画圆和画直线的算法说明.ppt

WHERE TO DRAW A LINE?? Line drawing is accomplished by calculating intermediate positions along the line path between specified end points. Precise definition of line drawing Given two points P and Q in the plane, both with integer coordinates, determine which pixels on a raster screen should be on in order to make a picture of a unit-width line segment starting from P and ending at Q. Line drawing (cont) The thinnest line is of one-pixel wide. We will concentrate on drawing a line of 1 pixel resolution. The Cartesian slope-intercept equation for a straight line is y= m. x + b m is the slope of the line and b is the y intercept. Given the endpoints of a line segment. m = y2-y1 / x2-x1 b= y1-m.x1 Line Drawing (cont) Also for any given interval ?x along a line, we can compute the corresponding y interval ?y from ?y= m. x Similarly we can obtain the x interval ?x corresponding to a specified ?y as ?x= ?y / m These equations form the basis for determining deflection voltages in analog devices. Line Drawing (cont) Also , for any given x interval ?x along a line, we can compute the corresponding y interval ?y from ?y= m. ? x These equations form the basis for determining deflection voltages in analog devices. On Raster systems, lines are plotted with pixels, and step sizes in the horizontal and vertical directions are constrained by pixel separations. Hence we ought to “sample” a line at discrete positions and determine the nearest pixel to the line at each sampled position. Symmetry If we could draw lines with positive slope (0=slope=1) we would be done. For a line with negative slope (0=slope=-1) We negate all Y values For a line with slope 1 or slope -1 we just swap x and y axes Code for drawing a line DDA ALGORITHM The digital differential analyzer (DDA) samples the line at unit intervals in one coordinate corresponding integer values nearest the line pat