Day 5_Part_1 - 1 1 1 1 z y x d d d D 1 z y x h p p p p 1 1...

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Day 05 Rigid Body Transformations 1/25/2012 1
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Homogeneous Representation 1/25/2012 2 translation represented by a vector d vector addition rotation represented by a matrix R matrix-matrix and matrix-vector multiplication convenient to have a uniform representation of translation and rotation obviously vector addition will not work for rotation can we use matrix multiplication to represent translation?
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Homogeneous Representation 1/25/2012 3 consider moving a point p by a translation vector d z z y y x x z y x z y x d p d p d p d d d p p p d p z z y y x x z y x d p d p d p p p p ? not possible as matrix-vector multiplication always leaves the origin unchanged
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Homogeneous Representation 1/25/2012 4 consider an augmented vector p h and an augmented matrix D
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Unformatted text preview: 1 1 1 1 z y x d d d D 1 z y x h p p p p 1 1 1 1 1 1 z z y y x x z y x z y x h d p d p d p p p p d d d Dp Homogeneous Representation 1/25/2012 5 the augmented form of a rotation matrix R 3x3 1 3x3 R R 1 1 1 3x3 3x3 p R p p p R Rp z y x h...
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Day 5_Part_1 - 1 1 1 1 z y x d d d D 1 z y x h p p p p 1 1...

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