Detailed Explanation with Examples
1. Fill-Area Primitives
Definition: An area in a graphical image filled with a solid color or pattern. Typically represented as
polygons with at least three vertices connected by edges.
Types of Polygons:
- Convex: All interior angles <= 180 degrees. Easier for graphics libraries like OpenGL to process.
- Concave: At least one interior angle > 180 degrees. Often split into convex polygons for simplicity.
Example: A rectangle (convex) and a star-shaped figure (concave).
2. Splitting Concave Polygons
Splitting concave polygons into convex components simplifies filling and processing.
Technique: Use a vector cross-product to find edges that need splitting. Extend edges to form new
vertices.
Example: For a star-shaped polygon, splitting results in multiple triangles.
3. Inside-Outside Tests
Purpose: Determine whether a point lies inside or outside a polygon.
- Odd-Even Rule: Draw a line from the point to infinity. Count edge crossings:
- Odd: Point is inside.
- Even: Point is outside.
- Nonzero Winding Rule: Consider edges as vectors. Add/subtract 1 based on edge orientation
(right-to-left or left-to-right). Nonzero result implies the point is inside.
Example: For a pentagon:
- Odd-Even Rule: A point inside crosses 3 edges.
- Nonzero Winding Rule: Adding vectors gives a nonzero result.
4. Polygon Tables
Used to store 3D objects as polygonal meshes:
- Vertex Table: Lists coordinates of each vertex.
- Edge Table: Links vertices to edges.
- Surface-Facet Table: Links edges to polygon surfaces.
Example: For a cube:
- Vertex table: (0, 0, 0), (1, 0, 0), ...
- Edge table: [(1, 2), (2, 3), ...].
- Surface-facet table: [(1, 2, 3, 4), ...].
5. Polygon Color Filling
Filling involves highlighting all interior pixels.
- Seed Fill:
- Picks a seed point inside the polygon.
- Expands outward until the boundary is reached.
- Types: 4-connected and 8-connected.
- Scan Line Algorithm:
- Identifies intersections of scan lines with edges.
- Fills between intersection pairs.
Example: Fill a triangle:
- Seed Fill: Starts from a center point.
- Scan Line: Scans from bottom to top edge.
6. Text and Characters
OpenGL lacks text routines but uses GLUT for rendering.
- Bitmap Fonts:
- Simple pixel grids.
- Fast rendering but not scalable.
- Example: glutBitmapCharacter(GLUT_BITMAP_9_BY_15, 'A').
- Stroke Fonts:
- Line/curve primitives.
- Scalable with transformations like glScalef.
- Example: glutStrokeCharacter(GLUT_STROKE_ROMAN, 'A').
Comparison: Bitmap fonts are faster but less flexible. Stroke fonts are slower but scalable.
Example Application:
Design a graphical interface with:
- Polygons: Draw a house using convex polygons for walls and roof.
- Filling: Use the scan line algorithm to color the house walls.
- Text: Display "My House" using stroke fonts for scalability.
