LNLib is a NURBS Algorithms Kernel Library.
These algorithms are primary referenced from The NURBS Book 2nd Edition.
For NURBS Curve | Surface | Volume
| Project | API Language | Instruction |
|---|---|---|
| LNLib | C++ | Run build.bat first to construct Native C++ solution by CMake |
| LNLibjs | WebAssembly | Run script in emscripten folder |
| PyLNLib | Python3.x | Switch ENABLE_PYTHON_API to ON in CMakeLists.txt and run build.bat |
| LNLibSharp | .NET8.0 | Switch ENABLE_DOTNET_API to ON in CMakeLists.txt and run build.bat, LNLibSharp depends on CApi.dll generated by CAPI project for P/Invoke |
notice: Unit tests now only cover Native C++ APIs on Windows System.
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 |
|---|---|
| NURBS Curve | Curve Curvature and Normal Curve Split/Segment/Merge/Offset Curve IsLinear/IsArc Curve Approximate Length Curve Extension (Tangent/Arc/Natural) Curve Tessellation Line/Cubic Hermite (as NURBS) Creation |
| NURBS Surface | Surface AABB and OBB BoundingBox Surface Curvature and Normal Surface Approximate Area Surface Triangulation |
| NURBS Volume | Volume Degree Elevation Volume Knot Insertion/Refinement Volume Point Inversion Volume Split Extract Surface From Volume Extract IsoCurve From Volume Volume Swap and Reverse |
XYZ center(10, 0, 0);
XYZ xAxis(-1, 0, 0);
XYZ yAxis(0, 1, 0);
double startRad = 0;
double endRad = Constants::Pi;
double radius = 5;
LN_NurbsCurve arc;
NurbsCurve::CreateArc(center, xAxis, yAxis, startRad, endRad, radius, radius, arc);
int degreeU = 3;
int degreeV = 3;
std::vector<double> kvU = { 0,0,0,0,0.4,0.6,1,1,1,1 };
std::vector<double> kvV = { 0,0,0,0,0.4,0.6,1,1,1,1 };
std::vector<std::vector<XYZW>> controlPoints(6, std::vector<XYZW>(6));
controlPoints[0][0] = XYZW(0, 0, 0, 1);
controlPoints[0][1] = XYZW(6.666666, 0, 4, 1);
controlPoints[0][2] = XYZW(16.666666, 0, 22, 1);
controlPoints[0][3] = XYZW(33.333333, 0, 22, 1);
controlPoints[0][4] = XYZW(43.333333, 0, 4, 1);
controlPoints[0][5] = XYZW(50, 0, 0, 1);
controlPoints[1][0] = XYZW(0, 6.666667, 0, 1);
controlPoints[1][1] = XYZW(6.6666667, 6.666667, 9.950068, 1);
controlPoints[1][2] = XYZW(16.6666666, 6.666667, 9.65541838, 1);
controlPoints[1][3] = XYZW(33.3333333, 6.666667, 47.21371742, 1);
controlPoints[1][4] = XYZW(43.3333333, 6.666667, -11.56982167, 1);
controlPoints[1][5] = XYZW(50, 6.6666667, 0, 1);
controlPoints[2][0] = XYZW(0, 16.666666, 0, 1);
controlPoints[2][1] = XYZW(6.6666667, 16.666666, -7.9001371, 1);
controlPoints[2][2] = XYZW(16.6666666, 16.666666, 46.6891632, 1);
controlPoints[2][3] = XYZW(33.3333333, 16.666667, -28.4274348, 1);
controlPoints[2][4] = XYZW(43.3333333, 16.666667, 35.1396433, 1);
controlPoints[2][5] = XYZW(50, 16.6666667, 0, 1);
controlPoints[3][0] = XYZW(0, 33.3333333, 0, 1);
controlPoints[3][1] = XYZW(6.6666667, 33.3333333, 29.2877911, 1);
controlPoints[3][2] = XYZW(16.6666666, 33.3333333, -30.4644718, 1);
controlPoints[3][3] = XYZW(33.3333333, 33.3333333, 129.1582990, 1);
controlPoints[3][4] = XYZW(43.3333333, 33.3333333, -62.1717142, 1);
controlPoints[3][5] = XYZW(50, 33.333333, 0, 1);
controlPoints[4][0] = XYZW(0, 43.333333, 0, 1);
controlPoints[4][1] = XYZW(6.6666667, 43.333333, -10.384636, 1);
controlPoints[4][2] = XYZW(16.6666666, 43.333333, 59.21371742, 1);
controlPoints[4][3] = XYZW(33.3333333, 43.333333, -37.7272976, 1);
controlPoints[4][4] = XYZW(43.3333333, 43.333333, 45.1599451, 1);
