Two isosceles right triangles, one larger ($\triangle ABC$) than the other ($\triangle DEF$), superimposed such that the smaller fits completely within the boundary of the larger.
However, $\triangle DEF$ should be sized and placed such that the following constraints are met for a given $\triangle ABC$:
- $DE$ is a fixed distance, $h$ from $AB$
- $EF$ is a fixed distance, $g$ from $BC$
- $DF$ is a fixed distance, $i$ from $AC$
It is simple to calculate $E$ but I'm struggling to calculate the coordinates for $D$ and $F$.
- $D(h, ?)$
- $E(h, g)$
- $F(?, g)$
Alternatively, given the offset $E$, what should be the lengths of $DE$ and $EF$ to satisfy the constraint for distance $i$.
For a given outer isosceles right triangle, $\triangle ABC$, I wish to define an inner isosceles right triangle, $\triangle DEF$, where the distance between all parallel sides are also given.
Geometric dilation works where the distances are all equal but I haven't found an analytical solution for where they are all different.
I am trying to produce a parameterized CAD drawing of a hollow triangular shaped box, where the thickness of each wall can be different and defined for any size box (using OpenSCAD).