Final Exam 09

# James obrien page 11 of 16 17 if a surface is defined

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: ________________________________ ￿ cos(# ) cos(________________________________ # ) ￿￿ dx s(x , x ) ￿ Z ||x￿ − x￿￿||2 ￿ ￿￿ cos(# ) cos(# ) x￿, x￿￿) , x￿) + &quot;x￿(x, x￿￿)Ls(________________________________￿￿ dx ￿ − x￿￿||2 ||x S ￿ ￿￿ ￿ ￿￿ Final Exam CS 184: Foundations of Computer Graphics Fall 2009 Prof. James O’Brien page 11 of 16 17. If a surface is defined explicitly by the function x = f (u, v) , write out the equation you would use to compute the surface’s normal at some point. 4 points 18. Consider this diagram showing a four-joint arm in 2D where each joint is a simple pin joint and the base is fixed in space. If we are solving an IK problem to place the tip of the arm (the black dot) at a particular location, what is the size of the Jacobian matrix we will be working with? 3 points Draw any one configuration of the arm where two columns of the Jacobian will be parallel vectors. 5 points In the drawing you made above, clearly show the direction of the parallel vectors. 3 points In the drawing you ma...
View Full Document

Ask a homework question - tutors are online