Institute for Visualization and Perception Research 1 © Copyright 2000 Haim Levkowitz Raster graphics alg’s for drawing 2D primitives Points of view Application.

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Presentation transcript:

Institute for Visualization and Perception Research 1 © Copyright 2000 Haim Levkowitz Raster graphics alg’s for drawing 2D primitives Points of view Application programmer's Package implementor's Scan-converted clipped primitives

Institute for Visualization and Perception Research 2 © Copyright 2000 Haim Levkowitz Overview … Implications of display-system architecture … Output pipeline...

Institute for Visualization and Perception Research 3 © Copyright 2000 Haim Levkowitz Implications of disp-sys architecture … Output & input pipelines … Displays with frame buffers & display controllers … Displays with frame buffers only … Hardcopy devices...

Institute for Visualization and Perception Research 4 © Copyright 2000 Haim Levkowitz Output & input pipelines Output Input

Institute for Visualization and Perception Research 5 © Copyright 2000 Haim Levkowitz Output Primitive-generation function: What to generate Attribute functions: How to generate copyPixel: How to modify image Canvas-control functions: Where

Institute for Visualization and Perception Research 6 © Copyright 2000 Haim Levkowitz Input User interaction (display) --> measure values ==> modify model or image

Institute for Visualization and Perception Research 7 © Copyright 2000 Haim Levkowitz Displays with frame buffers & display controllers …

Institute for Visualization and Perception Research 8 © Copyright 2000 Haim Levkowitz Displays with frame buffers only …

Institute for Visualization and Perception Research 9 © Copyright 2000 Haim Levkowitz Hardcopy devices … One scan line at a time Package: generate complete bitmap Scan out 1 line at a time Entire frame (page) Raster Image Processor (RIP): built-in scan-conversion HW PostScript engine: interpret program Device independent ==> Primitives + attributes

Institute for Visualization and Perception Research 10 © Copyright 2000 Haim Levkowitz Output Pipeline … Clip primitives then scan-convert ==> Fewer to scan-convert Scissoring: Scan-covert then clip Write only visible pixels Temp. canvas, copy only clip rectangle Wastes time & space Easy to implement Often for text Incremental methods: minimize number of calculations

Institute for Visualization and Perception Research 11 © Copyright 2000 Haim Levkowitz Scan Converting Primitives primitives

Institute for Visualization and Perception Research 12 © Copyright 2000 Haim Levkowitz Clipping Overview – Hearn & Baker Ch. 6

Institute for Visualization and Perception Research 13 © Copyright 2000 Haim Levkowitz

Institute for Visualization and Perception Research 14 © Copyright 2000 Haim Levkowitz

Institute for Visualization and Perception Research 15 © Copyright 2000 Haim Levkowitz

Institute for Visualization and Perception Research 16 © Copyright 2000 Haim Levkowitz

Institute for Visualization and Perception Research 17 © Copyright 2000 Haim Levkowitz Clipping endpoints … Cases for clipping lines … Solving simultaneous equations … Cohen-Sutherland Algorithm … Parametric Line-Clipping Algorithm...

Institute for Visualization and Perception Research 18 © Copyright 2000 Haim Levkowitz Clipping endpoints x min  x  x max y min  y  y max

Institute for Visualization and Perception Research 19 © Copyright 2000 Haim Levkowitz Cases for clipping lines …

Institute for Visualization and Perception Research 20 © Copyright 2000 Haim Levkowitz Solving Simultaneous Equations … Both endpoints inside ==> trivially accept One inside, one outside ==> find intersection point Both outside: may / may not intersect Brute force: line equation + clip rectangle edges equation

Institute for Visualization and Perception Research 21 © Copyright 2000 Haim Levkowitz Cohen-Sutherland Algorithm … 1. Check endpoints: trivially accept? 2. Region checks: trivially reject? 3. Divide into 2 segments s.t. one can be trivially rejected Iterative clip Trivially accept? / reject? Example …

Institute for Visualization and Perception Research 22 © Copyright 2000 Haim Levkowitz Cohen-Sutherland (cont.)

Institute for Visualization and Perception Research 23 © Copyright 2000 Haim Levkowitz Cohen-Sutherland example

Institute for Visualization and Perception Research 24 © Copyright 2000 Haim Levkowitz Parametric Line-Clipping -- overview Example...

Institute for Visualization and Perception Research 25 © Copyright 2000 Haim Levkowitz Parametric Line-Clipping example

Institute for Visualization and Perception Research 26 © Copyright 2000 Haim Levkowitz Parametric Line-Clipping -- theory in detail als/HyperGraph/scanline/clipping/lbth.htm

Institute for Visualization and Perception Research 27 © Copyright 2000 Haim Levkowitz Parametric Line-Clipping -- The algorithm als/HyperGraph/scanline/clipping/lbalg.ht m

Institute for Visualization and Perception Research 28 © Copyright 2000 Haim Levkowitz Parametric Line-Clipping – detailed example als/HyperGraph/scanline/clipping/lbex.htm

Institute for Visualization and Perception Research 29 © Copyright 2000 Haim Levkowitz Clipping circles and ellipses Accept / reject against square extent If intersects, divide into quadrants, repeat accept / reject Divide into octants if necessary Compute intersection of edge-circle analytically Simultaneous equations Scan convert resulting arcs Fast scan conversion ==> scissoring faster Filled: clip spans then fill

Institute for Visualization and Perception Research 30 © Copyright 2000 Haim Levkowitz Clipping Polygons General … Sutherland-Hodgman Algorithm … Four cases …

Institute for Visualization and Perception Research 31 © Copyright 2000 Haim Levkowitz

Institute for Visualization and Perception Research 32 © Copyright 2000 Haim Levkowitz General

Institute for Visualization and Perception Research 33 © Copyright 2000 Haim Levkowitz Sutherland-Hodgman Algorithm

Institute for Visualization and Perception Research 34 © Copyright 2000 Haim Levkowitz Four cases

Institute for Visualization and Perception Research 35 © Copyright 2000 Haim Levkowitz

Institute for Visualization and Perception Research 36 © Copyright 2000 Haim Levkowitz

Institute for Visualization and Perception Research 37 © Copyright 2000 Haim Levkowitz

Institute for Visualization and Perception Research 38 © Copyright 2000 Haim Levkowitz Antialiasing Increasing resolution … Area sampling … Weighted Unweighted Other

Institute for Visualization and Perception Research 39 © Copyright 2000 Haim Levkowitz Increasing Resolution Best, but Limitations Jaggies / staircasing Aliasing / antialiasing

Institute for Visualization and Perception Research 40 © Copyright 2000 Haim Levkowitz Area sampling Area represented by pixel Unweighted area sampling All pixels equal Weighted area sampling Some contribute more than others Based on weight function