1. Computer Graphics- SCC 342
Chapter 4: Graphics Output Primitives
Dr. Doaa Hegazy

2. 2D Graphics Primitives
Graphics drawing is based on basic geometric structures called graphics primitives
Points
Lines
Circles
Conic Sections

3. 4.1 Coordinate Reference Frames
To describe a picture, first decide upon a convenient Cartesian coordinate system, called the world-coordinate reference frame
WCR can be 2D or 3D
Objects in pictures described by:
positions in world coordinates
Color
coordinate extents = the minimum and maximum x, y, and z values for each object

4. 4.1 Coordinate Reference Frames
Screen Coordinates
Locations on a video monitor are referenced in integer screen coordinates, which correspond to the pixel positions in the frame buffer
Pixel coordinate values give the scan line number (the y value) and the column number (the x value along a scan line)
Scan-line algorithms for the graphics primitives use the defining coordinate descriptions to determine the locations of pixels that are to be displayed

5. 4.1 Coordinate Reference Frames
Screen Coordinates
For the present, we assume that each integer screen position references the center of a pixel area

6. 4.1 Coordinate Reference Frames
Absolute and Relative Coordinate Specifications
Absolute coordinate values: the values specified are the actual positions within the coordinate system in use
Relative coordinates: we can specify a coordinate position as an offset from the last position that was referenced (called the current position)

7. 4.6 File Area Primitives
Another useful component beside geometric objects is describing an area with filled color
Referred to as fill area or filled area
Most graphics routins require the fill area to specified as polygon
- their boundries are described by linear equations.
- most surface can be approximated by polygons (called surface tessellation)

8. 4.7 Polygon Fill Area
Polygons: plane figure specified by three or more vertices and connected by edges
Has all vertices within plane- no edge crossing
Polygon classification:
- Convex: interior angle = or less than 180 degrees
- Concave: interior angle greater than 180 degrees
Implementations for filling algorithms are complicated for concave polygons
convex
concave

9. 4.7 Polygon Fill Area
Identifying concave polygons - extension of some edges will intersect other edges - take a look at the polygon vertex positions relative to the extension line of any edge: some vertices are on one side and some are on the other

10. 4.7 Polygon Fill Area Splitting concave polygons
Split concave polygons into a set of convex polygons
Using edge vectors and edge cross products
Use vertex position relative to edge extension line.

11. 4.7 Polygon Fill Area Splitting concave polygons
Assume all polygons in xy plane
Ek = Vk+1 – Vk
Calculate cross product of successive edge vectors
- if at least z component of one vector is negative, then concave polygon.
- no successive vertices are collinear.
Split along the line of the first edge vector in the cross product pair.

12. 4.7 Polygon Fill Area
Splitting concave polygons

13. 4.7 Polygon Fill Area
Splitting concave polygons

14. 4.7 Polygon Fill Area Splitting concave polygons
Another method is a rotational method

15. 4.7 Polygon Fill Area
Splitting convex polygons into triangle (tessellation) - define any sequence of three consecutive vertices to a triangle. - delete middle vertex from the original list - continue forming triangle - stop when only three vertices are remaining.

16. 4.7 Polygon Fill Area Inside-Outside test Also called odd-even test PQ

17. 4.7 Polygon Fill Area Winding-Number test
Count counterclockwise encirclements of point P Q

18. 4.7 Polygon Fill Area Polygon tables
objects in a scene are described as sets of polygon surface facets
Object description includes:
- Coordinate information (geometry for the polygon facets)
- Surface parameters(color, transparency, and light-reflection properties)
Object information are organized in tables.

19. 4.7 Polygon Fill Area
Polygon tables

20. 4.7 Polygon Fill Area Polygon tables
Important for check for consistency and completeness:
1. each pixel is an end point for at least two edges.
2. every edge is part of at least one polygon
3. every polygon is closed
4. each polygon has at least one shared edge