We consider a spatial voting model where candidates and voters are positioned in $d$-dimensional Euclidean space, and each voter ranks candidates based on their proximity to the voter's ideal point. We focus on the scenario where information about voters' ideal points is incomplete; for each dimension, only an interval of possible values is known. Here, we investigate the computational complexity of determining possible winners under positional scoring rules. We show the possible winner problem in one dimension is solvable in polynomial time for all $k$-truncated voting rules with constant $k$. For some scoring rules where the problem is NP-complete, such as approval voting for any dimension or $k$-approval for $d \geq 2$, we give an FPT algorithm parameterized by the number of candidates. Finally, we classify tractable and intractable settings of the weighted possible winner problem in one dimension, resolving the complexity for all two-valued positional scoring rules when $d=1$.