Void rotatedouble theta void rotatedouble theta double

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Unformatted text preview: $ 0 '$ &# Subtract points "v % " v ×s $ x' $x v × s = $ vy ' × s = $ vy × s $ ' $ $ ' $ #0& #0 % ' ' ' ' & Scalar Mul:ply Add vectors "p % "q $ x'$ x p − q = $ py ' − $ q y $ '$ $ '$ #1&#1 $ & & & & % % ' ' ' ' & !p $ !v x &# x # p + v = # py & + # v y # &# # &# "1%"0 $ ! p +v &# x x & = # p + vy &# 1 &# %" Point + Vector $ & & & & % Transla:ng Vectors •  A vector has no posi:on, so transla:ng it shouldn’t change anything. ! x ' $ ! 1 0 t x $! x $ ! x $ &# # &# &# & # y ' & = # 0 1 t y &# y & = # y & # 0 & # 0 0 1 &# 0 & # 0 & " %# %" % &" " % Rota:on Matrix •  Vectors: ! x ' $ ! cosθ # &# # y ' & = # sin θ #0&# 0 " %" ! − sin θ ? $! x $ # x cosθ − y sin θ &# & cosθ ? &# y & = # x sin θ + y cosθ 0 ? &# 0 & # 0 %" %" $ & & & % ! − sin θ ? $! x $ # x cosθ − y sin θ &# & cosθ ? &# y & = # x sin θ + y cosθ 0 ? &# 1 & # 1 %" %" $ & & & % •  Points ! x ' $ ! cosθ # &# # y ' & = # sin θ #1&# 0 " %" Scaling Matrix •  Vectors: ! x ' $ ! sx # &# # y' &...
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This note was uploaded on 03/19/2013 for the course CSC 101 taught by Professor Merl during the Fall '12 term at Arizona State University at the West Campus.

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