1. The Cognitive Gap: From Visual Realism to Engineering Usability

In recent years, multimodal large language models have made major progress in generating content across many dimensions. In computer-aided design (CAD) and 3D modeling demos, models can quickly produce structurally complex part assemblies, continuous rotating views, and smooth exploded-view animations from natural language instructions. These results look highly realistic on the surface, which has led the industry to expect automated generation of engineering models.

In serious engineering and research settings, however, a model that looks right is not necessarily structurally correct. Industrial manufacturing and scientific research require more than a rendered outline. They depend on internal topology, dimensional tolerances, mechanical fit, and compliance with physical laws. Many polished models generated by AI show serious defects when they reach downstream engineering analysis or CNC machining. Common problems include interference between parts, confused assembly logic, uneven wall thickness, and stress concentrations. Such models cannot go directly into production.

When benchmarks move from traditional 2D view generation quality to rigorous tests on real cross-disciplinary 3D data, the performance of leading multimodal models drops sharply. The data covers biomolecules, crystal structures, medical imaging, architecture, and mechanical engineering. In evaluations that require autonomous manipulation of 3D objects and quantitative analysis, leading frontier models generally fail to reach a passing score. This result shows that current large models still have significant fundamental weaknesses in 3D geometric understanding and spatial reasoning.

2. Mechanism Analysis: Why Models Draw Convincingly but Incorrectly

To understand why models struggle with 3D understanding, we need to examine their underlying representation learning paradigm and spatial perception mechanisms.

2.1 Projection Ambiguity and Loss of Depth Information

Most multimodal models are pretrained primarily on arrays of 2D pixels. When a 3D world is projected into a 2D image, one dimension necessarily collapses. Depth, surface normals, and occlusion relationships for hidden surfaces become implicit and must be inferred. Models typically estimate 3D shape from visual cues such as shadows and perspective lines. This process is statistical probability matching, not explicit modeling in a 3D Euclidean coordinate system. When analyzing occlusion in complex assemblies, models are highly prone to hallucination.

2.2 Conflict Between Autoregressive Generation and Continuous Geometry

Mainstream large language models generate output autoregressively over discrete tokens. This approach works well for discrete symbols and natural language. However, when handling continuous spatial manifolds, non-uniform rational B-splines (NURBS), and high-precision algebraic surfaces, these models lack continuous calculus constraints by design. Engineering CAD requires more than mesh appearance. It depends on parametric construction history (CSG) and boundary representation (B-Rep). Small deviations in coordinate parameters from discrete generation can cause topological collapse in later Boolean operations, including union, difference, and intersection.

2.3 Lack of Explicit Physics and Assembly Geometry Kernels

When human engineers model in 3D and review drawings, they apply strict physical reasoning. This includes degrees of freedom (DOF), mating relationships such as coaxial, flush, and tangent fits, tolerance zones, and stress transfer paths. Current text-only and image-text large models have no built-in parametric geometry solver or physics simulation kernel. They cannot solve constraint equations during generation. As a result, a generated model may look complete while its parts have hidden spatial penetration or uncontrolled degrees of freedom.

3. Core Evaluation Dimensions for Cross-Disciplinary Spatial Reasoning

True 3D spatial intelligence is not simply mesh reconstruction. It requires models to work like professional scientists and engineers, with dynamic observation, quantitative measurement, and geometric reasoning across scales and disciplines. Rigorous scientific benchmarks mainly test the following three dimensions.

3.1 Mechanical and Architectural CAD: Assembly Topology and Functional Fit

In engineering drawing, models must handle strict reverse engineering and compliance checks:

• Interference and clearance checks: Determine whether two adjacent components penetrate each other under dynamic operating conditions, and whether the clearance meets lubrication or thermal expansion allowances.
• Constraint-based assembly tree reconstruction: Infer datum planes, rotation axes, and locating pin fits from an unordered 3D mesh.
• Engineering tolerance reasoning: Derive geometric tolerances, such as cylindricity, coaxiality, and perpendicularity, from force analysis instead of assigning dimensions arbitrarily.

3.2 Biomacromolecules and Microstructures: Spatial Conformation and Chemical Microenvironment

In biophysics and chemistry, measuring 3D structure is closely tied to quantitative geometry:

• Local microenvironment distance measurement: In complex protein assemblies, locate ligand molecules at active sites. Measure hydrogen bond distances and van der Waals radii between specific atoms and surrounding ions and water molecules.
• Multi-conformation transition analysis: Derive dihedral angle changes as macromolecules twist in space. Evaluate how steric hindrance affects biological activity.

3.3 Crystal Chemistry and Materials Science: Point Group Symmetry and Periodic Extension

Crystal structures are a typical test of a model’s abstract 3D capability:

• Unit cell symmetry operations: Based on space group symmetry, predict how a crystal stacks in 3D space through translation, rotation, and inversion.
• Coordination polyhedron identification: Identify the geometry of polyhedra formed by anions around a central cation, such as octahedra and distorted tetrahedra.

4. An Engineering Verification Workflow for 3D Spatial Reasoning

To address the spatial geometry weaknesses of pure LLMs, modern engineering architectures often use multimodal large models as task planners. These planners work with parametric geometry kernels in a closed-loop verification system. The following is a conceptual sketch of spatial constraint checking:

```python

Conceptual engineering architecture: LLM instruction parsing and

closed-loop verification with geometric constraint solving

import numpy as np

class AssemblyConstraintEngine:
def init(self):
self.parts = {}
self.constraints = []

def register_part(self, part_id, mesh_data, transformation_matrix):
    """Register a part with exact 3D vertices and a pose matrix"""
    self.parts[part_id] = {
        "mesh": mesh_data,
        "transform": np.array(transformation_matrix)
    }
def add_coaxial_constraint(self, part_a, axis_a, part_b, axis_b, tolerance=1e-4):
    """Add a coaxiality assembly constraint"""
    self.constraints.append({
        "type": "coaxial",
        "targets": (part_a, part_b),
        "axes": (axis_a, axis_b),
        "tol": tolerance
    })
def verify_assembly(self):
    """Call low-level algebraic geometry computations to perform
    physical and geometric plausibility self-checks"""
    verification_report = {"valid": True, "interferences": [], "alignment_errors": []}
    # 1. Axis collinearity and tolerance check
    for c in self.constraints:
        if c["type"] == "coaxial":
            p_a, p_b = c["targets"]
            v_a = self.parts[p_a]["transform"][:3, :3] @ c["axes"][0]
            v_b = self.parts[p_b]["transform"][:3, :3]