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Dr. Sunayana Ghosh | Computational Geometry & Geospatial ML Consultant
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Mesh2NURBS: From Medical Scans to CAD Surfaces

·3 mins
Research Medtech CAD NURBS Computational Geometry Research C++ OpenCascade
Dr. Sunayana Ghosh
Author
Dr. Sunayana Ghosh
PhD in Computational Geometry • 15+ years in Medtech & Climate Tech • Building data solutions that matter
Table of Contents

Mesh2NURBS
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Presented: Group Meeting, Zuse Institute Berlin, February 2016 Collaborators: T. Amiranashvili, M. Bindernagel, H. Lamecker, H. Ramm Institutions: Zuse Institute Berlin (ZIB) — Computational Medicine Group · 1000 Shapes (ZIB spin-off)

The Problem
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Modern medical imaging (CT, MRI) produces detailed 3D surface meshes of anatomical structures. CAD systems used for designing implants and surgical instruments, however, require smooth parametric surfaces — specifically NURBS (Non-Uniform Rational B-Splines). Bridging this gap automatically and accurately is a fundamental challenge in patient-specific medical device manufacturing.

STL mesh of a bone (left) converted to a NURBS patchwork (right)
The core problem: discrete STL mesh to smooth NURBS patchwork

A triangulated STL mesh from a CT scan — for example a long bone — must become a structured NURBS surface suitable for CAD tools and biomechanical simulation. The challenge is making this conversion automatic, accurate, and topologically valid.

Why NURBS?
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NURBS surfaces are the standard representation in medical CAD for several reasons:

  • Simulation-ready — naturally support deformation modelling of living tissue, effects of drugs on organs, and interaction with surgical devices
  • Implant design — provide a smooth, controllable substrate for designing patient-specific artificial implants
  • Surgical device integration — enable simulation of anatomical structures interacting with instruments and diagnostic tools
  • Compact — significantly smaller file sizes than equivalent STL meshes

Approach
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Femur with colour-coded QuadPatch network overlaid
QuadPatch network derived from a femur mesh — the topological foundation for NURBS fitting

The project was a feasibility study exploring automated conversion of triangulated surface meshes into smooth NURBS surfaces. The core insight is that NURBS surfaces require a quadrilateral topology as their foundation — they cannot directly fit over triangular meshes.

The approach proceeds in three conceptual stages:

  1. Deriving a quadrilateral patch network from the input triangulated mesh
  2. Fitting a smooth NURBS surface patch to each quad region
  3. Stitching the individual patches into a coherent, watertight surface approximation

Result
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NURBS surface approximation of anatomical geometry
Final NURBS surface approximation — smooth parametric surfaces fitted to anatomical mesh geometry

The prototype demonstrated that automatic mesh-to-NURBS conversion is feasible for anatomical geometry. The resulting surfaces are smooth, compact, and compatible with standard CAD workflows for medical device design.

Relevance
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This work connects directly to later roles:

  • Ottobock — NURBS surface approximation for prosthetic socket fitting, where the same mesh-to-smooth-surface challenge appeared in a clinical production workflow
  • Fiagon — 3D surface processing for surgical navigation, where accurate registration between patient anatomy and device geometry required the same geometric foundations

The core problem — bridging discrete geometry and smooth CAD representations — recurs throughout computational medicine, medical device engineering, and orthotics.

Domain: Medical technology · Computational geometry · CAD/CAGD · NURBS surface fitting

Institutions: Zuse Institute Berlin · 1000 Shapes