Line Drawing Algorithm Research Articles

Parallel line drawing algorithm based on probability theory and mathematical morphology

Parallel lines drawing frequently happens in the Geographic Information System (GIS) development.In the traditional drawing algorithms,nodes of parallel lines are in the opposite direction or far away from the polyline when the angle is very small.To solve these two cases,a correction method based on probability theory was proposed.At the same time,mathematical morphology was adopted to correct the results,which made it aesthetic,and made the very sharp angle smooth.The experimental results show that the proposed algorithm is effective.

Real-Time Shape Illustration Using Laplacian Lines

This paper presents a novel object-space line drawing algorithm that can depict shapes with view-dependent feature lines in real time. Strongly inspired by the Laplacian-of-Gaussian (LoG) edge detector in image processing, we define Laplacian lines as the zero-crossing points of the Laplacian of the surface illumination. Compared to other view-dependent feature lines, Laplacian lines are computationally efficient because most expensive computations can be preprocessed. We further extend Laplacian lines to volumetric data and develop the algorithm to compute volumetric Laplacian lines without isosurface extraction. We apply the proposed Laplacian lines to a wide range of real-world models and demonstrate that Laplacian lines are more efficient than the existing computer generated feature lines, and can be used in interactive graphics applications.

Dissections, orientations, and trees with applications to optimal mesh encoding and random sampling

We present a bijection between some quadrangular dissections of an hexagon and unrooted binary trees with interesting consequences for enumeration, mesh compression, and graph sampling. Our bijection yields an efficient uniform random sampler for 3-connected planar graphs, which turns out to be determinant for the quadratic complexity of the current best-known uniform random sampler for labelled planar graphs. It also provides an encoding for the set P ( n ) of n -edge 3-connected planar graphs that matches the entropy bound 1/ n log 2 | P ( n )| = 2 + o (1) bits per edge (bpe). This solves a theoretical problem recently raised in mesh compression as these graphs abstract the combinatorial part of meshes with spherical topology. We also achieve the optimal parametric rate 1/ n log 2 | P ( n , i , j )| bpe for graphs of P ( n ) with i vertices and j faces, matching in particular the optimal rate for triangulations. Our encoding relies on a linear time algorithm to compute an orientation associated with the minimal Schnyder wood of a 3-connected planar map. This algorithm is of independent interest, and it is, for instance, a key ingredient in a recent straight line drawing algorithm for 3-connected planar graphs.

Drawing lines by uniform packing

In this paper, we introduce a new approach to line drawing that attempts to maintain a uniform packing density of horizontal segments to diagonal segments throughout the line. While the conventional line drawing algorithms perform linear time computations to find the location of the pixels, our algorithm takes logarithmic time. Also, experimental results show that the quality of line is acceptable and comparable to the well-known Bresenham's line-drawing algorithm.

BRDC: binary representation of displacement code for line

In raster graphics, a line is displayed as a sequence of connected pixels that best approximate the line with minimum deviation. The displacement code of a line is a sequence of binary codes, each of which represents the displacement of a pixel on the line to its immediate predecessor pixel on the line. In fact, the displacement code records the entire process of drawing a line with successive pixels and it is deterministic for each specific line. In this paper, we study the important properties of the binary representation of displacement code, called BRDC, including calculation formula, periodicity, complement, decomposition etc. At last, we put forward an efficient adaptive multi-pixel line drawing algorithm based on exploited properties of BRDC, which demonstrates that BRDC is significant for designing efficient line drawing algorithms.

Running the line: Line drawing using runs and runs of runs

The efficiency of line drawing algorithms underwrites the performance of many rendering and visualisation systems. Therefore to significantly improve the process of line drawing, techniques have been developed to draw the line not pixel by pixel but by using higher order primitives such as runs and run length slices. In this paper we present a line drawing algorithm based on runs of runs, which is the next step in this progression. We will also discuss a number of special cases in the structure of runs and runs of runs within the line that can be used to short circuit the drawing process. These special cases can be used to help counter a common criticism that run-based techniques are less applicable for very short lines. In fact we will argue that the use of higher order primitives provides additional structural information that can be used to accelerate secondary processes within the graphics system, such as within the raster memory management.

