Fast line scan-conversion

Abstract

A major bottleneck in many graphics displays is the time required to scan-convert straight line segments. Most manufacturers use hardware based on Bresenham's [5] line algorithm. In this paper an algorithm is developed based on the original Bresenham scan-conversion together with the symmetry first noted by Gardner [18] and a recent double-step technique [31]. This results in a speed-up of scan-conversion by a factor of approximately 4 as compared to the original Bresenham algorithm. Hardware implementations are simple and efficient since the property of using only shift and increment operations is preserved.

Directly Rasterizing Straight Line by Calculating the Intersection Point

“…Consider line from (0, 1) to (6,4). Rastering this line yields initial calculations: x=0, y=1, deltax=6, deltay=3, pixelnum=0, and pixelseq=0.…”

“…In Bresenham's algorithm, the next point is obtained by checking the sign of error, and only integer computation is used in inner loop calculating. With regard to Bresenham's middle algorithm, there are many fast algorithms and implementations, such as in [2], [3], [4], [5], [6], [7], and [8]. Some of these methods emphasize on the distribution of line's direction; others require that the line drawn is not to be very short.…”

Aplicaciones de la aritmética en coma fija a la representación de primitivas gráficas de bajo nivel.

“…5. Combinar soluciones ya existentes para obtener mejoras [ROKNE90] basándose en el algoritmo de Bresenham, aplicando las matrices 2x2 [WU87] y el dibujo simétrico desde los dos extremos simultáneamente hacia el centro de Gardner. Teóricamente se deberían obtener mejoras del orden de un 400%.…”

“…[RANKI91], [GRAHA95] Sincretista [ROKNE90] Degeneración de splines cúbicas [SMITH89] División de la recta en subsegmentos [CHEN97] Mejora Interpolación lineal [ROKNE92], [GRAHA94] Aritmética en coma flotante D.D.A. [ARMST73] [ NEWMA79] Máquinas masiv.…”

“…Aplicar la teoría del doble paso ya utilizada por Wu [WU87] o Rokne [ROKNE90] en líneas a los círculos [WU89]. Este método puede llegar a acelerar hasta un 65% en la práctica la versión de Pitteway [PITTE67].…”