For this activity, we were tasked to obtain the area of shapes using greens theorem. using the edge function of scilab, we are to obtain the area and by analytically solving for the area, we are to compare the results from the greens theorem to the analytically solved area.
first, I obtained the area of 10 circles. The result of the edge function is also shown. (I only show one circle).
Figure: the circle on top, the result of the edge function on the bottom.
After obtaining the edge, I obtain the area using the discretized green’s function. I repeat the process for 10 different circles to obtain the average deviation from the answer using the equation for the area. I obtained a deviation of 0.62%.
I also did the same thing for rectangles.
Figure: Edge detection of a rectangle
After doing the same process for rectangles, I obtain a deviation of 0.46%.
We are also tasked to obtain the area of any location of interest using the greens theorem. I chose to find the area of the Quezon Memorial Circle, which has an area of 27 hectares, or 270,000 square meters. After isolating the Quezon Memorial Center and obtaining the edge, I have the following images:
After applying the Green’s theorem, i obtained an area of 233935.44 square pixels. Using the scale bar, 90 pixels is 100 meters, therefore 8100 square pixels is 10000 square meters. using ration and proportion, the area of the memorial center is 288809.1853 sq. m. or 28.88 hectares. This value is 7.0% from the theoretical value.
I obtained the area of the Quezon memorial center from:
http://www.1stphilippines.com/pc-30f6af23af986d2e822e18015fd22ce1.html
The author gives himself a grade of 9/10 since he was only able to do the rectangle and the circle.
Wynn186 