An algorithm for drawing the curve f(x,y) = 0

Sutcliffe, Dale C.

doi:10.1093/comjnl/19.3.246

Cited by 21 publications

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“…The segments are traced by numbering the intersections in anticlockwise directions and numbering intersections 1 and 2 on the first edge and 3 and 4 on the second edge. The segments are then traced in the intervals [1,4] and [2,3]. The second case of four-intersections arises when an edge has two intersections and the remaining two intersections lie on two other edges of the triangle as shown in Fig.…”

Section: Mathematical Formulations and Contouring Algorithmsmentioning

confidence: 99%

“…When the number of intersections is 4, we can have ordering as given in Fig. 9(c) or (d), i.e., the two contour segments may lie either in the intervals [1,2] and [3,4] or in the intervals [1,4] and [2,3]. These two cases can be differentiated on the basis of locating a contour point in the interval [1,2] (or [1,4]) and determining whether the point lies inside the triangle or not.…”

Section: Mathematical Formulations and Contouring Algorithmsmentioning

confidence: 99%

“…There are three possible cases having the number of intersections 2 or 4 as shown in Fig. 10 When the number of intersections is 4, the contour line segments may lie either in the intervals [1,4] and [2,3] or in the intervals [1,2] and [3,4]. These two cases can be identified by deriving the coordinates of a contour point in a given interval and determining whether the contour point lies inside the triangle or not.…”

Section: Mathematical Formulations and Contouring Algorithmsmentioning

confidence: 99%

“…The scheme published by Meek and Beer [2] is based on linear interpolation on any isoparametric element surface in 2D domains. Sutcliffe [3] describes an algorithm which traces the curve f (x, y) = 0, in a region over which there is a method of calculating f , using a series of straight lines of length one and two times the step size assumed for the graph plotter or display unit. It does this by determining the sign of the function in the region of the curve and plotting a path between positive and negative values.…”

Section: Introductionmentioning

confidence: 99%

“…Number of intersections 4: intervals are[2,3] and[4,1]. Number of intersections 6: intervals are[2,3],[4,5] and[6,1].…”

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confidence: 99%

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Accurate contour plotting using 6-node triangular elements in 2D

Singh

2009

Finite Elements in Analysis and Design

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Section: Mathematical Formulations and Contouring Algorithmsmentioning

confidence: 99%

Section: Mathematical Formulations and Contouring Algorithmsmentioning

confidence: 99%

Section: Mathematical Formulations and Contouring Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Number of intersections 4: intervals are[2,3] and[4,1]. Number of intersections 6: intervals are[2,3],[4,5] and[6,1].…”

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Accurate contour plotting using 6-node triangular elements in 2D

Singh

2009

Finite Elements in Analysis and Design

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An interpolation method for an irregular net of nodes

Liszka¹

1984

Numerical Meth Engineering

188

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SUMMARYA local interpolation method for an irregular mesh of nodal points is proposed. The method is based on a Taylor expansion of the unknown function combined with the minimization of errors. Some numerical tests as well as a computer program are presented. Applicability and stability of the method are shown. By the appropirate definition of weighting coefficients, this method may be viewed as an interpolation or approximation in the sense of minimum deviation from given values. Applications in finite element and finite difference methods are shown.

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Algorithm 35 an algorithm for non-smoothing contour representations of two-dimensional arrays

Schultheis

1978

Computing

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--Zusammenfassung Algorithm 35. An Algorithm for Non-Smoothing Contour Representations of Two-Dimensional Arrays.The FORTRAN code calculates, plots and labels approximate contour lines z (x, y)= c for data that are given as a rectangular array z,k = z (x~, Yk). The present algorithm has been developed for the study of local energy minima and saddle points in nuclear fission theory. Here the precise assignment of contour lines to grid cells is essential whereas the degree of accuracy achieved within each grid cell is unimportant. Therefore, smooth contour plotting methods that envolve derivatives, small step sizes or curve fitting procedures (like those of Lewis [7], McLain [8], and Sutcliffe [9]) are less appropriate.The correct correspondence between curve and cell is particularly important for contours with degeneracies. Therefore, the present algorithm treats the problems of degenerate cells and degenerate nodes in a proper way. Degenerate nodes are treated without approximations by taking also the corners of each grid celt into account (cf. Fig.

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An algorithm for drawing the curve f(x,y) = 0

Cited by 21 publications

References 0 publications

Accurate contour plotting using 6-node triangular elements in 2D

Accurate contour plotting using 6-node triangular elements in 2D

An interpolation method for an irregular net of nodes

Algorithm 35 an algorithm for non-smoothing contour representations of two-dimensional arrays

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