Page 174 - DCAP504_Computer Graphics

Unit 11: Hidden Surfaces

From Equations 11.2 and 11.3, we can say that in order to check the direction of two vectors V and N, it
is enough to check the sign of the Z co-ordinate of the normal vector N. If the sign of the Z co-ordinate
of the normal vector is positive then the surface in test is visible, otherwise it is invisible.
Similarly for a left-handed system, the conditions will be reversed.
11.8 Summary

• The surfaces and edges which are not visible to the viewer are known as hidden surfaces and
hidden edges. The process of determining which lines or surfaces of the objects are visible is
known as hidden surfaces or hidden line elimination, or visible surface determination.

• When 3-D shapes are projected onto 2-D computer screen, then for every (X, Y) screen location,
there is one or more 3-D surface points.
• Binary Space Partitioning (BSP) tree is an algorithm independent of the viewpoint location.

• The painter’s algorithm works similarly in the manner as an artist paints his canvas with
background and foreground colors.
• The Warnock algorithm also known as the area subdivision method is an image space method but
it makes use of the object space method for depth comparison.

• The ray tracing algorithm provides the flexibility to handle both flat and curved surfaces. The back
face algorithm is based on the inside test.
• Rasterization, often referred to as Scan line rendering, is the process that captures an outline
representation of 3-D objects, transforms it into screen space, and projects the resulting 2-D
geometry on the screen.
• The hidden surface determination process is often referred to as hiding, and such an algorithm is
sometimes called a hider.
• Octrees provide the facility to search and insert data at a fast rate. However, the process of
deleting and moving a data entry is very slow.
11.9 Keywords

Algorithm: This is a step by step procedure to perform a task.
Leaf node: The node having no child-node.
Rasterize: A process used to convert a digital image into a format suitable to be displayed on a
computer monitor or printout.
Tracing: This is the exact replication made by superimposing the transparent sheet on original sheet and
drawing the lines.
11.10 Self Assessment

1. State whether the following statements are true or false:
(a) Errors are usually an Object space method that differentiates objects and parts of objects from
each other to decide the visibility.
(b) A 3-D shape is a collection of 3-D surfaces or planar surface patches in 3-D world.

(c) BSP trees are also used to slow down ray tracing and in planning the motion of robots.
(d) The process of hidden surface determination is often referred to as hiding.
(e) The Warnock algorithm also known as the area subdivision method is an image space
method.
(f) Any object in computer graphics is made of polygons and surfaces.

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