page 129
done properly then z = depth in the view plane.)
• The point mapped to the computer screen can then be converted to a single pixel using a simple scaling calculation. (Note: It is not shown, but if a point is off the screen, then it cannot be drawn.)
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•Visual display can be done using,
-CRT monitors with Frame Buffer memory to store the image.
-plotters which draw one line at a time
-printers using special and proprietary graphics languages
•For the sake of simplicity, the remaining graphics methods ignore some trivial operations such as screen coordinates, line clipping at edge of screen, etc.
•The ‘z’ value after the perspective transform gives a relative depth of a point. This can be used later for depth sorting, or to set light intensity to cue the user to view depth.
12.3 LINE DRAWING
•A wireframe object is simply rendered using the lines (straight, and curved) in a geometric model, then it is converted to screen coordinates using the Perspective Transformation.
•The process is as pictured below,
page 130
Geometric |
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Convert |
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Clip lines |
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Draw Lines |
Model |
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Perspective |
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Transform |
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•If the geometric model is in some other form, such as CSG (Constructive Solids Geometry), it may have to be converted to lines before it may be used.
•Advantages,
-Very fast, allows real time manipulation
-Easy to see features normally hidden
-Supported by almost all computer technology
-This display method works with most displays
•Disadvantages,
-Drawings can become very crowded, very fast
-Hard to visualize solid properties
•Almost all computer graphics packages offer a wireframe display option.
12.3.1 Hidden Lines
•While the results seem similar, this method requires more sophisticated algorithms.
•Polygons must be used for surface representation.
page 131
• The diagram below shows the basic steps in the method of rendering
Geometric |
Polygons |
Polygons are |
Model (in |
Transformed |
roughly depth |
Polygons) |
using |
sorted (may |
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Perspective |
still overlap) |
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Transform |
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Polygon Lines |
Lines are |
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drawn into |
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Frame Buffer |
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•Advantages,
-similar advantages of wireframe
-overcomes the drawing crowding
-can be simplified if polygons do not overlap
•Disadvantages,
-Consumes more computer time
-Does not support simple elemental geometric models
•Clipping algorithms may be difficult, and often use tricks like subdividing polygons into triangles. (There are only 5 cases to consider with overlapping triangles)