1. Clipping

Clipping is the process of removing parts of graphics primitives (lines, polygons) that lie outside a defined viewing area or window.

• The viewing area is often called the clip window.
• Clipping ensures that only visible parts of objects are drawn, improving performance.

1.1 Types of Clipping

A. Point Clipping

• Check if a point lies inside or outside the clipping window.

B. Line Clipping

• Remove portions of a line outside the clip window.

• Common algorithms:

  1. Cohen–Sutherland Algorithm

     • Divides space into 9 regions.
     • Uses region codes to determine trivial acceptance or rejection.

  2. Liang–Barsky Algorithm

     • Uses parametric line equations for efficient clipping.

C. Polygon Clipping

• Remove portions of a polygon outside the clip window.

• Common algorithms:

  1. Sutherland–Hodgman Algorithm

     • Clips polygon edge by edge against each boundary.

  2. Weiler–Atherton Algorithm

     • Handles complex polygons and holes.

1.2 Example: Cohen–Sutherland Line Clipping

• Assign a 4-bit code to each endpoint based on position relative to window.

• Use logical AND/OR operations to decide if line is:

  • Completely inside → draw fully.
  • Completely outside → reject.
  • Partially inside → compute intersection with window boundaries.

2. Polygonal Fill

Polygonal fill is the process of coloring the interior of a polygon.

• After clipping, polygons may need to be filled for rendering solid shapes.
• Filling determines which pixels inside the polygon should take the polygon’s color.

2.1 Polygon Filling Algorithms

A. Scan-Line Algorithm

• Process the polygon row by row (scanlines).

• Steps:

  1. Compute intersections of polygon edges with the scanline.
  2. Sort intersections by x-coordinate.
  3. Fill pixels between pairs of intersections.

• Efficient and widely used.

B. Flood Fill Algorithm

• Start at a seed point inside polygon.
• Recursively (or iteratively) fill neighboring pixels until boundary is reached.
• Slower for large polygons; good for irregular shapes.

C. Boundary Fill Algorithm

• Similar to flood fill but uses boundary color instead of interior color for stopping.

2.2 Scan-Line Polygon Fill Example

For a polygon with vertices:

1. Determine Ymin and Ymax.

2. For each scanline from Ymin to Ymax:

   • Find intersection points with polygon edges.
   • Sort intersections by X.
   • Fill pixels between pairs of intersections.

3. Summary Table

Key Points:

• Clipping → ensures only visible parts of graphics primitives are drawn.
• Polygon fill → fills the interior of polygons for rendering solid objects.
• Scan-line and flood-fill are fundamental filling techniques, often used in raster graphics.