Cartesian Coordinate System Scan Conversion

Cartesian coordinate system scan conversion refers to the process of converting geometrical representations into raster images in computer graphics.

It involves mapping mathematical representations of shapes defined in a cartesian (x,y) coordinate system to pixel positions on a discrete grid.

Common examples include scan converting lines, circles etc. This rasterization process transforms the continuous coordinates into discrete pixels.

Key aspects include determining which pixels to activate based on the math coordinates and handling corner/edge cases properly.

Solution

Here is code to scan convert a line from (x1,y1) to (x2,y2) using Digital Differential Analyzer (DDA) algorithm:

Java

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void scanConvertLine(int x1, int y1, int x2, int y2) {
  
  int dx = x2 - x1;
  int dy = y2 - y1;

  float steps = abs(dx) > abs(dy) ? abs(dx) : abs(dy);
  
  float xInc = dx/steps; 
  float yInc = dy/steps;

  float x = x1;
  float y = y1;

  for (int i=0; i<steps; i++) {
    setPixel(Math.round(x), Math.round(y));
    x += xInc;
    y += yInc;
  }
}

C++

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void scanConvertLine(int x1, int y1, int x2, int y2) {

  int dx = x2 - x1;
  int dy = y2 - y1;

  float steps = abs(dx) > abs(dy) ? abs(dx) : abs(dy);

  float xInc = dx/steps;
  float yInc = dy/steps;

  float x = x1; 
  float y = y1;

  for (int i=0; i<steps; i++) {
    setPixel(round(x), round(y));
    x += xInc; 
    y += yInc;
  }
}

Python

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def scan_convert_line(x1, y1, x2, y2):
  
  dx = x2 - x1
  dy = y2 - y1

  steps = abs(dx) if abs(dx) > abs(dy) else abs(dy)

  x_inc = dx/steps
  y_inc = dy/steps

  x = x1 
  y = y1

  for i in range(steps):
    set_pixel(round(x), round(y))
    x += x_inc
    y += y_inc

This implements DDA line scan conversion by linear incremental interpolation between end points.

Description: Cartesian Coordinate System Scan Conversion

Cartesian Coordinate System Scan Conversion is a technique in computer graphics for rendering geometrical shapes onto a raster display. Essentially, it’s a way to convert mathematical equations of geometrical shapes to pixels on a grid. It is widely used for drawing shapes such as lines, circles, and polygons.

Solution:

Here are sample implementations of the line-drawing algorithm using Cartesian Coordinate System Scan Conversion in Java, C++, and Python.

Java

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public class CartesianConversion {
    public static void drawLine(int x1, int y1, int x2, int y2) {
        int dx = x2 - x1;
        int dy = y2 - y1;
        int x = x1;
        int y = y1;
        
        for (int i = 0; i <= dx; i++) {
            System.out.println("Pixel at: (" + x + "," + y + ")");
            x++;
            y += dy/dx;
        }
    }

    public static void main(String[] args) {
        drawLine(0, 0, 5, 5);
    }
}

C++

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#include <iostream>

void drawLine(int x1, int y1, int x2, int y2) {
    int dx = x2 - x1;
    int dy = y2 - y1;
    int x = x1;
    int y = y1;
    
    for (int i = 0; i <= dx; i++) {
        std::cout << "Pixel at: (" << x << "," << y << ")\n";
        x++;
        y += dy/dx;
    }
}

int main() {
    drawLine(0, 0, 5, 5);
    return 0;
}

Python

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def drawLine(x1, y1, x2, y2):
    dx = x2 - x1
    dy = y2 - y1
    x = x1
    y = y1
    
    for i in range(dx + 1):
        print(f"Pixel at: ({x}, {y})")
        x += 1
        y += dy/dx

if __name__ == "__main__":
    drawLine(0, 0, 5, 5)

Key Takeaways:

Cartesian Coordinate System Scan Conversion is crucial in computer graphics for rendering geometrical shapes.
The technique uses mathematical formulas to find the appropriate pixels to color in order to form a shape.
The sample code illustrates a simple line-drawing algorithm, showing how you can convert the coordinates of a line into pixels.