Hidden Line Algorithm Research Articles

Hidden-line algorithm based on range searching

An algorithm for curved surfaces is presented that uses a searching technique to eliminate the hidden lines. The visibility determination for the grid points, and the bisection process for the intermediate points, are carried out in such a way that they are reduced to orthogonal range queries, a special form of range-searching problems. Given a point set in the plane and a rectangle, an orthogonal range query asks for the points that lie in the rectangle. A simple cell-list structure is used to process the queries. A linear time growth with respect to the number of grid points can be expected, as shown by test results given for grids of up to 60 000 points.

Removal of hidden lines by recursive subdivision

A new hidden-line algorithm is proposed for illustrating objects whose faces are plane or nearly plane polygons. The algorithm shows how the number of comparisons between edges and edges, and between faces and segments can be reduced by recursively subdividing the picture before analysing it. The algorithm overcomes some of the shortcomings of purely sorting strategies and it is particularly intended for illustrating complex objects. Illustrations are provided as examples.

Hidden-line algorithm for curved surfaces

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.

A hidden-line algorithm for graphical reconstruction of serially sectioned objects.

An algorithm for hidden-line removal in graphical reconstructions of serially sectioned biological objects is developed for PC-like computer configurations. The aim is to handle complicated structures defined by vast numbers of coordinate pairs and intersections between contours, without requiring excessive computing time. The procedure depends upon a fast searching routine for the localization of intersections and visibility.

Algorithm for splitting planar faces

An algorithm is presented that converts an object, defined by a set of intersecting planar faces, to a set of nonintersecting faces — that is, it splits the faces that intersect each other into several smaller faces that touch only at common edges and vertices. All singularities are handled in a uniform manner. The algorithm is currently used as a preprocessor for a hidden-line algorithm and as a component of a solid modeller.

A geometric hidden-line processing algorithm

This paper presents a new geometric hidden-line algorithm applicable to complex three-dimensional vector graphics scenes. The algorithm has advantages of generality, coding simplicity, and is particularly appropriate to parallel processing. The algorithm works accurately for any axonometric or oblique projection and can be adapted to work with the central projection. It applies to any nuimber of three-dimensional polyhedral objects which may have holes partially or fully through them, or other shape complexities. The algorithm does not require any particular ordering of polygon vertices and operates in both object and image space. An application of this algorithm to a computer aided learning package for engineering students is described.

A microcomputer-based graphical reconstruction technique for serial sectioned objects, with hidden line removal.

The presented software package fulfills the need for processing serial sections with a microcomputer configuration, enabling three-dimensional reconstruction with hidden line removal. The language used is an interpreted BASIC-dialect (HPL). The input is performed via an interactive program. The object can be rotated in space. The Hidden Line algorithm does not depend upon a raster technique. Points of intersection of successive contours are calculated and inserted, thus providing drawings of high resolution and quality. The handling time can be said to be short, especially when considering the capacities of the microcomputer configuration used.

Classification of edges and its application in determining visibility

A new hidden-line algorithm is proposed for illustrating objects consisting of plane faces. The algorithm determines the degree of edge and classifies edges and faces into contoural and non-contoural. To reduce memory requirements, sequential files and sorting are used. The algorithm is particularly intended for illustrating complex objects, eg curved surfaces approximated by plane faces.

A simple linear hidden-line algorithm for star-shaped polygons

A very simple, linear-running-time algorithm is presented for solving the hidden-line problem for star-shaped polygons. The algorithm first decomposes the visibility regions into edge-visible polygons and then solves the hidden-line problem for these simpler polygons. In addition to simplicity the algorithm possesses the virtue of affording a very easy proof of correctness. Some applications where this problem arises are mentioned.

Interactions of molecules with nucleic acids. IX. Evaluation and presentation of electrostatic contours on a steric surface with the removal of hidden lines

AbstractA technique to generate electrostatic contours on a steric surface is presented and applied to the presentation of molecules that interact with DNA. A set of electrostatic points at predetermined values along with their derivatives are obtained on the steric contours as they are generated. The steric contours are generated in a set of parallel planes. Points with given electrostatic values are then connected between and within the contours mathematically with a Taylor's expansion and two rules: the first to tentatively line up points that can be connected, and the second to check to insure that the remaining points can be connected. This method insures that contours will not cross by requiring that a possible connection of two points leaves an even number of remaining points for each electrostatic value in isolated regions of unused points bounded by points that have already been connected. The hidden line algorithm used previously to draw molecules in a space‐filling model within the context of steric contours is applied to the complete problem of the presentation of a molecule bound to DNA with steric contours in parallel planes, and with electrostatic contours drawn on this steric surface.

