Windows to viewport transformation
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The document discusses the window-to-viewport transformation process which maps a 2D scene to device coordinates. It involves developing formulas to proportionally map points from the world window to the viewport. The scale and translation factors that relate the world window and viewport coordinates are defined. Changing the viewport position, using multiple viewports, or adjusting the viewport dimensions allows manipulating the displayed scene. Distortion may occur if the aspect ratios of the world window and viewport differ.
Windows to viewport transformation
- 1. WINDOWS TO VIEWPORT TRANSFORMATION Made By:Kaushik Kumar Shiyani 00721102012
- 2. Window -to-viewport transformation Window-to-Viewport mapping is the process of mapping or transforming a two-dimensional, world-coordinate scene to device coordinates. In particular, objects inside the world or clipping window are mapped to the viewport. The viewport is displayed in the interface window on the screen. In other words, the clipping window is used to select the part of the scene that is to be displayed. The viewport then positions the scene on the output device.
- 3. Example
- 4. Development of the Window-To-Viewport transformation This transformation involves developing formulas that start with a point in the world window, say (xw, yw). The formula is used to produce a corresponding point in viewport coordinates, say (xv, yv). We would like for this mapping to be "proportional" in the sense that if xw is 30% of the way from the left edge of the world window, then xv is 30% of the way from the left edge of the viewport. Similarly, if yw is 30% of the way from the bottom edge of the world window, then yv is 30% of the way from the bottom edge of the viewport.
- 5. Continue…….
- 6. Using this proportionality, the following ratios must be equal.
- 7. By solving these equations for the unknown viewport position (xv, yv), the following becomes true:
- 8. The scale factors (Sx, Sy) would be:
- 9. And the translation factors (Tx, Ty) would be:
- 10. The position of the viewport can be changed allowing objects to be viewed at different positions on the Interface Window. Multiple viewports can also be used to display different sections of a scene at different screen positions. Also, by changing the dimensions of the viewport, the size and proportions of the objects being displayed can be manipulated. Thus, a zooming affect can be achieved by successively mapping different dimensioned clipping windows on a fixed sized viewport. If the aspect ratio of the world window and the viewport are different, then the image may look distorted.