I'm a little confused with a simulation I'm about to implement soon. I could use a little help in vector displacement (if I got this part right), I'm really dumb at figuring this out. Please consider the following problem I formulated to give you an intuition on what I'm trying to calculate.
Problem (Please View Attached Diagram)
Given a point with the following details:
- Initial Coordinate: $(x_1, y_1)$
- Displacement Direction (Always from North): $\theta$
- Displacement Magnitude: $s$ units
What is the new coordinate $(x_2, y_2)$, for the above point being displaced from its initial coordinate $(x_1, y_1)$?
In general, I'd like some sort of formula to compute the new coordinates $(x_2, y_2)$ based on any given initial coordinates $(x_1, y_1)$, displacement angle $\theta$ from North, and some displacement magnitude $s$.
Angle Convention
Sorry about the weird angle, I'm trying to start from North, $0^o$ and move in a clockwise direction. Therefore, here are some angles:
- North: $0^o$
- North-East: $45^o$
- South: $180^o$
- South-West: $225^o$
- North-West: $315^o$