Lecture 8 Notes

# Sjll not enough never enough 3 22014 some physical

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Unformatted text preview: d = d/2; Xeno.m x = 0; d = 1; for k = 1:20 DrawDisk(x+d/2,0,d/2,'y') x = x+d; d = d/2; end Insight Through CompuJng •  Shouldn’t we see 20 disks? •  Since screen is a grid of dots – called pixels •  As disks get smaller they don’t get drawn correctly (how could they?) •  The 20th disk has radius < .000001 •  Mac ReJna = 2560x1600 – Awesome! •  Zooming “in” shows eﬀect of storing image/ screen data as discrete grid •  PixilaJon, Jaggies, etc. –  SJll “not enough” (never enough) 3 2/20/14 Some Physical Pixels Color •  Color of these pixel are determined by the amount of red (R) green (G) and blue (B) they produce –  RGB are primary colors when working with light (addiJve mixing) ~ Cyan Magenta Yellow paint –  Using RGB you can create any color you like They are so small, that at the “usual” distance your eyes just see dots. Color Finiteness •  Matlab allows you to specify color using a an RGB vector, [r g b], 0<= r,g,b <=1 –  E.g., DrawDisk(0,0,10, [1 .4 .7]) gives a pink disk It shows up all over the place in compuJng. •  Computer displays are limited in terms of how many RGB combinaJons they can display (more discreteness!) –  Eg. 24 bit color => 2^24 colors available •  256 reds x 256 blues x 256 greens colors Insight Through CompuJng 4 2/20/14 Plovng ConJnuous FuncJons Can only display a bunch of dots Another “collision” between the inﬁnite and the ﬁnite. (More later.) Insight Through CompuJng The Discrete Display of Sine N = 100; X_spacing = 4*pi/N; Dot_radius = X_spacing/3; for k=0:N x = k*X_spacing; y = sin(x); DrawDisk(x,y,Dot_Radius,'r') end Insight Through CompuJng The Moral To produce realisJc plots/renderings you must appreciate screen granularity. Insight Through CompuJng Similar Finite “Behavior” with Computer ArithmeJc As discussed before •  Memory hardware is ﬁnite. •  Computer cannot explicitly store never- ending decimals like pi, sqrt(2), 1/3 Remark •  Symbolic math systems –  Store “descripJons” of numbers and have rules for manipulaJng the descripJons. Great for short calculaJons, but does not work for long calculaJons (the descripJons get too long) Insight Through Comp...
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## This document was uploaded on 03/11/2014 for the course CSCI 004 at Brown.

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