Mumbai University > Computer Engineering > Sem 4 > Computer Graphics

Marks: 10 Marks

Year: Dec 2016

When we view a picture containing non-transparent objects and surfaces, then we cannot see those objects from view which are behind from objects closer to eye. We must remove these hidden surfaces to get a realistic screen image. The identification and removal of these surfaces is called Hidden-surface problem.

There are two approaches for removing hidden surface problems − Object-Space method and Image-space method.The Object-space method is implemented in physical coordinate system and image-space method is implemented in screen coordinate system.

Back-Face Detection

• A fast and simple object-space method for identifying the back faces of a polyhedron is based on the "inside-outside" tests. A point (x, y, z) is "inside" a polygon surface with plane parameters A, B, C, and D if When an inside point is along the line of sight to the surface, the polygon must be a back face (we are inside that face and cannot see the front of it from our viewing position).
• We can simplify this test by considering the normal vector N to a polygon surface, which has Cartesian components (A, B, C).

• In general, if V is a vector in the viewing direction from the eye (or "camera") position, then this polygon is a back face if

  V.N > 0

• Furthermore, if object descriptions are converted to projection coordinates and your viewing direction is parallel to the viewing z-axis, then −

  V = (0, 0, Vz) and V.N = VZC

• So that we only need to consider the sign of C the component of the normal vector N.

• In a right-handed viewing system with viewing direction along the negative ZVZV axis, the polygon is a back face if C < 0. Also, we cannot see any face whose normal has z component C = 0, since your viewing direction is towards that polygon. Thus, in general, we can label any polygon as a back face if its normal vector has a z component value −

  C <= 0

  

• Similar methods can be used in packages that employ a left-handed viewing system. In these packages, plane parameters A, B, C and D can be calculated from polygon vertex coordinates specified in a clockwise direction (unlike the counterclockwise direction used in a right-handed system).

• Also, back faces have normal vectors that point away from the viewing position and are identified by C >= 0 when the viewing direction is along the positive ZvZv axis. By examining parameter C for the different planes defining an object, we can immediately identify all the back faces.