tinynurbs
This is a lightweight header-only C++14 library for Non-Uniform Rational B-Spline curves and surfaces. The API is simple to use and the code is readable while being efficient.
Some of the main features include:
- Supports non-rational and rational curves and surfaces of any order
- Evaluate point and derivatives of any order
- Knot insertion, splitting without affecting the original shape
- Wavefront OBJ format I/O
The library is under development.
Dependencies
- glm (version 0.9.9 where PR #584 is merged is required since tinynurbs uses the
glm::vec<dim, T>type) - C++14 compliant compiler
Usage
The entire API consists of free functions named curve* and surface* which accept a Curve / RationalCurve and Surface / RationalSurface object, respectively.
Some example usage is given below.
Create a non-rational planar curve:
tinynurbs::Curve<float> crv; // Planar curve using float32
crv.control_points = {glm::vec3(-1, 0, 0), // std::vector of 3D points
glm::vec3(0, 1, 0),
glm::vec3(1, 0, 0)
};
crv.knots = {0, 0, 0, 1, 1, 1}; // std::vector of floats
crv.degree = 2;Check if created curve is valid:
if (!tinynurbs::curveIsValid(crv)) {
// check if degree, knots and control points are configured as per
// #knots == #control points + degree + 1
}Evaluate point and tangent on curve:
glm::vec3 pt = tinynurbs::curvePoint(crv, 0.f);
// Outputs a point [-1, 0]
glm::vec3 tgt = tinynurbs::curveTangent(crv, 0.5f);
// Outputs a vector [1, 0]Insert a single knot at u=0.25 and double knot at u=0.75:
crv = tinynurbs::curveKnotInsert(crv, 0.25);
crv = tinynurbs::curveKnotInsert(crv, 0.75, 2);Left: original curve, Right: after knot insertion
Write the curve to an OBJ file:
tinynurbs::curveSaveOBJ("output_curve.obj", crv);creates a file with the following contents:
v -1 0 0 1
v -0.75 0.5 0 1
v 0 1.25 0 1
v 0.5 0.75 0 1
v 0.75 0.5 0 1
v 1 0 0 1
cstype bspline
deg 2
curv 0 1 1 2 3 4 5 6
parm u 0 0 0 0.25 0.75 0.75 1 1 1
end
Create a rational surface shaped like a hemisphere:
tinynurbs::RationalSurface<float> srf;
srf.degree_u = 3;
srf.degree_v = 3;
srf.knots_u = {0, 0, 0, 0, 1, 1, 1, 1};
srf.knots_v = {0, 0, 0, 0, 1, 1, 1, 1};
// 2D array of control points using tinynurbs::array2<T> container
// Example from geometrictools.com/Documentation/NURBSCircleSphere.pdf
srf.control_points = {4, 4,
{glm::vec3(0, 0, 1), glm::vec3(0, 0, 1), glm::vec3(0, 0, 1), glm::vec3(0, 0, 1),
glm::vec3(2, 0, 1), glm::vec3(2, 4, 1), glm::vec3(-2, 4, 1), glm::vec3(-2, 0, 1),
glm::vec3(2, 0, -1), glm::vec3(2, 4, -1), glm::vec3(-2, 4, -1), glm::vec3(-2, 0, -1),
glm::vec3(0, 0, -1), glm::vec3(0, 0, -1), glm::vec3(0, 0, -1), glm::vec3(0, 0, -1)
}
};
srf.weights = {4, 4,
{1, 1.f/3.f, 1.f/3.f, 1,
1.f/3.f, 1.f/9.f, 1.f/9.f, 1.f/3.f,
1.f/3.f, 1.f/9.f, 1.f/9.f, 1.f/3.f,
1, 1.f/3.f, 1.f/3.f, 1
}
};Split the surface into two along v=0.25:
tinynurbs::RationalSurface<float> left, right;
std::tie(left, right) = tinynurbs::surfaceSplitV(srf, 0.25);Left: original surface, Right: after splitting
Write the surface to an OBJ file:
tinynurbs::surfaceSaveOBJ("output_surface.obj", srf);creates a file with the following contents:
v 0 0 1 1
v 2 0 1 0.333333
v 2 0 -1 0.333333
v 0 0 -1 1
v 0 0 1 0.333333
v 2 4 1 0.111111
v 2 4 -1 0.111111
v 0 0 -1 0.333333
v 0 0 1 0.333333
v -2 4 1 0.111111
v -2 4 -1 0.111111
v 0 0 -1 0.333333
v 0 0 1 1
v -2 0 1 0.333333
v -2 0 -1 0.333333
v 0 0 -1 1
cstype rat bspline
deg 3 3
surf 0 1 0 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
parm u 0 0 0 0 1 1 1 1
parm v 0 0 0 0 1 1 1 1
end
Primary Reference
- "The NURBS Book," Les Piegl and Wayne Tiller, Springer-Verlag, 1995.