Line DDA Algorithm (Digital Differential Analyer)

Explanation

This C code implements the Digital Differential Analyzer (DDA) algorithm, a fundamental line-drawing algorithm in computer graphics, to draw a simple face-like figure on the screen. It utilizes the graphics.h library, which is a legacy library primarily used with DOS-based compilers like Turbo C/C++.

The core logic resides in the lineDDA function. This function takes the starting coordinates (xa, ya) and ending coordinates (xb, yb) of a line segment. It calculates the difference in x (dx) and y (dy) coordinates. To draw the line, it determines which axis (x or y) has the larger absolute difference. This larger difference dictates the number of "steps" needed to draw the line. It then calculates small increments (xInc, yInc) for x and y for each step. Starting from the initial point, it iteratively adds these increments to the current x and y coordinates, rounding them to the nearest integer before plotting each pixel using putpixel. This process effectively "walks" along the line, plotting individual pixels to form a continuous segment.

The main function initializes the graphics mode using initgraph, which sets up the graphical display. It then makes multiple calls to the lineDDA function with different coordinate pairs. Each call draws a specific line segment. Together, these segments form a simple outline of a face: an outer square for the head, two smaller squares for eyes, a triangular nose, a rectangular mouth, and two triangular ears. Finally, getch() waits for a key press before closegraph() shuts down the graphics system and returns to text mode.

Algorithm

The Digital Differential Analyzer (DDA) algorithm for line drawing, as implemented in this code, follows these steps:

1. Input: Obtain the starting coordinates (xa, ya) and ending coordinates (xb, yb) of the line.
2. Calculate Differences: Compute the differences in x and y coordinates:
   • dx = xb - xa
   • dy = yb - ya
3. Determine Steps: Find the number of steps required to draw the line. This is determined by the larger absolute difference between dx and dy.
   • If |dx| > |dy|, then steps = |dx|.
   • Else, steps = |dy|.
   • This ensures that the line is sampled at least once per unit along the dominant axis, preventing gaps.
4. Calculate Increments: Determine the fractional increments for x and y for each step.
   • xInc = dx / (float) steps
   • yInc = dy / (float) steps
   • Casting steps to float is crucial to ensure floating-point division.
5. Initialize Current Position: Set the current plotting position to the starting point:
   • x = xa
   • y = ya
6. Plot Initial Pixel: Plot the starting pixel by rounding the current x and y coordinates to the nearest integer.
   • putpixel(ROUND(x), ROUND(y), WHITE)
7. Iterate and Plot: Loop steps times to draw the rest of the line:
   • In each iteration k (from 0 to steps - 1):
     • Update the current x and y coordinates:
       • x = x + xInc
       • y = y + yInc
     • Plot the new pixel by rounding the updated x and y coordinates to the nearest integer.
       • putpixel(ROUND(x), ROUND(y), WHITE)