I am trying to calculate the (x1,y1), (x2,y2) coordinates of a line. From the image consider the rectangle of width w, height h, center c and angle θ.
If the same is given in a graph with X and Y axis then we can draw a tangent with angle θ from the center to the edge of the circle. To calculate the point using formula, I know I can use
x = cos(θ) * r
y = sin(θ) * r
Is there a formula to find the x1,x2,y1,y2?
On
Instead of using the formulas $x=r\cos \theta$, $y=r\sin\theta$, I suggest you just look at the triangle in your picture and use the definition of $\tan$ and $\cot$.
Case 1: $-\cot\frac{h}{w} \leq \theta \leq \cot\frac{h}{w}$. In this case, the green line intersects the right vertical red side. Note that $x_1=\frac{w}{2}$ and $y_1 = x_1 \tan\theta = \frac{w}{2}\tan\theta$.
Case 2: $\cot\frac{h}{w} \leq \theta \leq \pi - \cot\frac{h}{w}$. In this case, the green line intersects the upper horizontal red side. Note that $y_1=\frac{h}{2}$ and $x_1 = y_1 \cot\theta = \frac{h}{2}\cot\theta$.
The remaining two following cases are similar
Case 3: $\pi-\cot\frac{h}{w} \leq \theta \leq \pi+\cot\frac{h}{w}$.
Case 4: $\pi+\cot\frac{h}{w} \leq \theta \leq -\cot\frac{h}{w}$.
From $x=r\cos \theta,\; y=r\sin\theta$ you get $x=y\cot\theta.$
Notice that $$y_1=\frac{h}{2},$$ from the above you obtain $$x_1=\frac{h}{2}\cot\theta.$$
Can you find $x_2$ and $y_2?$