I have a line with coordinates $(a1, b1)$ and $(b2, b2)$. I want to calculate the $(x1, y1)$ and $(x2, y2)$ as shown in image below such that the line will form a rectangle. Given, I know the height of the rectangle, how what is the easiest way to calculate $(x1, y1)$ and $(x2, y2)$?
Calculate rectangle coordinates from line and height
1
$\begingroup$
geometry
-
1The slope of your given segment is $\frac{b_2-b_1}{a_2-a_1}$; take the negative reciprocal of that for the perpendicular, and then you should be able to reckon how to get the two other points needed... – 2011-12-22
2 Answers
3
As J.M. says, the line from $(a1,b1)$ to $(x1,y1)$ has slope $\sigma = -\frac{a2-a1}{b2-b1}$. So points on the line have the form $(x,y) = (a1+t, b1+\sigma t)$You have to choose $t$ so that $(x1,y1)$ is at a distance $h$ from $(a1,b1)$. The distance is $t\sqrt{1+\sigma^2}$, so put $t=h/\sqrt{1+\sigma^2}$
The same $t$ serves to calculate $(x2,y2)$.
-
0Excellent and easy. Thanks @TonyK! – 2011-12-22
0
Let's denote Height as $h$. You should solve following system of equations :
$\begin{cases} h=\sqrt{(x_1-a_1)^2+(y_1-b_1)^2} \\ h=\sqrt{(x_2-a_2)^2+(y_2-b_2)^2} \\ \sqrt {(b_2-b_1)^2+(a_2-a_1)^2}=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\ \frac{y_2-y_1}{x_2-x_1}=\frac{b_2-b_1}{a_2-a_1} \end{cases}$
-
0@TonyK,It's good to "see" you...you are my favorite critic :-) – 2011-12-22