Draw2Think: Harnessing Geometry Reasoning through Constraint Engine Interaction

• URL: http://arxiv.org/abs/2605.20743v1
• Date: Wed, 20 May 2026 05:46:14 GMT
• Title: Draw2Think: Harnessing Geometry Reasoning through Constraint Engine Interaction
• Abstract summary: Vision-language models solve geometry problems with rising accuracy, yet their intermediate states remain latent and unverifiable.<n>We present Draw2Think, a framework that recasts geometric reasoning from latent spatial inference into agentic interaction with the GeoGebra constraint engine.
• Score: 59.47026381165585
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Vision-language models solve geometry problems with rising accuracy, yet their intermediate states remain latent and unverifiable: a relation expressed in textual reasoning or drawing code carries no guarantee that a constraint-satisfying configuration realizes it. We observe that existing externalization methods based on rendered pixels or one-shot scripts fail to provide exact, per-action geometric guarantees. Enforcing geometric relations by algebraic definition closes this gap: the workspace becomes a constraint-checked evolving canvas. We present Draw2Think, a framework that recasts geometric reasoning from latent spatial inference into agentic interaction with the GeoGebra constraint engine. In a Propose-Draw-Verify loop, Draw2Think externalizes hypotheses onto an executable canvas, measures exact geometric quantities, and feeds structured observations back to the model, so subsequent reasoning proceeds from checked canvas state grounded by the shared workspace. This externalization makes two properties separately auditable: model-level Construction Fidelity (whether the canvas realizes the intended configuration) and engine-level Measurement Faithfulness (exact values and relations from canvas constraints). Across construction, outcome, and rendering evaluations, Draw2Think builds canvases that pass 95.9% predicate-level and 84.0% strict problem-level construction checks on GeoGoal, improves outcome accuracy by up to 4.1%/16.4% on planar/solid benchmarks, and attains 68.2%/90.5% strict/relaxed rendering scores on GenExam-math. Project page is available at https://draw2think.github.io/

