write a c function to draw a bezier curve. the function to plot points is void plot(int x,int y)

google/gemma-4-12b-qat
To draw a Bézier curve, we use the formula for a Cubic Bézier Curve, which is the standard for smooth shapes in computer graphics.

A cubic Bézier curve is defined by four points:

P0: Start Point
P1: Control Point 1
P2: Control Point 2
P3: End Point
The formula for a point B(t) at time t (where t ranges from 0 to 1) is:
    B(t) = (1-t)^3*P0 + 3(1-t)^2*t*P1 + 3(1-t)*t^2*P2 + t^3*P3
 

C Implementation
Here is a clean, modular way to write this. I have used float for the calculations to ensure smoothness, as integer math would result in a very jagged line.



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

// The function provided by your environment
// (In a real scenario, this would draw to a screen or buffer)
void plot(int x, int y);

/**
 * Draws a cubic Bezier curve.
 * @param x0, y0: Start Point
 * @param x1, y1: Control Point 1
 * @param x2, y2: Control Point 2
 * @param x3, y3: End Point
 * @param steps:  Number of segments to calculate (higher = smoother)
 */
void drawBezier(float x0, float y0, float x1, float y1, 
                 float x2, float y2, float x3, float y3, int steps) {
    
    for (int i = 0; i <= steps; i++) {
        // t goes from 0.0 to 1.0
        float t = (float)i / (float)steps;
        
        // Calculate the coordinates using the cubic Bezier formula
        // B(t) = (1-t)^3*P0 + 3(1-t)^2*t*P1 + 3(1-t)*t^2*P2 + t^3*P3
        float invT = 1.0f - t;
        
        float x = (invT * invT * invT * x0) +
                   (3 * invT * invT * t * x1) +
                   (3 * invT * t * t * x2) +
                   (t * t * t * x3);
                   
        float y = (invT * invT * invT * y0) +
                   (3 * invT * invT * t * y1) +
                   (3 * invT * t * t * y2) +
                   (t * t * t * y3);
        
        // Call the provided plot function
        // We cast to int because plot expects integers
        plot((int)x, (int)y);
    }
}

// Example usage:
int main() {
    // Start at (10, 10), end at (100, 100) with some curves in between
    drawBezier(10, 10, 50, 150, 150, 50, 100, 100, 100);
    return 0;
}



Key Explanations:
The steps parameter: A Bézier curve is a mathematical line. To "draw" it on a pixel grid, we must sample it at many points. If steps is 10, you get a very jagged line. If steps is 100 or more, it looks like a smooth curve.
Type Casting: I used float for the internal math because t is a decimal (e.g., 0.5). I cast the final result to (int) inside the plot function because pixel coordinates are usually integers.
Complexity: This is an O(n) operation where n is the number of steps. It is very efficient and the standard way to render paths in engines like OpenGL or SVG.