Willem F. Bronsvoort
Abstract
An algorithm is presented for ray tracing generalized cylinders, that is, objects defined by sweeping a two-dimensional contour along a three-dimensional trajectory. The contour can be any 'well-behaved' curve in the sense that it is continuous, and that the points where the tangent is horizontal or vertical can be determined, the trajectory can be any spline curve. First a definition is given of generalized cylinders in terms of the Frenet frame of the trajectory. Then the main problem in ray tracing these objects, the computation of the intersection points with a ray, is reduced to the problem of intersecting two two-dimensional curves. This problem is solved by a subdivision algorithm. The three-dimensional normal at the intersection point closest to the eye point, necessary to perform shading, is obtained by transforming the two-dimensional normal at the corresponding intersection point of the two two-dimensional curves. In this way it is possible to obtain highly realistic images for a very broad class of objects.
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Index Terms
- Ray tracing generalized cylinders
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Reviews
Mike A. Evans
This paper reports on research that extends the technique of ray tracing to objects formed from a swept cylinder primitive. Computer graphics researchers and developers are increasingly interested in ray tracing, a technique for visualizing computer images on raster displays. The method traces a ray from the eye point to each pixel of the screen and calculates the color, intensity, and shade at the first intersection with the surface of the object being viewed. The paper describes this technique and its main difficulty: the calculation of the intersection points of a ray with the surface of the object being visualized. The paper provides references to earlier works that provide algorithms for simple primitives. Swept cylinders are particularly appropriate in mechanical engineering to define complex shapes such as an exhaust manifold with a simple user interface. Generalized cylinders are the shape generated when an arbitrary two-dimensional contour defining the cross-section is swept along an arbitrary three-dimensional trajectory defining the axis. The paper expounds the mathematics of generalized cylinders and presents a method that reduces the problem of calculating the intersection to that of intersecting two two-dimensional curves. This algorithm is then developed using a subdivision technique to improve performance and eliminate some special cases where the curve exhibits complex behavior. The paper concludes with illustrated examples. The research is clearly reported in a well-structured form. The paper is readable and about the right length to comprehend in one reading. It would benefit from even more diagrams to explain the relationship between the coordinate systems. Special cases bedevil work in computer modeling. The limits of the algorithms in such special cases could be explained more clearly. The work is warmly recommended. Despite the current performance limitations, it is highly relevant to workers who wish to improve a designer's understanding of a computer model by providing him with a realistic image.
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