Printing the Underdetermined: Materializing Multi-solutionness in Figurative Paintings

Abstract

Figurative paintings are often approached as if they depict a single recoverable 3D scene: viewers infer depth and occlusion, and reconstruction pipelines attempt to converge to one stable model. We instead foreground multi-solutionness, the non-uniqueness of 3D configurations compatible with a single painted image, and propose a workflow that keeps this non-uniqueness visible and material. Multi-solutionness arises from two sources: unobserved content, where backsides and occluded volumes admit multiple plausible completions, and observed cues, where perspective, shading, and occlusion still underconstrain geometry. When additional views are synthesized by a video generative model without explicit 3D constraints, small frame-level drifts become inevitable rather than exceptional. Our pipeline samples multiple camera-orbit multi-view video sequences from one painting, reconstructs each sequence with 3D Gaussian Splatting into a point-based Gaussian scene representation where density halos and ghosting expose unresolved degrees of freedom, and fabricates these representations as physical artifacts using DreamPrinting. By treating multiple compatible interpretations as explicit outputs rather than residual error, we provide a computational framework for spatial readings of figurative painting that can be inspected, compared, and discussed in both digital and physical form.