Lab-03-Circle-Raster

Lab 03 — Circle Drawing using Raster Graphics

Course: Computer Graphics (CSC209)
Semester: III
Author: Sanil Sthapit | github.com/Sanil-Sth

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📌 Title

Circle Drawing using Raster Graphics (Trigonometric / Polynomial Method)

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📖 Theory

A circle is defined as the set of all points at a fixed distance (radius r) from a center point (cx, cy). Mathematically:

(x - cx)² + (y - cy)² = r²

However, a computer screen is made of discrete pixels — so we cannot plot a continuous circle. We need an algorithm to decide which pixels to turn on so that they appear as a circle.

The Raster Graphics (Polynomial) Method is the most straightforward approach. It uses the equation of a circle directly:

• Step along the X axis from cx - r to cx + r
• At each X, calculate the corresponding Y using: y = sqrt(r² - (x - cx)²)
• Plot both (x, cy + y) and (x, cy - y) to draw both the upper and lower halves

Why plot both halves?

Because the square root always returns a positive value, only the upper half is computed. Negating it gives the lower half. Together they form a complete circle.

Advantages

• Simple and easy to understand
• Directly based on the mathematical definition of a circle

Disadvantages

• Uses floating point sqrt() — slow and computationally expensive
• Uneven pixel spacing — gaps appear on steep parts of the circle
• Not suitable for real-time or hardware rendering

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❓ Question

Write a program to draw a circle using the Raster Graphics (Polynomial) method.

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🔢 Algorithm

Step 1: Start
Step 2: Input center (cx, cy) and radius r
Step 3: Set x = cx - r
Step 4: Repeat while x <= cx + r:
            Calculate: y = sqrt(r*r - (x-cx)*(x-cx))
            Plot pixel at (x, cy + round(y))   ← upper half
            Plot pixel at (x, cy - round(y))   ← lower half
            x = x + 1
Step 5: Stop

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💻 Source Code

#include <stdio.h>
#include <conio.h>
#include <graphics.h>
#include <math.h>

void drawCircleRaster(int cx, int cy, int r, int color) {
    int x = cx - r;

    while (x <= cx + r) {
        // Calculate y using circle equation: x² + y² = r²
        double y = sqrt((double)(r * r) - (double)((x - cx) * (x - cx)));

        // Plot upper and lower halves
        putpixel(x, cy + (int)round(y), color);
        putpixel(x, cy - (int)round(y), color);

        x++;
    }
}

int main() {
    int gd = DETECT, gm;
    initgraph(&gd, &gm, (char*)"");

    int cx, cy, r;

    printf("Enter center (cx cy): ");
    scanf("%d %d", &cx, &cy);
    printf("Enter radius r: ");
    scanf("%d", &r);

    drawCircleRaster(cx, cy, r, WHITE);

    getch();
    closegraph();
    return 0;
}

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🖼️ Output

1. Console Output

Shows the user input for center and radius

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2. GUI Output

The BGI graphics window showing the circle drawn by the Raster method

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3. Zoomed Output

Zoomed in view showing individual pixels and gaps caused by the polynomial method

💡 The zoomed view clearly shows the limitation of the Raster method — uneven pixel gaps appear on steep sections of the circle because we only step along X, not along the curve itself.

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✅ Conclusion

In this lab, we successfully implemented the Raster Graphics (Polynomial) Circle Drawing Method in C using graphics.h. The program accepts a center and radius from the user and draws a circle by computing Y values directly from the circle equation.

While simple to understand, this method has clear limitations — it relies on floating point sqrt() at every step, making it slow, and it produces uneven pixel spacing leading to visible gaps. These limitations motivate the need for better algorithms like the Midpoint Circle Algorithm, which we will implement in Lab 04.

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Previous: Lab 02 — Bresenham's Line Drawing Algorithm
Next: Lab 04 — Midpoint Circle + Arc & Sector