CS488 - Introduction to Computer Graphics - Lecture 10

Comments and Questions


Review

  1. Non-rigid transformations
  2. Normalized Device Coordinates

Clipping

What is it?

Representations of Lines

  1. Parametric
  2. Implicit

Clip a Point against a Half-space.

Representation of a Half-space.

Calculate ( R - P ) . n

Clip a Line Segment to a Half-space.

The line segment

Test if each of R and S are inside. Calculate

  1. ( R - P ) . n
  2. ( S - P ) . n

There are three cases

  1. Both inside: keep the segment as is.
  2. Both outside: discard the segment.
  3. One inside, one outside: the segment crosses the boundary of the half-space.

Clip a Line Segment to a Rectangle

Straightforward, BUT what if the line segment crosses a corner?


Perspective Projection

What is a projection?

Projective transformations are a superset of affine transformations.

  1. They do not preserve ratios of distance.
  2. They do not preserve affine combinations.
  3. They do not map vectors.
  4. They do preserve the cross ratio.

Show 1D transformation on the board

  1. Illustration in 2D. What does this mean? (Hint. homogeneous coordinates)
  2. Projection point on one of the lines.
  3. Relevance of the intersection point of two lines.
  4. How the transformation changes as the projection point moves around.


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