DDA Line Drawing

CSC-214 · Semester III · Computer Graphics

beginner20 minAvailable

DDA Line Drawing

Digital differential analyzer — stepping by the larger delta.

x0y0x1y1

Current pixel

step 0: x=2.0, y=2.0 → pixel (2,2)

Algorithm

Compute dx, dy; steps = max(|dx|, |dy|).
x_inc = dx/steps, y_inc = dy/steps.
Start at (x0,y0); repeatedly add increments and round to the nearest pixel.

This example: dx=33, dy=15, steps=33.

Lab brief

Objective

Plot a line between two endpoints with the DDA algorithm and observe how rounding maps continuous coordinates to pixels.

Theory & concepts

The DDA algorithm samples a line at unit steps along the dominant axis. It computes dx, dy and takes steps = max(|dx|, |dy|) increments of (dx/steps, dy/steps), plotting the rounded position each time. The visualization animates the cursor and shows the ideal line overlaid on the pixel grid.

Rendering diagram…

DDA line drawing loop

steps = max(|dx|, |dy|)
xinc = dx / steps;  yinc = dy / steps
for k = 0..steps:  plot(round(x), round(y));  x += xinc;  y += yinc

Dominant axis

The axis with the larger endpoint difference. The algorithm always takes one pixel step per unit along this axis, which keeps the plotted line connected with no gaps.

Prerequisites

Lesson: DDA line drawing algorithm
Lesson: Scan conversion and the raster pipeline

Instructions

1Set the two endpoints of the line on the grid (e.g. (0, 0) and (6, 4)).
2Click Step to advance the DDA one increment at a time.
3Watch the cursor move by xinc and yinc and the rounding that selects each pixel.
4Use Play to run the full line and compare the plotted pixels with the ideal line.
5Try a steep line (dx < dy) and observe how the dominant axis changes the stepping.
6Reset and draw a vertical and a horizontal line; check that no rounding artifacts appear.

Tasks

Plot (0,0) to (6,4)
Step through the algorithm and record the seven plotted pixels.
Find the drift
Draw a long line and observe whether the last pixel deviates from the ideal endpoint.
Steep line
Draw a line with |dy| > |dx| and explain why the algorithm steps along y.

Self-check

The plotted pixels match the expected rounding of the DDA increments.
The student can explain the role of steps, xinc and yinc.
The student identifies floating-point accumulation drift on long lines.

Environment

pixel grid canvasendpoint pickerstep/play animationideal line overlaystep counter