Project 2 - Motion Control in Computer-Aided Modeling

Team Members: Daniel West, Lado Tonia

Problem 1: Lado
Problem 2: Lado
Problem 3: Lado
Problem 4: Daniel/Lado
Problem 5: Daniel/Lado
Problem 6: Daniel/Lado
Problem 7: Daniel
Website: Daniel

Write a matlab function that uses adaptive quadrature to compute the arc length from t=0 to t = T for a given T <= 1

To accomplish this we "borrowed" Dr. Sauer's code for adaptive quadrature and entered in the function from the book.

Results: "Arc length from 0 to .5 is 0.57266"

Code - Adaptive Quadrature Code
Code - Arc Len
Code - Problem 1

Write a program that finds the time value at a specific percentage of the overall arc length.

The bracketing interval we used was [0,1].
Results: "Time Position at 50 percent of the curve length with a tolerance of .001 is 0.8008"

Code - Bisection Method
Code - Problem 2

Equipartition the path of Figure 5.6 into n subpaths of equal length. To do this we used our bisection method from Problem 2.



Code - Bisection Method
Code - Problem 3

Replace the Bisection Method in Step 2 with Newton's Method and repeat steps 2 and 3. For this we used the arc length function as the derivative and for our initial guess we used .5. As expected we saw increased performance with the newton's method.

Results: "Time Position at 50 percent of the curve length with a tolerance of .001 is 0.8006"

Use MatLab's animation commands to demonstrate travelling along the path.
Red is variable speed
Blue is the constant speed


Code - Problem 5

In this problem we chose 4 points random, crafted a Bezier spline and partitioned it into 4 equal segments. From there we wrote an application that traversed the curve at a constant, s^(1/3) and s^2.
Red - Cube Root
Green - Squared
Blue - Constant



Code - Problem 6/7