The Rasmah Handbook

Welcome to the Rasmah Handbook — a book-style guide to Rasmah, a differentiable, programmatic CAD and computational-geometry framework for Julia.

The Handbook is written like a book, not a reference list. Each chapter opens with the idea — explained in plain language, with the mathematics where it matters — and then documents the functions that put the idea into practice, with their algorithms, their arguments, and worked examples you can run.

The rendered 3D views throughout the Handbook are interactive, not static images: drag to rotate, scroll (or pinch) to zoom, and use the on-screen toolbar to pan, change the view, and inspect the model.

How the Handbook is organized

The chapters build on one another. Start at the top and read down.

Chapter	What you will learn
Geometry & modeling	The central idea of Rasmah — a CAD model as a differentiable program — plus the three geometry backends (SDF, BRep, mesh).
Primitives, SDFs, and CSG	The basic solid shapes, how signed distance fields represent them exactly, and how to combine them with boolean operations and transforms.
Sketches, extrusion, and revolution	2D sketches and the two operations that sweep them into 3D solids.
Modeling operations	Hollowing, offsetting, mirroring, patterns, lofting, sweeping, and edge treatments.
NURBS and the exact BRep	The exact boundary representation, topological naming, NURBS curves, and snapping.
Meshing	The two mesh types — surface and volume — and the canonical shape-to-mesh workflow.
Surface meshing	The triangle surface mesh — the exact icosphere, marching cubes, dual contouring, and the adaptive octree.
Volume meshing	The tetrahedral mesh that fills a solid's interior, plus the quality metrics that keep a solve healthy.
Mesh repair	Diagnosing and fixing the defects of a mesh imported from a scanner or file.
From points to mesh	Rebuilding a mesh from a point cloud — normals, reconstruction, and RANSAC primitive fitting.
The finite element method	From a differential equation to the linear system `K u = f` — the assemblers, solvers, and stress recovery.
Solving with physics	Running a simulation in one line by naming the physics, the material, and the boundary conditions.
Nonlinear solid mechanics	Finite-strain hyperelasticity and J2 plasticity — large deformation and permanent yielding.
Coupled multiphysics	Piezoelectricity, thermoelectricity, and poroelasticity — two fields driving each other.
Electrostatics & magnetostatics	The electric and magnetic scalar potentials — Laplace's equation solved for `φ` and `ψ`.
Electromagnetic waves	Full-wave vector Maxwell — cavity modes, the magnetic vector potential, and time-domain FETD.
Fluid flow	Creeping Stokes and inertial Navier–Stokes — the coupled velocity–pressure saddle problem.
Eigenproblems	Natural frequencies, buckling loads, and acoustic cavity modes — the eigenvalue problems of a structure.
Structural elements	The slender-member elements — trusses, beams, plates, and shells — that replace solid meshes with a few bars or a surface.
Materials & phase-field physics	Constitutive models and phase fields — plasticity, viscoelasticity, fracture, and phase separation.
Transport & coupled physics	Bioheat, electrolytes, MHD, waves, and the J-integral and topological-derivative analyses.
Topology optimization	The SIMP density method — carve a light structure out of a design space by scaling each element's stiffness.
Materials	What a body is made of — stiffness, density, conductivity, strength — and how to build solid, anisotropic, composite, and fluid materials.
Optimization	Gradient-based minimization — quasi-Newton descent and Brent's method for finding the best design.
Nonlinear solvers	Root finding with Newton's method and the family of nonlinear solvers behind `solve_nonlinear`.
Assembly & registration	Composing named parts into one model, and aligning shapes by registering their pose.
Sparse linear algebra	The sparse matrices, direct factorizations, iterative solvers, and multigrid preconditioners behind every solve.
Model reduction	Compressing fields with POD, reading dynamics with DMD, and fitting non-intrusive surrogates.
Neural networks	The native MLP core — layers, activations, initializers, and Adam training over a flat parameter vector.
Neural signed distance fields	Representing geometry as a network — SIREN activations, the eikonal regularizer, and fitting.
Physics-informed neural networks	Solving a PDE by training a network to satisfy its residual — mesh-free simulation.
Units	Physical dimensions on every quantity — SI inside, your units at the boundary.
Manufacturing	Turning a design into machine instructions — the tool path and cutter model at the heart of CAM.
Milling, turning, and cutting	Subtractive machining: pockets, profiling, surfacing, turning, and wire/beam cutting.
Additive manufacturing	3D printing: slicing, perimeters, infill, and the extrusion-balanced G-code.
File I/O	Reading and writing the exchange formats — meshes, exact CAD, volumes, and point clouds, all round-tripped.
Exact CAD exchange	STEP and IGES — the formats that preserve exact topology, not just triangles.
Volumes and point clouds	Medical imaging (DICOM/NIfTI), scan data (XYZ/PCD), and time-series PVD.
The Rasmah GUI	The browser-based interface — the Geometry → FEA → TopOpt workspace pipeline and its script generation.

Where the other resources live

The Tutorials walk through concrete, end-to-end examples (geometry, meshing, simulation, topology optimization). Each is a self-contained Quarto notebook.

Next steps

Start with Geometry & modeling.