3D Fundamentals

Coordinate Systems

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Coordinate sytems are the measured frames of reference within which geometry is defined, manipulated and viewed.

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1-D Coordinate Systems

• Direction and magnitude along a single axis, with reference to an origin
• Locations are defined by a single coordinate
• Can define points, segments, lines, rays
• Can have multiple origins (frames of reference) and transform coordinates among them

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2-D Coordinate Systems

• Direction and magnitude along two axes, with reference to an origin
• Locations are defined by x, y coordinate pairs
• Can define points, segments, lines, rays, curves, polygons, (any planar geometry)
• Can have multiple orignins (frames of reference and transform coordinates among them

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3-D Coordinate Systems

• 3D Cartesian coordinate systems
• Direction and magnitude along three axes, with reference to an origin
• Locations are defined by x, y, z triples
• Can define cubes, cones, spheres, etc., (volumes in space) in addition to all one- and two-dimensional entities
• Can have multiple orignins (frames of reference and transform coordinates among them

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Left-handed versus Right-handed

• Determines orientation of axes and direction of rotations
• Thumb = pos x, Index up = pos y, Middle out = pos z
• Most world and object axes tend to be right handed
• Left handed axes often are used for cameras

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• ``Right Hand Rule" for rotations: grasp axis with right hand with thumb oriented in positive direction, fingers will then curl in direction of positive rotation for that axis

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Y-up versus Z-up

• z-up typically used by designers
• y-up typically used by animators
• orientaion by profession supposedly derives from past work habits
• often handled differently when moving from application to application

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Global and Local Coordinate Systems

• Local coordinate systems can be defined with respect to global coordinate system
• Locations can be relative to any of these coordinate system
• Locations can be translated or "transformed" from one coordinate system to another.

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Mulitple Frames of Reference in a 3-D Scene

• In fact, there usually are multiple coordinate systems within any 3-D screen
• Application data will be transformed among the various coordinate systems, depending on what's to be accomplished during program execution
• Individual coordinate systems often are hierarchically linked within the scene