully utilised. The results of tests with a range of typical objects and scenes are provided in chapter 5. These results show that the hybrid algorithm is significantly faster than full ray tracing algorithms

Algorithmic commonalities in the parallel environment

The ultimate aim of this project was to analyze procedures from substantially different application areas to discover what is either common or peculiar in the process of conversion to the Massively Parallel Processor (MPP). Three areas were identified: molecular dynamic simulation, production systems (rule systems), and various graphics and vision algorithms. To date, only selected graphics procedures have been investigated. They are the most readily available, and produce the most visible results. These include simple polygon patch rendering, raycasting against a constructive solid geometric model, and stochastic or fractal based textured surface algorithms. Only the simplest of conversion strategies, mapping a major loop to the array, has been investigated so far. It is not entirely satisfactory

Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays

The goal of this paper is to introduce a new method in computer-aided geometry of solid modeling. We put forth a novel algebraic technique to evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with regularized operators of union, intersection, and difference, i.e., any CSG tree. The result is obtained in three steps: first, by computing an independent set of generators for the d-space partition induced by the input; then, by reducing the solid expression to an equivalent logical formula between Boolean terms made by zeros and ones; and, finally, by evaluating this expression using bitwise operators. This method is implemented in Julia using sparse arrays. The computational evaluation of every possible solid expression, usually denoted as CSG (Constructive Solid Geometry), is reduced to an equivalent logical expression of a finite set algebra over the cells of a space partition, and solved by native bitwise operators.Comment: revised version submitted to Computer-Aided Geometric Desig

Machine vision and the OMV

The orbital Maneuvering Vehicle (OMV) is intended to close with orbiting targets for relocation or servicing. It will be controlled via video signals and thruster activation based upon Earth or space station directives. A human operator is squarely in the middle of the control loop for close work. Without directly addressing future, more autonomous versions of a remote servicer, several techniques that will doubtless be important in a future increase of autonomy also have some direct application to the current situation, particularly in the area of image enhancement and predictive analysis. Several techniques are presentet, and some few have been implemented, which support a machine vision capability proposed to be adequate for detection, recognition, and tracking. Once feasibly implemented, they must then be further modified to operate together in real time. This may be achieved by two courses, the use of an array processor and some initial steps toward data reduction. The methodology or adapting to a vector architecture is discussed in preliminary form, and a highly tentative rationale for data reduction at the front end is also discussed. As a by-product, a working implementation of the most advanced graphic display technique, ray-casting, is described