A new antialiased line drawing algorithm

Consider a line f (x)=mx+b , 0⩽ m ⩽1 . Conventional line drawing algorithms sample (x, f (x)) on the line, where x must be an integer, and then map (x, f (x)) to the frame buffer according to the defined filter and f (x) . In this paper, we propose to simulate a sampled point (x, f (x)) by the four pixels around it where x and f (x) are not necessary to be integers. Based on the proposed low-pass filtering, we show that the effect of sampling at infinite number of points along a line segment can be achieved since the closed form of the intensities assigned to pixels exists. Furthermore, we show the coherence properties that can reduce the cost for computing these intensities.

A fast black run rotation algorithm for binary images

In this article, we propose a fast black run rotation algorithm. We rotate an image efficiently by extracting the two end points of black runs and adopting a line drawing algorithm. We could achieve more than twice the speed-up compared with the other rotation methods and successfully eliminate the holes existing on a rotated plane by using the run breakdown method.

Bi-directional incremental linear interpolation

Two algorithms for incremental linear interpolation are developed. The first algorithm is a double-step bi-directional linear interpolation algorithm which is derived based on a previously developed double-step linear interpolation algorithm. The second algorithm carries the ideas of the first algorithm further to develop a double-step bi-directional run-length slice line drawing algorithm.

Hidden-curve algorithm for correct grid surface representation of functions of two variables

A common method for visualizing a function of two variables is to consider it as a nontransparent grid surface in 3-D space and to project it onto a view plane. Various computer algorithms exist which map such surfaces onto a screen. Each of these conventional techniques has its own disadvantage: either the graphical results are not very accurate, because the algorithm approximates the surface by a polygon mesh consisting of quadrilaterals or, indeed, the algorithm produces sufficiently true images of the grid curves, but is restricted to special viewing conditions. This paper gives details and a pseudocode of a new, universal line-drawing algorithm which yields correct images of grid surfaces conserving their geometrical properties such as smoothness or discontinuities. The functions to be represented may be continuous or piecewise continuous. Almost any position of the surface in relation to the viewer's eye and in relation to the view plane can be chosen and any parallel or perspective projection can be applied.

Improved recursive bisection line drawing algorithms

In this paper, we present modifications which reduce the logarithmic space requirements of an existing fractal line drawing algorithm to a constant while increasing its speed. The resulting algorithm is faster than many existing line drawing algorithms, especially when the lines being drawn are at or near horizontal, diagonal and vertical. Furthermore, a detailed error analysis of these algorithms is given.

Double- and triple-step incremental linear interpolation

Incremental linear interpolation determines the set of n+1 equidistant points on an interval [a,b] where all variables involved (n, a, b, and the set of equidistant points) are integers and n>0. Our method of linear interpolation generalizes the findings of a variable-step line-drawing algorithm. The resulting interpolation algorithm has as many loops as the line-drawing algorithm, but fewer restrictions on its input variables. Furthermore, its benefits over the fixed-step interpolation algorithms are similar to those of the variable-step line-drawing algorithm. That is, the double- and triple-step interpolation algorithm can reduce the number of loop iterations of the double-step interpolation algorithm (by 12.5% on average) while keeping the code complexity, initialization costs, and worst-case performance the same. The improvement in speed over the single-step B5 algorithm is even greater. >

