Introduction

LNLib is a C++ NURBS Algorithms Library.
These algorithms are primary referenced from The NURBS Book 2nd Edition.
The APIs are re-designed to make it more friendly to users.

Run LNLib

Please run build.bat first to construct C++ solution by CMake.

Features

Basic Elements:

• UV
• XYZ
• XYZW
• Matrix4d
• LNObject

Algorithms in The Nurbs Book:

Chapter	Content
Chapter 1	Basis Function Computation
Chapter 1 to 4	Bezier/B-Spline/NURBS Curve and Surface
Chapter 5	Curve and Surface Decomposition Knot Insertion/Refinement/Removal Degree Elevation and Reduction
Chapter 6	Curve/Surface Point Inversion Surface Tangent Vector Inversion Curve/Surface Reparameterization Curve Transform and Reverse Surface Swap and Reverse
Chapter 7	Create Arc/Conic Curve
Chapter 8	Create Bilinear/Cylindrical/Ruled/Revolved/CornerFillet Surface
Chapter 9	Global/Local Curve/Surface Interpolation and Approximation
Chapter 10	Create Swung/Loft/Sweep/Gordon/Coons Surface
Chapter 11	Curve Modification in Control Point Locations or Weight Values
Chapter 12	Curve Clamp/UnClamp/IsClamp KnotVector IsUniform Curve IsClosed/IsPeriodic

Additional Algorithms:

Description	Content
Basic Properties	Curve/Surface Curvature and Normal Curve Split/Segment/Merge/Offset Curve IsLinear/IsArc Curve Approximate Length Surface Approximate Area
Curve Creation	Create Line/Cubic Hermite
Tessellation	Curve Tessellation Surface Triangulation

Visualization

LNLibViewer based on VTK

NURBS Fitting by Neural Network

ND-LNLib based on LibTorch (PyTorch C++ version)

Convert to OpenCascade NURBS surface

#include "LNObject.h"
#include "XYZ.h"
#include "XYZW.h"
#include "NurbsSurface.h"
#include "KnotVectorUtils.h"
#include <Geom_BSplineSurface.hxx>

void ConvertToOpenCascadeSurface(const LNLib::LN_NurbsSurface& surface, Handle(Geom_BSplineSurface)& internalSurface)
{
    LNLib::NurbsSurface::Check(surface);

    std::vector<double> knotU = surface.KnotVectorU;
    std::vector<double> knotV = surface.KnotVectorV;

    const int numPolesU = static_cast<int>(surface.ControlPoints.size());
    const int numPolesV = static_cast<int>(surface.ControlPoints[0].size());

    TColgp_Array2OfPnt poles(1, numPolesU, 1, numPolesV);
    TColStd_Array2OfReal weights(1, numPolesU, 1, numPolesV);

    for (int i = 0; i < numPolesU; i++) {
        for (int j = 0; j < numPolesV; j++) {
            const LNLib::XYZW& wcp = surface.ControlPoints[i][j];
            const LNLib::XYZ& cp = wcp.ToXYZ(true);
            poles.SetValue(i+1, j+1, gp_Pnt(cp.GetX(), cp.GetY(), cp.GetZ()));
            weights.SetValue(i+1, j+1, wcp.GetW());
        }
    }

    std::map<double, int> mapU = LNLib::KnotVectorUtils::GetKnotMultiplicityMap(knotU);
    TColStd_Array1OfReal knotsU(1, static_cast<int>(mapU.size()));
    TColStd_Array1OfInteger multsU(1, static_cast<int>(mapU.size()));
    
    std::vector<double> Ukeys;
    Ukeys.reserve(mapU.size());
    std::vector<int> UMults;
    UMults.reserve(mapU.size());
    for (auto it = mapU.begin(); it != mapU.end(); ++it) {
        Ukeys.emplace_back(it->first);
        UMults.emplace_back(it->second);
    }
    for (int i = 0; i < Ukeys.size(); i++) {
        knotsU.SetValue(i+1, Ukeys[i]);
    }
    for (int i = 0; i < UMults.size(); i++) {
        multsU.SetValue(i+1, UMults[i]);
    }

    std::map<double, int> mapV = LNLib::KnotVectorUtils::GetKnotMultiplicityMap(knotV);
    TColStd_Array1OfReal knotsV(1, static_cast<int>(mapV.size()));
    TColStd_Array1OfInteger multsV(1, static_cast<int>(mapV.size()));

    std::vector<double> Vkeys;
    Vkeys.reserve(mapV.size());
    std::vector<int> VMults;
    VMults.reserve(mapV.size());
    for (auto it = mapV.begin(); it != mapV.end(); ++it) {
        Vkeys.emplace_back(it->first);
        VMults.emplace_back(it->second);
    }
    for (int i = 0; i < Vkeys.size(); i++) {
        knotsV.SetValue(i+1, Vkeys[i]);
    }
    for (int i = 0; i < VMults.size(); i++) {
        multsV.SetValue(i+1, VMults[i]);
    }

    internalSurface = new Geom_BSplineSurface(
        poles, weights, knotsU, knotsV,
        multsU, multsV,
        surface.DegreeU, surface.DegreeV);
}

More Details could be found in LNLibEx Library, which used for export nurbs surfaces to STEP or IGES format file.

Online Document

Welcome to use https://deepwiki.com/BIMCoderLiang/LNLib powered by Devin.

Contributing

Welcome join this project including discussions in Issues and make Pull requests.

Author

LNLib is created by Yuqing Liang (BIMCoder Liang).

• bim.frankliang@foxmail.com
• 微信公众号：BIMCoder

License

The source code is published under LGPL 2.1, the license is available here.

Primary Reference

The NURBS Book 2nd Edition by Les Piegl & Wayne Tiller