Applications of a two-dimensional hidden-line algorithm to other geometric problems

Recently ElGindy and Avis (EA) presented anO(n) algorithm for solving the two-dimensional hidden-line problem in ann-sided simple polygon. In this paper we show that their algorithm can be used to solve other geometric problems. In particular, triangulating anL-convex polygon and finding the convex hull of a simple polygon can be accomplished inO(n) time, whereas testing a simple polygon forL-convexity can be done inO(n 2) time.

A Hidden-Line Algorithm for Hyperspace

An object-space hidden-line algorithm for higher-dimensional scenes has been designed and implemented. Scenes consist of convex hulls of any dimension, each of which is compared against the edges of all convex hulls not eliminated by a hyperdimensional clipper, a depth test after sorting and a minimax text. Hidden and visible elements are determined in accordance with the dimensionality of the selected viewing hyperspace. When shape alone is the attribute of interest, hidden-line elimination need be performed only in that hyperspace. The algorithm is of value in the production of shadows of hyperdimensional models, including but not limited to four-dimensional space-time models, the hyperdimensional elementary catastrophe models and multivariate statistical models.

Hidden-line algorithm for scenes of high complexity

A new approach to the hidden-line problem is presented. The main tools of the method are calculation of edge intersections, test on appearance or disappearance of edges, and record sort. Special treatment of coherence and singularities is required. The programs are written in FORTRAN and are very short and simple. The computation time of the algorithm is short enough to handle scenes of high complexity.

An exact hidden sphere algorithm that operates in linear time

This paper presents an exact hidden line algorithm, SPHERES, that operates in linear expected time. The algorithm is exact because it works in object space, and so calculates the visible lines accurately to within the floating point tolerance of the host machine. In contrast to all image space algorithms, SPHERES' calculations take no more time for a high-resolution display. SPHERES operates on a 3-D scene composed of spheres, as in a space-filling molecular model, but nothing in the underlying concepts depends on this. In contrast to all other hidden line algorithms, SPHERES' execution time does not depend much on the depth complexity of the scene, even if it is as high as 30. This has been verified experimentally, as has the linear time dependence on the number of input spheres, up to 10,000.

Tape-oriented hidden-line algorithm

A hidden line algorithm for a restricted class of objects is presented. Internal memory requirements are reduced by sequencing geometrical data on magnetic tapes. The object is represented by a data structure which changes dynamically as the object is scanned. Statistical methods are used to predict an optimal configuration for the structure. A new point-in-polygon test is introduced. The algorithm is compared quantitatively with an earlier method. Examples of pictures are given.

NUDES 2

A system is described for producing 16 mm animated films of moving humanoid figurines and other figures composed of concatenated articulated interpenetrating ellipsoids. For such figures, the hidden line algorithm used consists in solving the quartic equations which result from simultaneous pairs of ellipses viz. (a) the projection of the outline of one being drawn, and (b) that of one potentially obscuring it. This is done in terms of Cohen's parameter, resulting in an ordered list of compacted hidden arcs of each outline. The visible outlines are then generated to the required fidelity separately. Where two ellipsoids interpenetrate, the outline of each is drawn up to the points where it disappears into the other. These points can be found by the simultaneous solution of the ellipse equations of (a) the projection of the outline being drawn, and (b) the projection of the ellipse of intersection of the obscuring ellipsoid with the plane of the outline of the drawn ellipsoid. The viewing window is assumed to be an ellipse also. Parts of objects projecting outside this ellipse are not drawn. The number of quartics to be solved is reduced significantly by testing each pair of ellipsoids for non-intersection of projected outlines by comparing the projected separation of centres with the sum of their maximum semiaxis lengths, and taking advantage of the total obscuration of one ellipsoid by another when discovered.

A system for sculpting 3-D data

A major research area in 3-D computer graphics is the inputting of complex descriptions. This paper describes our current attempt at solving that problem: creation of a sculptor's studio-line environment in which the user is provided with various tools to shape, cut and join objects. The emphasis of the implementation has been on naturalness and habitability. The issues involved in designing such a system, especially in a minicomputer-based color raster-scan animation environment, are discussed. The basic algorithms are described in some detail and a fast efficient implementation of a hidden-line algorithm is explained.

Computer Graphics for 3-D Finite Element Models

A description is given of a computer graphics program for detecting errors in three-dimensional finite element models and reducing finite element analysis data to a usable form. An efficient hidden line algorithm for mixed sets of polygons and polyhedra is presented together with a general line classification scheme. They are used to produce the variety of plots necessary to detect errors in the model. They also provide an “uncluttered” surface for displaying stress, temperature, and displacement data.