Parallel solutions to geometric problems in the scan model of computation

This paper describes several parallel algorithms that solve geometric problems. The algorithms are based on a vector model of computation-the scan model . The purpose of this paper is both to show how the model can be used and to formulate a set of practical algorithms. The scan model is based on a small set of operations on vectors of atomic values. It differs from the P-RAM models both in that it includes a set of scan primitives, also called parallel prefix computations, and in that it is a strictly data-parallel model. A very useful abstraction in the scan model is the segment abstraction, the subdivision of a vector into a collection of independent smaller vectors. The segment abstraction permits a clean formulation of divide-and-conquer algorithms and is used heavily in the algorithms described in this paper. Within the scan model, using the operations and routines defined, the paper describes a k -D tree algorithm requiring O (lg n ) calls to the primitives for n points, a closest-pair algorithm requiring O (lg n ) calls to the primitives, a line-drawing algorithm requiring O (1) calls to the primitives, a line-of-sight algorithm requiring O (1) calls to the primitives, and finally, three different convex-hull algorithms. The last convex-hull algorithm, merge-hull, utilizes a generalized binary search technique using divide-and-conquer with the segment abstraction. The paper also describes how to implement the CREW version of Cole's merge sort in O (lg n ) calls to the primitives. All these algorithms should be noted for their simplicity rather than their complexity; many of them are parallel versions of known serial algorithms. Most of the algorithms discussed in this paper have been implemented on the Connection Machine, a highly parallel single instruction multiple data computer.

A Run-Length Slice Line Drawing Algorithm without Division Operations

Of the two major approaches to line drawing, run-length slice algorithms are seldom used because of the division operation deemed necessary in these algorithms. The biggest advantage of these algorithms, the reduction of additions used, is considered outweighed by the division used. In this paper, a new run-length slice algorithm that does not require a division operation is presented. Furthermore, it uses the double-stepping paradigm in incremental line drawing algorithms to reduce the number of additions used by at least half. For sufficiently long lines, this algorithm uses at least 50% fewer arithmetic operations than Wu et al.'s bi-directional double-step incremental algorithm. But because of its high initialization cost, for short lines, it is less efficient. For a line with endpoints (0,0) and (δx, δy), the strategy is then to use the bi-directional Bresenham algorithm for very short lines (δx 110).

Scans as primitive parallel operations

A study of the effects of adding two scan primitives as unit-time primitives to PRAM (parallel random access machine) models is presented. It is shown that the primitives improve the asymptotic running time of many algorithms by an O(log n) factor, greatly simplifying the description of many algorithms, and are significantly easier to implement than memory references. It is argued that the algorithm designer should feel free to use these operations as if they were as cheap as a memory reference. The author describes five algorithms that clearly illustrate how the scan primitives can be used in algorithm design: a radix-sort algorithm, a quicksort algorithm, a minimum-spanning-tree algorithm, a line-drawing algorithm, and a merging algorithm. These all run on an EREW (exclusive read, exclusive write) PRAM with the addition of two scan primitives and are either simpler or more efficient than their pure PRAM counterparts. The scan primitives have been implemented in microcode on the Connection Machine system, are available in PARIS (the parallel instruction set of the machine).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Design and Performance Evaluation of EXMAN: An EXtended MANchester Data Flow Computer

Data flow computers are high-speed machines in which an instruction is executed as soon as all its operands are available. This paper describes the EXtended MANchester (EXMAN) data flow computer which incorporates three major extensions to the basic Manchester machine. As extensions we provide a multiple matching units scheme, an efficient, implementation of array data structure, and a facility to concurrently execute reentrant routines. A simulator for the EXMAN computer has been coded in the discrete event simulation language, SIMULA 67, on the DEC 1090 system. Performance analysis studies have been conducted on the simulated EXMAN computer to study the effectiveness of the proposed extensions. The performance experiments have been carried out using three sample problems: matrix multiplication, Bresenham's line drawing algorithm, and the polygon scan-conversion algorithm.

Incremental linear interpolation

Two incremental linear interpolation algorithms are derived and analyzed for speed and accuracy. The first is a version of a “simple” digital differential analyzer (DDA) employing fixed-point arithmetic, whereas the second is a new algorithm that uses only integral arithmetic and is a generalization of Bresenham's line-drawing algorithm. The new algorithm is shown to achieve perfect accuracy and, depending on the underlying processor, may be faster than the fixed-point algorithm.

Special Feature a New Approach to High-Speed Computer Graphics: The Line

The design of a better line drawing algorithm led to some general strategies for boosting software efficiency.