An area-oriented analytical visibility method for displaying parametrically defined tensor-product surfaces

Hornung, Christoph; Lellek, Wolfgang; Rehwald, Peter; Straßer, Wolfgang

doi:10.1016/0167-8396(85)90025-1

Cited by 21 publications

(8 citation statements)

References 2 publications

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“…Object space techniques use geometric tests on the object descriptions to determine which objects overlap and where. Initiated by Appel's edge-intersection algorithm [1], the idea of quantitative invisibility which determines visible and invisible regions in advance was developed [9,18,11]. Image space approaches compute visibility only to the precision required to decide what is visible at a particular pixel, exemplified by [2].…”

Section: Introductionmentioning

confidence: 99%

“…Further, in both methods [22,17], visibility is determined for the endpoints of straight lines and hence, they fail to detect invisibility occurring in the interior region of a line when both endpoints are visible. To remove hidden lines from curved surfaces without polygonal approximation, Hornung et al [11] extended the idea of quantitative invisibility to bi-quadratic patches, and Newton's method was employed to solve for intersections between curves. Elber and Cohen [7] applied Hornung's technique to nonuniform rational B-splines and extended it to treat trimmed surfaces.…”

Section: Introductionmentioning

confidence: 99%

“…Nishita et al [21] used their Bezier Clipping technique for the hidden curve elimination. These methods [11,7,21] are aimed at eliminating the hidden curves from line drawings of surfaces (not shaded drawings). Krishnan and Manocha [16] presented an algorithm for the elimination of hidden surfaces using a combination of symbolic techniques and results from numerical linear algebra.…”

Section: Introductionmentioning

confidence: 99%

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Simultaneous Precise Solutions to the Visibility Problem of Sculptured Models

Seong

Elber

Cohen

2006

Geometric Modeling and Processing - GMP 2006

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We present an efficient and robust algorithm for computing continuous visibility for two-or three-dimensional shapes whose boundaries are NURBS curves or surfaces by lifting the problem into a higher dimensional parameter space. This higher dimensional formulation enables solving for the visible regions over all view directions in the domain simultaneously, therefore providing a reliable and fast computation of the visibility chart, a structure which simultaneously encodes the visible part of the shape's boundary from every view in the domain. In this framework, visible parts of planar curves are computed by solving two polynomial equations in three variables (t and r for curve parameters and θ for a view direction). Since one of the two equations is an inequality constraint, this formulation yields two-manifold surfaces as a zero-set in a 3-D parameter space. Considering a projection of the two-manifolds onto the tθ-plane, a curve's location is invisible if its corresponding parameter belongs to the projected region. The problem of computing hidden curve removal is then reduced to that of computing the projected region of the zero-set in the tθ-domain. We recast the problem of computing boundary curves of the projected regions into that of solving three polynomial constraints in three variables, one of which is an inequality constraint. A topological structure of the visibility chart is analyzed in the same framework, which provides a reliable solution to the hidden curve removal problem. Our approach has also been extended to the surface case where we have two degrees of freedom for a view direction and two for the model parameter. The effectiveness of our approach is demonstrated with several experimental results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simultaneous Precise Solutions to the Visibility Problem of Sculptured Models

Seong

Elber

Cohen

2006

Geometric Modeling and Processing - GMP 2006

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“…Critical points are intersection points between projected polygon primitives. The technique was extended to bi-quadratic patches in [12]. The primitives are subdivided at each critical point which guarantees that the interior of each segment has homogeneous visibility.…”

Section: Introductionmentioning

confidence: 99%

Hidden curve removal for free form surfaces

ElberGershon

CohenElaine

1990

SIGGRAPH Comput. Graph.

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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.

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“…These algorithms use different techniques employed in polygon-oriented methods. Strasser4 and Forest5 use a z-buffer algorithm; Griffiths'5'7 and Ohno's8 algorithms are based on depth comparison between points of a grid defined in the patch and some subpatches; Hornung et al 9 simply compute the boundaries of constant visibility areas in the patch.…”

mentioning

confidence: 99%

A parametric-space-based scan-line algorithm for rendering bicubic surfaces

1988

Computer-Aided Design

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In recent years hidden-surface-removal algorithms have been proposed to render curved surfaces, especially bicubic (or bipolynomial) patches. Most of these algorithms use the scan-line principle to determine the scene visibility. Lane, Carpenter, Whitted, and Blinn' proposed three different methods. The first algorithm is a subdivision method that stops when a desired degree of surface flatness is achieved. Then subpatches are approximated by polygons processed by a polygonoriented algorithm. Whitted's method computes the exact intersection of some curves in the patch with every scan plane and approximates the patch's intersection with the plane by a polygonal line defined by these points. The exact intersection curves are the cubics defining the boundaries of the patch, isoparametric curves in the patch, and cubic approximations of the silhouettes. Finally, Blinn proposes a method that is essentially a z-buffer algorithm in which numerical problems are simplified using the intersection of the scan planes with the boundaries and the silhouettes of the patch.Lane and Carpenter2 later improved and generalized their algorithm, and Schweitzer and Cobb3 proposed an algorithm similar to Whitted's method that offered higher quality silhouettes. Some methods compute curved-surface visibility in parametric space. These algorithms use different techniques employed in polygon-oriented methods. Strasser4 and Forest5 use a z-buffer algorithm; Griffiths'5'7 and Ohno's8 algorithms are based on depth comparison between points of a grid defined in the patch and some subpatches; Hornung et al.9 simply compute the boundaries of constant visibility areas in the patch.Griffiths'°has proposed a scan-line algorithm that does some work in the parametric plane. This algorithm obtains an approximation of the patch silhouettes in the parametric space. Griffiths' method approximates the intersection of the scan plane and the patch with chains of straight segments instead of considering the segments separately, as other algorithms do. In this way his method speeds up the visibility calculation considerably.We will present a new scan-line algorithm for curved surfaces that does most of the computations in the para-

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An area-oriented analytical visibility method for displaying parametrically defined tensor-product surfaces

Cited by 21 publications

References 2 publications

Simultaneous Precise Solutions to the Visibility Problem of Sculptured Models

Simultaneous Precise Solutions to the Visibility Problem of Sculptured Models

Hidden curve removal for free form surfaces

A parametric-space-based scan-line algorithm for rendering bicubic surfaces

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