Im trying to do a simulation using Matlab to solve some fluid problem. For this problem I have the following shape:
For each black point I know the (x,y) coordinates.
I need to find the coordinates of the blue points which are located at 75% of the x coordinate between each two black dots and at the middle between the y coordinate of each two black dots.
I have been trying for a while but cant find simple method.
If someone can help with the logic/some code it will be much appreciated.
Thank you.
You can use standard isoparametric representation. For example, use the formula from slides 21 and 22 from http://www.rpi.edu/~des/Isoparametric.ppt
In your case for $(x_{i},y_{i})$, start with co-ordinate for top left corner for $(x_{1}, y_{1})$ and go counter-clockwise for the next three. Use $s=0.5$ and $t=0$ in the formulas below.
$$ x = \sum_{i} N_{i}(s,t) x_{i} $$ $$ y = \sum_{i} N_{i}(s,t) y_{i} $$ $$ \begin{matrix} N_{1}(s,t) & = & (1-s)(1-t)/4 \\ N_{2}(s,t) & = & (1+s)(1-t)/4 \\ N_{3}(s,t) & = & (1+s)(1+t)/4 \\ N_{4}(s,t) & = & (1-s)(1+t)/4 \end{matrix} $$