Window to Viewport Mapping

• Start with 3D scene, but eventually project to 2D scene
• 2D scene is infinite plane. Device has a finite visible rectangle.
  What do we do?
• Answer: map rectangular region of 2D device scene to device.

  Window:

  rectangular region of interest in scene.

  Viewport:

  rectangular region on device.

  Usually, both rectangles are aligned with the coordinate axes.

  \

• Window point maps to viewport point .

  Window has corners and ;
  Viewport has corners and .

  Length and height of the window are and ,
  Length and heigth of the viewport are and .

• Proportionally map each of the coordinates according to:

  

• To map to :

  

  and similarily for .

• If the image will be distorted.
  These quantities are called the aspect ratios of the window and viewport.

Readings: Hearn and Baker: Section 6-3. Red book: 5.5. White book: 5.4, Blinn: 16.

Intuitively, the window-to-viewport formula can be read as:

• Convert to a distance from the window corner.
• Scale this w distance to get a v distance.
• Add to viewport corner to get .