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Engineering design and CAx
cad-kernel
CAD geometry kernel
Parasolid, Open CASCADE
System
Techniques · 8
Primitives · 14
cad-kernel
B rep topology
geometry · medium: Boundary representation: solids as shells, faces, loops, edges and vertices with geometry attached
Delaunay triangulation
geometry · medium: Bowyer-Watson and incremental flips; maximizes minimum angles, dual of Voronoi
Geometric constraint solving
geometry · medium: Solve sketch constraints (distance, tangent, parallel) by graph decomposition and Newton iteration
Nurbs
geometry · medium: B-splines and NURBS curves and surfaces: knot vectors, de Boor evaluation, knot insertion
Polygon tessellation
geometry · medium: Triangulate polygons with holes (ear clipping, earcut, monotone sweep)
Solid boolean operations
geometry · medium: Union, intersection and difference of solids: classify, split and merge faces robustly
Surface surface intersection
geometry · medium: Intersect parametric surfaces by marching with subdivision and Newton refinement
Exact geometric predicates
geometry · low: Robust orient and incircle tests with adaptive-precision floats (Shewchuk) or exact arithmetic
Half edge mesh
graphics · low: Half-edge mesh connectivity for editable polygon meshes
Newton root finding
numerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.
›
Bézier curves
graphics · low: Smooth curves defined by 3-4 control points, evaluated and split with repeated linear interpolation (de Casteljau) and flattened to lines with a closed-form segment count.
›
Bounding volume hierarchy
physics · low: Binary tree of nested bounding boxes; prunes overlap and ray queries to O(log n) for any size distribution, and supports cheap insert/remove for moving objects.
›
Interval arithmetic
numerics · low: Rigorous bounds with outward rounding; root isolation and robust geometric tests
Floating-point error
numerics · low: How IEEE 754 rounding error accumulates and how to contain it: compensated (Kahan/Neumaier) and pairwise summation, error-free transformations with FMA, ULP comparisons.
›
Space filling curves
geometry · low: Z-order/Morton (geohash) and Hilbert curves mapping multi-dimensional points to sortable keys
Strongly connected components
graphs · low: Tarjan/Kosaraju SCCs for cycle detection in dependency graphs
Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
Finite differences
numerics · low: Replace derivatives with weighted differences of grid values; simple stencils plus a stability condition (CFL) turn PDEs like heat, advection and waves into array loops.
›
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
Explicit Euler
numerics · low: Step an ODE forward by its current slope, y += h·f(t, y); first-order, one evaluation per step, the baseline every other integrator is measured against.
›
Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
+ 1 more techniques
System
Techniques · 8
Primitives · 14
cad-kernel
B rep topology
geometry · medium: Boundary representation: solids as shells, faces, loops, edges and vertices with geometry attached
Delaunay triangulation
geometry · medium: Bowyer-Watson and incremental flips; maximizes minimum angles, dual of Voronoi
Geometric constraint solving
geometry · medium: Solve sketch constraints (distance, tangent, parallel) by graph decomposition and Newton iteration
Nurbs
geometry · medium: B-splines and NURBS curves and surfaces: knot vectors, de Boor evaluation, knot insertion
Polygon tessellation
geometry · medium: Triangulate polygons with holes (ear clipping, earcut, monotone sweep)
Solid boolean operations
geometry · medium: Union, intersection and difference of solids: classify, split and merge faces robustly
Surface surface intersection
geometry · medium: Intersect parametric surfaces by marching with subdivision and Newton refinement
Levenberg marquardt
numerics · medium: Damped Gauss-Newton nonlinear least squares for model calibration
Exact geometric predicates
geometry · low: Robust orient and incircle tests with adaptive-precision floats (Shewchuk) or exact arithmetic
Half edge mesh
graphics · low: Half-edge mesh connectivity for editable polygon meshes
Newton root finding
numerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.
›
Bézier curves
graphics · low: Smooth curves defined by 3-4 control points, evaluated and split with repeated linear interpolation (de Casteljau) and flattened to lines with a closed-form segment count.
›
Bounding volume hierarchy
physics · low: Binary tree of nested bounding boxes; prunes overlap and ray queries to O(log n) for any size distribution, and supports cheap insert/remove for moving objects.
›
Interval arithmetic
numerics · low: Rigorous bounds with outward rounding; root isolation and robust geometric tests
Floating-point error
numerics · low: How IEEE 754 rounding error accumulates and how to contain it: compensated (Kahan/Neumaier) and pairwise summation, error-free transformations with FMA, ULP comparisons.
›
Space filling curves
geometry · low: Z-order/Morton (geohash) and Hilbert curves mapping multi-dimensional points to sortable keys
Strongly connected components
graphs · low: Tarjan/Kosaraju SCCs for cycle detection in dependency graphs
Spline interpolation
numerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tables
Finite differences
numerics · low: Replace derivatives with weighted differences of grid values; simple stencils plus a stability condition (CFL) turn PDEs like heat, advection and waves into array loops.
›
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
Explicit Euler
numerics · low: Step an ODE forward by its current slope, y += h·f(t, y); first-order, one evaluation per step, the baseline every other integrator is measured against.
›
Thomas tridiagonal solver
numerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes
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