CS/MATH 3414 Assignment #9

Part 1:


1. (5 points) Problem 7.2.12 (page 346) of your textbook.
   
2. (10 points) Problem 7.2.13 (page 346) of your textbook.
   
3. (10 points) Problem 7.2.21 (page 347) of your textbook.
   
4. (10 points) Problem 7.2.22 (page 347) of your textbook.
   
   Part 2:
   
   
5. (15 points) Choose a free-form parametric curve in 2D. One example is the spiral on page 349 of your textbook. Another example could be a smooth letter of the alphabet such as "S", "C", or even "P" (but you have to be careful here, since it has sharp turns). Yet another example could be some logo or symbol, like the Yin-Yang. Draw your curve on graph paper, and record values of x and y for a resonable number of points. Reproduce it by using parameteric spline functions. For full credit, show your curve, how you recorded the data, MATLAB code showing the parameteric spline, and a picture of the spline itself.
   
   Depending on the continuity of your curve, you may need to use more than one spline (this can happen for either x, or y, or both). See, for instance Fig. 7.8 of your textbook (but that is not a parametric spline). More details on solving this problem were given in class on Wednesday, April 3. You are welcome to use the MATLAB spline function but notice that it imposes the extra conditions in a different way, not quite the "natural cubic spline" way we learned in class.
   Extra Credit: If you are truly adventurous, draw out your name as separate parametric splines.