22_2DGraphicsIntro.3up

# Void rotatedouble theta void rotatedouble theta double

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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' &...
View Full Document

## 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.

Ask a homework question - tutors are online