Computer Aided Design

Computer Aided Design (CAD) encompasses the digital authoring, modification and documentation of two- and three-dimensional models for engineering and manufacturing. At its core are two principal modelling paradigms: Constructive Solid Geometry (CSG), which builds complex parts by Boolean combinations of primitive solids, and Boundary Representation (B-Rep), which describes objects via their surfaces and topology. Modern CAD systems employ parametric, feature-based and constraint-driven tools that capture design intent through dimensions, relationships and parent–child feature hierarchies. Sketch-based geometry creation, automatic constraint solving and associative update propagate changes through parts, assemblies and downstream deliverables such as drawings, simulations or toolpaths. Extensions for mesh and surface modelling—using splines, subdivision schemes or procedural methods—permit free-form shape creation, adaptive refinement and topology management. CAD has evolved into an integrative platform for styling, analysis, optimization and digital manufacture, providing a unified digital product definition that underpins virtual prototyping, model-based enterprise workflows and automated downstream processes.

Research from Nature Portfolio

A new geometry-image parameterisation method ensures exact preservation of mesh topology by mapping 3D surface vertices to integer grid points and employing capacity-constrained Delaunay triangulation to establish blue-noise distributions. The resulting images incur only floating-point rounding error when stored in 16-bit channels and eliminate reconstruction artefacts, enabling loss-free surface exchange for CAD/CAM and reverse-engineering pipelines.

A general framework for dilational surfaces produces mechanisms that uniformly scale arbitrary curved manifolds through tangent-plane pantograph assemblies. By triangulating a target surface and substituting each triangle with compliant pantograph linkages, the construction enables mechanical dilation to a single point without altering curvature, opening CAD-driven design of deployable architectural, aerospace and soft-robotic structures.

Research from all publishers

A robust parameterisation pipeline computes globally injective maps for disk-topology meshes with positional constraints by augmenting a valid scaffold mesh and iteratively eliminating element flips via edge-based remeshing. The method scales to complex geometries with minimal manual intervention, yielding injective surface charts for texture mapping, analysis and CAD data exchange.

The three-dimensional “motorcycle complex” generalises the motorcycle graph to volumetric settings, tracing collision events among propagating line-traces in hexahedral meshes or seamless parametrisations. The resulting block complex guarantees topologically sound decompositions suitable for structured hexahedral mesh generation, block-aligned spline spaces and isogeometric analysis applications.

Non-uniform interpolatory subdivision schemes with spatially varying refinement rules achieve higher smoothness than classical stationary counterparts within the same mask support. Newly derived binary and quaternary schemes produce C¹ and C² limit curves respectively, demonstrating that non-uniform refinement can yield smoother CAD-compatible curves without increasing computational footprint.

Computer Aided Design publication trend

The graph below shows the total number of articles in computer aided design across all publications each year (not limited to Nature Index journals).

Technical terms

Parametric modeling: Creation of geometry by defining dimensions and relations among features so that changes automatically propagate through the model.

Feature-based modeling: Assembly of a model from named engineering primitives (e.g. holes, pockets, fillets) that encapsulate design intent and manufacturing semantics.

Boundary Representation (B-Rep): An explicit description of a solid by its bounding faces, edges and vertices, capturing both geometry and topology.

Constructive Solid Geometry (CSG): A modelling approach that forms complex solids through Boolean operations on primitive shapes.

Geometry image: A parameterisation of a 3D surface onto a regular 2D grid, storing vertex positions in image pixels for compact exchange.

Injective parameterisation: A mapping from a surface to the plane that preserves local orientation and avoids fold-overs (negative Jacobians).

Pantograph mechanism: A linkage of bars configured to scale and reproduce shapes while maintaining geometric similarity, used here to effect dilational surfaces.

Subdivision scheme: An iterative algorithm that refines a control mesh via stencil masks to converge to a smooth limit curve or surface.

References

1. Major Technology 1: Computer Aided Design—CAD.
2. A novel geometry image to accurately represent a surface by preserving mesh topology. Scientific Reports (2021).
3. A general method for the creation of dilational surfaces. Nature Communications (2019).
4. Practical construction of globally injective parameterizations with positional constraints. Computational Visual Media (2023).
5. The 3D Motorcycle Complex for Structured Volume Decomposition. Computer Graphics Forum (2022).
6. Non-uniform interpolatory subdivision schemes with improved smoothness. Computer Aided Geometric Design (2022).