I have a circle of radius $r$, and I have a bounding box with 4 sides, $a$, $b$, $c$ and $d$ as illustrated in the below diagram:
Here are a few constraints
$r \geq a$ $r \geq b$ $c >> a$ $d >> a$ $c >> b$ $d >> b$
$a$ and $b$ must be perpendicular to $d$ segment.
Another condition is that the the circular sectors must touch one of the long line segment ( the top line segment in this case), base on another long segment ( the bottom line segment in this case) and must not go out from it.
What is the algorithm/equation that allows me to generate all the circular sectors that
- Touch one of the line segments
- Won't go out from it
- Fill the bounding box ( as defined by $a$, $b$, $c$ and $d$) as compactly as possible?