Visible surface algorithms for quadric patches

technical reportThis paper describes two algorithms which find the visible portions of surfaces in a picture of a cluster of three-dimensional quadric patches. A quadric patch is a portion of quadric surface defined by a quadratic equation and by zero, one or several quadratic inequalities. The picture is cut by parallel planes called scan planes; the visibility problem is solved in one scan plane at a time by making "a good guess" as t o what is visible according to the visible portions found in the previous can plane. The algorithm for intersecting patches works in a time roughly proportional to the number of patches involved (and not to the square of this number as with some previous algorithms)

ConTesse: Accurate Occluding Contours for Subdivision Surfaces

This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when a sampled occluding contour is valid, that is, when it may be assigned consistent visibility. Previous methods do not guarantee these conditions, which helps explain why smooth contour visibility has been such a challenging problem in the past. The paper then proposes an algorithm that, given a subdivision surface, finds sampled contours satisfying these conditions, and then generates a new triangle mesh matching the given occluding contours. The contours of the output triangle mesh may then be rendered with standard non-photorealistic rendering algorithms, using the mesh for visibility computation. The method can be applied to any triangle mesh, by treating it as the base mesh of a subdivision surface.Comment: Accepted to ACM Transactions on Graphics (TOG

Sweeping of three-dimensional objects

Evaluating the volume swept out by a three-dimensional (3D) object as it moves along an arbitrary path is of interest to many areas of CAD and CAM, such as mechanism design and robot path planning. This paper shows how envelope theory from differential geometry can be used to find the volumes swept out by the individual surfaces of a solid body, and how computer algebra methods may be of use to perform the computations involved. Finally, a new algorithm is presented which shows how the results of sweeping the individual surfaces of a solid body can be combined to form a new 3D model of the swept volume. This algorithm has strong resemblance to hidden line algorithms, but works in one dimension higher

Computer representation of graphical information with applications

PhD ThesisThe research work contained in this thesls lies mainly in the field of computer graphics. The initial chapters are concerned with methods of representing three dimensional solids in two dimensions. Chapter 2 describes a method by which points in three dimensions can be projected onto a two dimensional plane of This is an essential requirement in the projection. This is an essential requirement in the representation of three dimensional solids. Chapter 3 describes a method by which convex polyhedra can be represented by computer. Both the hidden polyhedra and visible face of the polyhedron can be represented by computer. Having tackled this problem, the more difficult problem of representing the non convex polyhedron has been attempted and the results of this work are presented in Chapter 4. Line drawings of the various polyhedra, produced on a graph plotter, are given as examples at the end of Chapters 2, 3 and 4. The problem of how to connect a given line drawing such that the distance travelled by the pen of some computer display is kept to a minimum is discussed in Chapter 5 and various definitions of the concepts involved are given. Theory associated with this 'Pen-Up Problem' has been developed and is explained in detail in the early part of Chapter 6. A method of obtaining an optimal solution to the problem is presented in the latter part of this chapter in addition to various enumerative schemes which have been developed to obtain good feasible solutions to the pen up problems under various conditions Extensive C.P.U. timing experiments have been carried out in Chapter 7 on the various enumerative schemes in Chapter 6 and it has introduced been possible to reach conclusions on the applicability of the various methods. Several topics of interest which have arisen during the main research work are presented as appendices. The programs which have been coded during the period of research are also inc1udeu as appendices

NBS monograph

From Introduction: "This is the second in a series of reports concerned with research and development requirements and areas of continuing concern in the computer and information sciences and technologies.

If you build it, will they come? Evolution towards the application of multi-dimensional GIS to fisheries-oceanography

The development of new technologies in science is a balance between existence and use. There are three versions of this duality – something is built and users come, something is built and users don’t come, and, finally, potential users show up but the ballpark has not yet been built. In each instance there is a combination of three factors at work. The first is a scientific need for a type of data or analysis. The second is a technology or technique developed to meet the need; and the third is a perception that using the technology is somehow "better" that the existing tools and that the tool is easy to use. This work examines closely the development of a tool within oceanography – the Stommel diagram for displaying the time and space spectra of oceanographic phenomena – and the spread of the use of the diagram to other disciplines. The diagram was the product of a number of elements - the mind of a truly original oceanographer, the development of equipment able to collect the detailed temporal and spatial data used to create the plot, and the rise of "big oceanography", which led Stommel to argue graphically for taking care in the design of expeditions. Understanding the spread of the Stommel plot provides a viewpoint for examining the unexpectedly slow development of multi-dimensional geographic information systems (GIS). The development of GIS’s began in the 1970's. Data structures to hold multi-dimensional data have been developed, tools for multidimensional map algebra have been created, and test applications have been developed. The current non-development of multi-dimensional GIS is examined as a background for creating and disseminating GeoModeler, a prototype of scientific GIS able to ingest and display multi-dimensional data. Taking advantage of recent technical developments, we have created a scientific GIS that can display three-dimensional oceanographic data. GeoModeler is used to visually explore and analyze the relationship between water temperature and larval walleye pollock (Theragra chalcogramma) growth in Shelikof Strait, Alaska