Clipping other primitives

• In hardware, we almost always clip line segments or points.
  • At some level, text, curves, ... are always represented by either pixels or lines.
  • Raster vs vector fonts.
  • EVERYTHING needs to be discretized
• But we may wish to clip BEFORE we send it to the hardware.
• Or at least partially clipped.
• A bounding box
  • is a rectangle (2D or 3D) which encloses the shape.
  • We want it to be as "Tight" as possible.
  • Sometimes we use a bounding sphere or circle.
  • But we want a bounding shape that is very easy to test for:
    • Clipping or exclusion (Our current topic)
    • Ray intersection (Most lighting models, ray tracing ...)
    • Collision detection.
  • For clipping, an axis aligned bounding box is really good.
  • The idea is to perform test on the bounding object.
    • If it is accepted or rejected no further interaction with the object is required.
    • If it is to be clipped, then we can further examine the object, (If we need to)
• he mentions that many APIs automatically append bounding boxes to objects.
• If we need to clip the curves themselves
  • We would like to turn it into line segments.
  • If we can't we do much more work determine what will be drawn.
  • This will (probably) be computationally expensive.
  • For shapes like circles, we can try to employ symmetry.
  • This is probably a case by case bases for non-polygon/line/point objects we wish to clip.
• Text
  • ALL-OR-Nothing on characters/strings
  • Vector characters - see previous
  • The nature of characters. (As before I hope)
• 3D clipping
  • The three algorithms we have discussed can be extended to 3d
    • Cohen-Sutherland - 6 bit outcode
    • Liang-Barsky -z(α) = (1-α)z₁ + αz₂
    • Sutherland-Hodgeman just add two more clippers to the pipeline
  • In all cases, we are clipping against a plane, not a line.
  • But we can rewrite the plane equations as we did the line equations.