Semi-Constructive Method for 3D Solid Reconstruction from Orthographic Views Using Planar Decomposition and Winged-Edge Topology

Reconstructing a 3D solid from its orthographic projections is a classical problem in computational geometry and computer-aided design (CAD). Although humans perform this task intuitively in technical drawing, algorithmic reconstruction is non-trivial due to ambiguity and incomplete spatial information.

This paper presents a semi-constructive computational method for reconstructing 3D polyhedral solids from orthographic projections (front, top, and side views). The approach integrates planar decomposition, graph-based cycle analysis, and a Winged-Edge boundary representation (BRep) structure to ensure geometric and topological consistency. Unlike universal reconstruction algorithms, the proposed method targets structured polyhedral objects and progressively refines candidate 3D edges through topological filtering. The methodology includes DXF parsing, vertex inference, candidate segment generation via planar intersections, cycle-based internal edge elimination, collinearity merging, and final BRep construction. The experimental results demonstrate correct reconstruction for a representative class of polyhedral objects and highlight both strengths and current limitations of the approach.

The method does not aim to solve the universal reconstruction problem but instead focuses on a structured family of polyhedral solids whose faces are predominantly planar and frequently parallel to projection planes.

The main contributions are as follows:

-A pipeline integrating 2D DXF parsing with 3D vertex inference.

-Exhaustive candidate segment generation using planar intersections.

-Graph-based cycle analysis to eliminate internal edges. \item A consistent Winged-Edge BRep construction.

-Export to STL with correct face orientation.