Chapter 8
3D Coordinate systems

• Right-handed. Customary in math

• Left-handed. Natural in graphics (z grows with distance)

• Conversion by negating z.

8.1 View Coordinates

• Uses left-handed coordinate system
• The eye/camera on Z_v-axis
• Y _v -axis determines the UP direction.
• The origin is called the CENTER OF INTEREST POINT.

8.2 Window

Within the X_v Y _v plane of the view coordinate system

8.3 World Coordinates

Traditionally defined in right-handed coordinate system.

8.4 Object Coordinates

Traditionally defined in right-handed coordinate system.

8.5 The Pipeline

• Create the objects in object coordinates
• Assemble the image in world coordinates
• Set view coordinates within world coordinates
  • Choose center of interest point
  • Z_v : eye to center of interest
  • Choose UP for Y _v
  • Set X_v for left-handed coordinate system
• Convert from world coordinates to view coordinates
• Choose window in X_vY _v plane
• Project to window plane

• Clip against window
• Map to viewport

8.6 View Piramid

• The visible portion of the world--determined by center of projection and window

Translation+Shear Transformations

• Origin of coordinates at center of window.
• Eye perpendicular to origin