Let's Make it Work!

Problem: lineSimple( ) does not give satisfactory results for slopes > 1

Solution: symmetry
 

public void lineImproved(int x0, int y0, int x1, int y1, Color color) {
    int pix = color.getRGB();
    int dx = x1 - x0;
    int dy = y1 - y0;

    raster.setPixel(pix, x0, y0);
    if (Math.abs(dx) > Math.abs(dy)) {          // slope < 1
        float m = (float) dy / (float) dx;      // compute slope
        float b = y0 - m*x0;
        dx = (dx < 0) ? -1 : 1;
        while (x0 != x1) {
            x0 += dx;
            raster.setPixel(pix, x0, Math.round(m*x0 + b));
        }
    } else
    if (dy != 0) {                              // slope >= 1
        float m = (float) dx / (float) dy;      // compute slope
        float b = x0 - m*y0;
        dy = (dy < 0) ? -1 : 1;
        while (y0 != y1) {
            y0 += dy;
            raster.setPixel(pix, Math.round(m*y0 + b), y0);
        }
    }
}
Lecture 5 Slide 6 6.837 Fall '98

It doesn't make sense to begin optimizing an algorithm before satisfies its design requirements! Code is usually developed under considerable time pressures. If you start optimizing before you have a working prototype you have no fall back position.

Our simple line drawing algorithm does not provide satisfactory results for line slopes greater than 1. The solution: symmetry. The assigning of one coordinate axis the name x and the other y was an arbitrary choice. Notice that line slopes of greater than one under one assignment result in slopes less than one when the names are reversed.

[Slope change after swapping axes]

We can modify the lineSimple( ) routine to exploit this symmetry as follows: 

    public void lineImproved(int x0, int y0, int x1, int y1, Color color)
    {
        int pix = color.getRGB();
        int dx = x1 - x0;
        int dy = y1 - y0;

        raster.setPixel(pix, x0, y0);
        if (Math.abs(dx) > Math.abs(dy)) {          // slope < 1
            float m = (float) dy / (float) dx;      // compute slope
            float b = y0 - m*x0;
            dx = (dx < 0) ? -1 : 1;
            while (x0 != x1) {
                x0 += dx;
                raster.setPixel(pix, x0, Math.round(m*x0 + b));
            }
        } else
        if (dy != 0) {                              // slope >= 1
            float m = (float) dx / (float) dy;      // compute slope
            float b = x0 - m*y0;
            dy = (dy < 0) ? -1 : 1;
            while (y0 != y1) {
                y0 += dy;
                raster.setPixel(pix, Math.round(m*y0 + b), y0);
            }
        }
    }