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Computer Graphics- SCC 342 Chapter 4: Graphics Output Primitives Dr. Doaa Hegazy 2D Graphics Primitives • Graphics drawing is based on basic geometric structures called graphics primitives – Points – Lines – Circles – Conic Sections 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 4.1 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 4.1 Coordinate Reference Frames Screen Coordinates • For the present, we assume that each integer screen position references the center of a pixel area 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) 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) 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 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 9 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. 10 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. 11 4.7 Polygon Fill Area Splitting concave polygons 12 4.7 Polygon Fill Area Splitting concave polygons 13 4.7 Polygon Fill Area Splitting concave polygons • Another method is a rotational method 14 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. 15 4.7 Polygon Fill Area Inside-Outside test • Also called odd-even test P Q 16 4.7 Polygon Fill Area Winding-Number test • Count counterclockwise encirclements of point P Q 17 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. 18 4.7 Polygon Fill Area Polygon tables 19 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 20