Related papers

• PolarSym: Polar Geometry-aware Attention for CAD Floorplan Parsing [1.8878225601735998]
  PolarSym is a polar-coordinate geometry-aware attention framework for CAD plan parsing.<n>We show that PolarSym surpasses the reproduced SymPoint V2 baseline by 1.73% PQ, 1.54% RQ and 4.31% mIoU under identical training settings.
  arXiv  Detail & Related papers  (2026-08-12T08:34:32Z)
• G$^2$TAM: Geometry Grounded Track Anything Model [49.05553245076823]
  We propose a unified framework for promptable instance tracking in 3D using only unordered RGB images or videos.<n>G$2$TAM employs spatially aligned geometric representations as implicit memory, ensuring stable instance identity and localization across frames and views.<n>At its core is a cross-modal spatial encoder that integrates visual and textual prompts into a shared geometric space, enabling end-to-end spatial reconstruction and instance-consistent mask prediction.
  arXiv  Detail & Related papers  (2026-07-04T09:32:13Z)
• Internalizing Geometric Law: Learning from Solver Residuals for Precision-Critical Generation [2.459492253868525]
  We study open-ended geometric synthesis from natural language.<n>We release PyGeoX, a programmable geometric DSL that compiles declarative constraints into a differentiable loss.<n>We propose Saturating Additive Rewards (SAR), which decompose the reward into bounded per-constraint terms.
  arXiv  Detail & Related papers  (2026-06-08T09:44:31Z)
• GeoBuildBench: A Benchmark for Interactive and Executable Geometry Construction from Natural Language [18.57905469277832]
  GeoBuildBench is a benchmark designed to evaluate whether large language models and multimodal agents can ground informal natural-language plane geometry problems into executable geometric constructions.<n>We evaluate several state-of-the-art multimodal models in a bounded iterative setting and show that, despite reasonable success rates, models frequently exhibit structural hallucinations, missing objects, and failures to satisfy geometric constraints.
  arXiv  Detail & Related papers  (2026-05-13T08:30:12Z)
• Mind the Gap: Geometrically Accurate Generative Reconstruction from Disjoint Views [0.8435195043404353]
  We introduce Generative Reconstruction from Disjoint Views as a new paradigm.<n>We propose GLADOS, a general, modular framework that operates through three stages.<n>As an architectureagnostic framework, GLADOS enables seamless integration of future advances in generation, reconstruction, and inpainting.
  arXiv  Detail & Related papers  (2026-05-08T10:24:23Z)
• SpatialEvo: Self-Evolving Spatial Intelligence via Deterministic Geometric Environments [75.60795462502949]
  SpatialEvo is a self-evolving framework for 3D spatial reasoning.<n>It formalizes 16 spatial reasoning task categories under explicit geometric validation rules.<n>It converts unannotated 3D scenes into zero-noise interactive oracles, replacing model consensus with objective physical feedback.
  arXiv  Detail & Related papers  (2026-04-15T17:59:12Z)
• Learning Hierarchical and Geometry-Aware Graph Representations for Text-to-CAD [22.163726324892256]
  We propose a hierarchical and geometry-aware graph as an intermediate representation.<n>Instead of mapping text directly to code, our framework first predicts structure and constraints, then conditions action sequencing and code generation.<n>Our method consistently outperforms existing approaches in both geometric fidelity and accurate satisfaction of geometric constraints.
  arXiv  Detail & Related papers  (2026-04-11T07:49:16Z)
• Make Geometry Matter for Spatial Reasoning [62.61667611352403]
  Vision-language models (VLMs) achieve strong image and video understanding, yet their ability to perform spatial reasoning in both static scenes and dynamic videos remains limited.<n>Recent advances try to handle this limitation by injecting geometry tokens from pretrained 3D foundation models into VLMs.<n>We propose GeoSR, a framework designed to make geometry matter by encouraging VLMs to actively reason with geometry tokens.
  arXiv  Detail & Related papers  (2026-03-27T17:45:12Z)
• ControlVP: Interactive Geometric Refinement of AI-Generated Images with Consistent Vanishing Points [32.23473666846317]
  We propose ControlVP, a user-guided framework for correcting vanishing point inconsistencies in generated images.<n>Our approach extends a pre-trained diffusion model by incorporating structural guidance derived from building contours.<n>Our method enhances global geometric consistency while maintaining visual fidelity comparable to the baselines.
  arXiv  Detail & Related papers  (2025-12-08T12:38:11Z)
• Geometrically-Constrained Agent for Spatial Reasoning [53.93718394870856]
  Vision Language Models exhibit a fundamental semantic-to-geometric gap in spatial reasoning.<n>Current paradigms fail to bridge this gap.<n>We propose a training-free agentic paradigm that resolves this gap by introducing a formal task constraint.
  arXiv  Detail & Related papers  (2025-11-27T17:50:37Z)
• DVMNet++: Rethinking Relative Pose Estimation for Unseen Objects [59.51874686414509]
  Existing approaches typically predict 3D translation utilizing the ground-truth object bounding box and approximate 3D rotation with a large number of discrete hypotheses.<n>We present a Deep Voxel Matching Network (DVMNet++) that computes the relative object pose in a single pass.<n>Our approach delivers more accurate relative pose estimates for novel objects at a lower computational cost compared to state-of-the-art methods.
  arXiv  Detail & Related papers  (2024-03-20T15:41:32Z)
• Geometric Representation Learning for Document Image Rectification [137.75133384124976]
  We present DocGeoNet for document image rectification by introducing explicit geometric representation. Our motivation arises from the insight that 3D shape provides global unwarping cues for rectifying a distorted document image. Experiments show the effectiveness of our framework and demonstrate the superiority of our framework over state-of-the-art methods.
  arXiv  Detail & Related papers  (2022-10-15T01:57:40Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.