  Surface reconstruction from point clouds is a crucial task in the fields of
computer vision and computer graphics. SDF-based methods excel at
reconstructing smooth meshes with minimal error and artefacts but struggle with
representing open surfaces. On the other hand, UDF-based methods can
effectively represent open surfaces but often introduce noise, leading to
artefacts in the mesh. In this work, we propose a novel approach that directly
predicts the intersection points between line segment of point pairs and
implicit surfaces. To achieve it, we propose two modules named Relative
Intersection Module and Sign Module respectively with the feature of point pair
as input. To preserve the continuity of the surface, we also integrate symmetry
into the two modules, which means the position of predicted intersection will
not change even if the input order of the point pair changes. This method not
only preserves the ability to represent open surfaces but also eliminates most
artefacts on the mesh. Our approach demonstrates state-of-the-art performance
on three datasets: ShapeNet, MGN, and ScanNet. The code will be made available
upon acceptance.
