2D Viewinrrrrrdddfddddffdrrrdddfdsssg.pptx
- 1. 2D VIEWING 4/16/2022 1 CS8092-Computer Graphics & Multimedia
- 2. TERMINOLOGY • World Coordinate System (Object Space) • Representation of an object measured in some physical units. • Window • The rectangle defining the part of the world we wish to display. • Image Coordinate System (Image Space) • The space within the image is displayed • Viewport • The rectangle area in image space where the image from the window will appear. • Viewing Transformation • The process of going from a window in world coordinates to a viewport in image coordinates. 4/16/2022 2 CS8092-Computer Graphics & Multimedia
- 3. WINDOWS AND VIEWPORTS Windo w Image Space Viewpo rt Information outside the viewport is clipped away 4/16/2022 3 CS8092-Computer Graphics & Multimedia
- 4. THE VIEWING PIPELINE • What’s the viewing pipe line? – Viewing transformation in several steps • A viewing transformation using standard rectangles for the window and viewport. • A world-coordinate area selected for display 🡪window (what is to be viewed) • An area on a display device to which a window is mapped 🡪 viewport (where it is to be displayed) • The mapping of a part of a world-coordinate scene to device coordinates 🡪 Viewing Transformation or Window-to-viewport Transformation or The Windowing Transformation. 4/16/2022 4 CS8092-Computer Graphics & Multimedia
- 5. THE VIEWING PIPELINE World Coordinates xvmin xvmax ywmax ywmin Device Coordinate xvmin xvmax ywmax ywmin 4/16/2022 5 CS8092-Computer Graphics & Multimedia
- 6. THE VIEWING PIPELINE (2/3) • The two-dimensional viewing-transformation pipeline Construct World Coordinate Scene Using Modeling-Coordinate Transformation Convert World- Coordinates to Viewing Coordinates Map Viewing Coordinates to Normalized Viewing Coordinates using Window-Viewport Map Normalized Viewport to Device MC VC WC MC NVC 4/16/2022 6 CS8092-Computer Graphics & Multimedia
- 7. THE VIEWING PIPELINE (3/3) • Setting up a rotated world window in viewing coordinates and the corresponding normalized-coordinate viewport Normalized Device Coordinates Viewpoint 0 1 1 World Coordinates y view x view y world y0 x0 x world 4/16/2022 7 CS8092-Computer Graphics & Multimedia
- 8. VIEWING COORDINATE REFERENCE FRAME • Used to provide a method for setting up arbitrary orientations for rectangular windows • Matrix for converting world-coordinate positions to viewing coordinate R: rotation matrix T: translation matrix 4/16/2022 8 CS8092-Computer Graphics & Multimedia
- 9. VIEWING COORDINATE REFERENCE FRAME • The steps in this coordinate transformation – A viewing coordinate frame is moved into coincidence with the world frame in two steps a) Translate the viewing origin to the world origin, then b) Rotate to align the axes of the two systems 4/16/2022 9 CS8092-Computer Graphics & Multimedia
- 10. WINDOW-TO-VIEWPORT COORDINATE TRANSFORMATION • Window-to-viewport mapping – A point at position (xw, yw) in a designated window is mapped to viewport coordinates (xv, yv) so that relative positions in the two areas are the same 4/16/2022 10 CS8092-Computer Graphics & Multimedia
- 11. WINDOW-TO-VIEWPORT COORDINATE TRANSFORMATION • To maintain the same relative placement • Solving these expressions for the viewport position (xv, yv) 4/16/2022 11 CS8092-Computer Graphics & Multimedia
- 12. WINDOW-TO-VIEWPORT COORDINATE TRANSFORMATION • The scaling factors • Conversion sequence of transformation 1. Perform a scaling transformation using a fixed-point position of (xwmin, ywmin) that scales the window area to the size of the viewport 2. Translate the scaled window area to the position of the viewport 4/16/2022 12 CS8092-Computer Graphics & Multimedia
- 13. WINDOW-TO-VIEWPORT COORDINATE TRANSFORMATION • The way of character string mapping – Maintaining character size • Using standard character fonts – Changing character size • Using characters formed with line segments • Workstation transformation – Opening any number of output devices in a particular application – Performing another window-to-viewport transformation for each open output device 4/16/2022 13 CS8092-Computer Graphics & Multimedia
- 14. WINDOW-TO-VIEWPORT COORDINATE TRANSFORMATION • Mapping selected parts of a scene in normalized coordinates to different video monitors with Workstation transformation 4/16/2022 14 CS8092-Computer Graphics & Multimedia