DDA line drawing algorithm in C++

Drawing lines plays a pivotal role in computer graphics, whether we are developing a game, designing a user interface, or creating intricate visualizations. The Digital Differential Analyzer (DDA) line drawing algorithm emerges as a prevalent choice to facilitate this fundamental operation. In this blog post, we embark on a journey through the DDA algorithm, offering an original C++ implementation with code, illustrative examples, and output. Along the way, we'll delve into the algorithm's inner workings and its significance in the world of computer graphics.

The Inner Workings of the DDA Line Drawing Algorithm

The DDA algorithm, renowned for its simplicity and efficiency, empowers the creation of lines on a digital grid, such as a computer screen. The algorithm operates on a set of straightforward principles:

Determine the Change in Coordinates: The first step involves calculating the differences in the x and y coordinates between the two endpoints of the desired line. These differences, denoted as dx and dy, lay the foundation for subsequent computations.
Identify the Number of Steps: Next, we need to establish the number of steps required to traverse from one endpoint to the other. This step ensures that the algorithm accommodates both steep and shallow lines, and achieved by evaluating the maximum absolute difference between dx and dy.
Compute Incremental Values: The increments in the x and y directions, represented as x_increment and y_increment, are crucial. They determine how much the algorithm should move horizontally and vertically in each iteration.
Initialization of Loop and Coordinates: A loop is initialized, and the current coordinates are set to the starting point of the line. It serves as the anchor for the subsequent plotting of points.
Point Plotting Along the Line: The algorithm enters a loop where it repeatedly updates the current coordinates by adding x_increment and y_increment until it reaches the endpoint. At each iteration, a point with integer coordinates is plotted, collectively forming the line.

Implementation in C++:

We'll create a C++ function capable of drawing lines based on user-defined starting and ending points to bring the DDA line drawing algorithm to life. Below is the code implementation:

#include <iostream>
#include <cmath>
 
void drawLineDDA(int x1, int y1, int x2, int y2) {
    // Calculate dx and dy
    int dx = x2 - x1;
    int dy = y2 - y1;
    
    // Determine the number of steps
    int steps = std::max(std::abs(dx), std::abs(dy));
    
    // Calculate increments
    float x_increment = static_cast<float>(dx) / steps;
    float y_increment = static_cast<float>(dy) / steps;
    
    // Initialize current coordinates
    float x = static_cast<float>(x1);
    float y = static_cast<float>(y1);
    
    // Plot the initial point
    std::cout << "(" << x << ", " << y << ")" << std::endl;
    
    // Perform the line drawing
    for (int i = 0; i < steps; ++i) {
        x += x_increment;
        y += y_increment;
        std::cout << "(" << round(x) << ", " << round(y) << ")" << std::endl;
    }
}
 
int main() {
    int x1 = 2, y1 = 3;
    int x2 = 9, y2 = 8;
    
    std::cout << "Drawing a line from (" << x1 << ", " << y1 << ") to (" << x2 << ", " << y2 << "):" << std::endl;
    drawLineDDA(x1, y1, x2, y2);
    
    return 0;
}

Output

Drawing a line from (2, 3) to (9, 8):
(2, 3)
(3, 3)
(4, 4)
(5, 5)
(6, 6)
(7, 7)
(8, 7)
(9, 8)

Conclusion:

In summary, the Digital Differential Analyzer (DDA) line drawing algorithm stands as an indispensable asset within the domain of computer graphics. Its innate simplicity and computational efficiency makes it an attractive choice for rendering lines on digital grids, adeptly accommodating lines of varying gradients. By methodically plotting points along the trajectory of the line, the DDA algorithm ensures effective precision in graphic rendering.

Through our practical C++ implementation and the elucidating example provided, we have effectively demonstrated the algorithm's real-world application. It effortlessly connects designated points with lines, underlining its multifaceted utility.

The DDA algorithm's serves as a fundamental cornerstone for an array of graphics-related pursuits. Aspiring graphics programmers and enthusiasts can harness its capabilities as a steppingstone to delve deeper into the captivating universe of computer graphics. Its underlying principles furnish a robust comprehension of line drawing, forming a sturdy foundation for the creation of intricate and sophisticated visual artistry. In essence, the DDA algorithm endures as an invaluable instrument in the arsenal of anyone embarking on a journey into the domain of visual computing.

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