This paper describes a hidden curve algorithm specifically designed for sculptured surfaces. A technique is described to extract the visible curves for a given scene without the need to approximate the surface by polygons. This algorithm produces higher quality results than polygon based algorithms, as most of the output set has an exact representation. Surface coherence is used to speed up the process. Although designed for sculptured surfaces, this algorithm is also suitable for polygonal data.

http://www.visgraf.impa.br/Courses/npr07/materials/0%20intro/3%20lines/p95-elber.pdf

Hidden curve removal for free form surfaces

This paper describes a hidden curve algorithm specifically designed for sculptured surfaces. A technique is described to extract the visible curves for a given scene without the need to approximate...

Computing the visible portions of free-form surfaces from a given viewpoint is of great interest in many applications. It is closely related to the hidden surface removal problem in computer graphics and machining applications in manufacturing. Most of the earlier work has focused on discrete methods based on polygonization or ray-tracing, hidden curve removals and local visibility computations based on Gauss maps. In this paper we present an eecient and accurate algorithm for hidden surface and global visibility computations on free form surfaces. Given a viewpoint, it decomposes the domain of each surface based on silhouettes and boundary curves. To compute the exact visibility, we introduce a notion of \visibility curves" obtained by projection of silhouette and boundary curves and decomposing the surface into non-overlapping regions. These curves are computed using marching methods and we present techniques to compute all the components. The non-overlapping and visible portions of the surface are represented as trimmed surfaces and we present an eecient representation based on polygon trapezoidation algorithms. Given the non-overlapping regions, we use randomized algorithms for visibility computations from a given viewpoint. We demonstrate the performance of the algorithm on diierent models.

Global Visibility and Hidden Surface Removal Algorithms for Free Form Surfaces

Computing the visible portions of curved surfaces from a given viewpoint is of great interest in many applications It is closely related to the hidden surface removal problem in computer graphics and machining applications in manufacturing Most of the earlier work has focused on discrete methods based on polygonization or ray tracing and hidden curve removal In this paper we present an algorithm for hidden surface computations on curved surfaces Given a viewpoint it decomposes the domain of each surface based on silhouettes and boundary curves To compute the exact visibility we introduce a notion of visibility curves obtained by projection of silhouette and boundary curves and decomposing the surface into non overlapping regions These curves are computed using marching methods and we present techniques to compute all the components The non overlapping and visible portions of the surface are represented as trimmed surfaces and we present a representation based on polygon trapezoidation algorithms The algorithms presented use some recently developed algorithms from computational geometry like triangulation of simple polygons and point location Given the non overlapping regions we use a simple randomized algorithm for visibility computations from a given viewpoint Supported in part by a Sloan Fellowship university research council grant NSF grant CCR ONR contract N ARPA contract DABT C NSF ARPA Science and Technology Center for Computer Graphics Scienti c Visualization and NSF Prime contract No

Hidden Surface Removal Algorithms for Curved Surfaces

Shaded display is popular for displaying curved surfaces because of the realistic appearance of the images produced. In the field of computer aided geometric design, however, line drawings are more commonly used. For accurate evaluation of the curved surfaces in these designs, the conventional method of approximating curved surfaces with polygons is insufficient. In this paper we will present a method of hidden line elimination without resorting to polygonal approximation. The method provides the designer smoother, more precise iso-parametric curves than traditional polygonal approximation methods. In addition, the method can draw precise silhouette curves, trimming curves, drawings of patterns represented by curves on the surface, and contour lines. Furthermore, the method is valid even for surfaces which penetrate each other.

Hidden curve elimination of trimmed surfaces using Be´zier clipping

A hidden-line algorithm for displaying curved surfaces by line drawing is presented. The algorithm divides the screen plane into small rectangles, unlike Ohno's algorithm, which divides the screen space into small 3D boxes and exploits quadrilateral coherence and depth coherence. The present algorithm is better than Ohno's in both speed and main memory requirements. Quantitative comparisons are given and examples shown.

Hidden-line algorithm for curved surfaces

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Hidden-line algorithm for curved surfaces