Advanced Graphics Intro_Part_3

Advanced Graphics Intro_Part_3 - Basis I I I in R3 a basis...

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Basis n in R 3 a basis is a set of 3 non-parallel vectors n common to use orthonormal basis u basis vectors are mutually orthogonal u basis vectors have unit magnitude n basis most students are familiar with [] [] [] 1 0 1 0 0 0 1 0 0 0 1 = = = = = = = = = k j i k j k i j i k j i T T T H H H H H H H H H H H H Direction (cont) n can write any vector as a linear combination of basis vectors k j i H H H 7 2 3 7 2 3 + + = ú ú ú û ù ê ê ê ë é
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Cross Product n Hill 4.4 n only defined in R 3 u defined in terms of standard basis [] [ ] c k b a b a j b a b a i b a b a b b b a a a b a x y y x z x x z y z z y T z y x T z y x H H H H H H = + + = × = × ) ( ) ( ) ( Cross Product (cont) n cross product of two vectors is a vector that is orthogonal to the original two vectors u direction given by right hand rule
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Cross Product (cont) n properties j i k i k j k j i b a s b a s c a b a c b a a b b a H H H H H H H H H H H H H H H H H H H H H H H H = × = × = × × = × ×
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Advanced Graphics Intro_Part_3 - Basis I I I in R3 a basis...

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