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CG-lecture02-2

# CG-lecture02-2 - Computer Graphics Lecture 2-2 Geometric...

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Computer Graphics Lecture 2-2 Geometric Transformation

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1.Coordinate System (1) Local Coordinate System (Point, 3D) (2) World Coordinate System (Point, 3D) (3) Camera Coordinate System (Point, 3D) (4) Screen Coordinate System (Pixel, 2D )
(1) Local Coordinate System Local coordinate system is used to describe the shape of single object. Every single object has its own local coordinate system. Local coordinate system is orthonormal . O X O Y O Z O

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(2) World Coordinate System World coordinate system is used to describe the whole virtual scene. The whole virtual scene has only one world coordinate system. World coordinate system is orthonormal . O X w Y w Z w
Local to World The virtual scene is composed of many virtual objects. When we place virtual objects in the virtual scene, we must perform the transformation from the local coordinate system to world coordinate system. Possible transformation: Rotation, Scaling, Translation O W X w Y w Z w Z O X O Y O O O

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Local to World The transformation between local system and world system can be represented as the equal vector transformation . With this opinion, the local system and the world system is the same system. O X w Y w Z w O O X O Y O Z O
(3) Camera (Viewing) Coordinate System The viewing coordinate system is used to describe the whole virtual scene based on the camera position and direction. Its purpose is to project 3D virtual objects to the retinal plane of the camera. O W X w Y w Z w Z C O C Y C X C

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World to Camera Before we project 3D object to retinal plane of the camera, we must perform the transformation from the world coordinate system to the viewing coordinate system.
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CG-lecture02-2 - Computer Graphics Lecture 2-2 Geometric...

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