controlPoints[4][5] = XYZW(50, 43.333333, 0, 1);
controlPoints[5][0] = XYZW(0, 50, 0, 1);
controlPoints[5][1] = XYZW(6.6666667, 50, 0, 1);
controlPoints[5][2] = XYZW(16.6666666, 50, 0, 1);
controlPoints[5][3] = XYZW(33.3333333, 50, 0, 1);
controlPoints[5][4] = XYZW(43.3333333, 50, 0, 1);
controlPoints[5][5] = XYZW(50, 50, 0, 1);
LNLib::LN_NurbsSurface surface;
surface.DegreeU = degreeU;
surface.DegreeV = degreeV;
surface.KnotVectorU = kvU;
surface.KnotVectorV = kvV;
surface.ControlPoints = controlPoints;
LN_NurbsVolume volume;
volume.DegreeU = 3;
volume.DegreeV = 1;
volume.DegreeW = 1;
volume.KnotVectorU = { 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0 };
volume.KnotVectorV = { 0.0, 0.0, 1.0, 1.0 };
volume.KnotVectorW = { 0.0, 0.0, 1.0, 1.0 };
volume.ControlPoints.resize(4);
for (int i = 0; i < 4; ++i) {
volume.ControlPoints[i].resize(2);
for (int j = 0; j < 2; ++j) {
volume.ControlPoints[i][j].resize(2);
}
}
double w_mid = std::sqrt(2.0) / 2.0;
w_mid = std::sqrt(3.0) / 2.0;
double tan_15 = 2.0 - std::sqrt(3.0);
double R_out = 10.0;
double out_x1 = R_out; double out_y1 = R_out * tan_15;
double out_x2 = R_out * tan_15; double out_y2 = R_out;
double R_in = 6.0;
double in_x1 = R_in; double in_y1 = R_in * tan_15;
double in_x2 = R_in * tan_15; double in_y2 = R_in;
volume.ControlPoints[0][0][0] = XYZW(R_out * 1.0, 0.0, 0.0, 1.0);
volume.ControlPoints[1][0][0] = XYZW(out_x1 * w_mid, out_y1 * w_mid, 0.0, w_mid);
volume.ControlPoints[2][0][0] = XYZW(out_x2 * w_mid, out_y2 * w_mid, 0.0, w_mid);
volume.ControlPoints[3][0][0] = XYZW(0.0, R_out * 1.0, 0.0, 1.0);
double Z_top = 5.0;
volume.ControlPoints[0][1][0] = XYZW(R_out * 1.0, 0.0, Z_top * 1.0, 1.0);
volume.ControlPoints[1][1][0] = XYZW(out_x1 * w_mid, out_y1 * w_mid, Z_top * w_mid, w_mid);
volume.ControlPoints[2][1][0] = XYZW(out_x2 * w_mid, out_y2 * w_mid, Z_top * w_mid, w_mid);
volume.ControlPoints[3][1][0] = XYZW(0.0, R_out * 1.0, Z_top * 1.0, 1.0);
volume.ControlPoints[0][0][1] = XYZW(R_in * 1.0, 0.0, 0.0, 1.0);
volume.ControlPoints[1][0][1] = XYZW(in_x1 * w_mid, in_y1 * w_mid, 0.0, w_mid);
volume.ControlPoints[2][0][1] = XYZW(in_x2 * w_mid, in_y2 * w_mid, 0.0, w_mid);
volume.ControlPoints[3][0][1] = XYZW(0.0, R_in * 1.0, 0.0, 1.0);
volume.ControlPoints[0][1][1] = XYZW(R_in * 1.0, 0.0, Z_top * 1.0, 1.0);
volume.ControlPoints[1][1][1] = XYZW(in_x1 * w_mid, in_y1 * w_mid, Z_top * w_mid, w_mid);
volume.ControlPoints[2][1][1] = XYZW(in_x2 * w_mid, in_y2 * w_mid, Z_top * w_mid, w_mid);
volume.ControlPoints[3][1][1] = XYZW(0.0, R_in * 1.0, Z_top * 1.0, 1.0);Visualization Tool LNLibViewer based on VTK.
More Samples could be found in tests folder.
Red one is the target and white one is fitting result.
More details could be found in ND-LNLib based on LibTorch (PyTorch C++ version).
#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 LNLibExtension Library, which used for export nurbs surfaces to STEP or IGES format file.
Welcome to use https://deepwiki.com/BIMCoderLiang/LNLib powered by Devin.
Welcome join this project including discussions in Issues and make Pull requests.
- Contributors:
- Algorithm Adviser: csulijunji
LNLib is created by Yuqing Liang (BIMCoder Liang).
- email: bim.frankliang@foxmail.com
- Weixin Official Account (微信公众号)：BIMCoder
The source code is published under LGPL 2.1, the license is available here.
The NURBS Book 2nd Edition by Les Piegl & Wayne Tiller