The quadratic distinct-angle conjecture in general position

For $d\in\{2,3\}$, let $A_{\mathrm{gen}}^{(d)}(n)$ denote the minimum number of distinct angles formed by a set of $n$ points in general position in $\mathbb R^d$, where general position means no three points are collinear and no four points lie on a circle. Quadratic distinct-angle conjecture. Both quantities satisfy

$$A_{\mathrm{gen}}^{(2)}(n)=\Theta(n^2)\qquad\text{and}\qquad A_{\mathrm{gen}}^{(3)}(n)=\Theta(n^2).$$

The paper gives $O(n^2)$ constructions in both dimensions, so the conjecture asserts that these constructions are optimal up to constant factors.