TinySpline is a small, yet powerful library for interpolating, transforming, and querying arbitrary NURBS, B-Splines, and Bézier curves. The core of the library is written in ANSI C (C89) with a C++ wrapper for an object-oriented programming model. Based on the C++ wrapper, auto-generated bindings for C#, D, Go, Java, Javascript, Lua, Octave, PHP, Python, R, and Ruby are provided.
MIT License - see the LICENSE file in the source distribution.
- Object-oriented programming model
- B-Splines of any degree and dimensionality
- Spline interpolation
- Cubic natural
- Centripetal Catmull–Rom
- Evaluation
- Knots
- Sampling (multiple knots at once)
- Equidistant points
- Components (find y for given x)
- Reparametrization by arc length
- Mapping length <--> knot
- Knot insertion (refinement)
- Sub-spline extraction
- Bézier curve decomposition
- (also known as subdivision)
- Derivative
- Degree elevation
- Computation of rotation minimizing frames
- Morphing
- Serialization (JSON)
- Vector math
Releases can be downloaded from the releases page. In addition, the following package manager are supported:
Conan (C/C++):
https://conan.io/center/tinyspline
NuGet (C#):
<PackageReference Include="tinyspline" Version="0.6.0.1" />Go:
go get github.com/tinyspline/go@v0.6.0Luarocks (Lua):
luarocks install --server=https://tinyspline.github.io/lua tinysplineMaven (Java):
<dependency> <groupId>org.tinyspline</groupId> <artifactId>tinyspline</artifactId> <version>0.6.0-1</version> </dependency>PyPI (Python):
python -m pip install tinysplineRubyGems (Ruby):
gem install tinysplineSee BUILD.md.
A variety of examples (tests) can be found in the test subdirectory.
The following listing shows a Python example:
from tinyspline import * import matplotlib.pyplot as plt spline = BSpline.interpolate_cubic_natural( [ 100, -100, # P1 -100, 200, # P2 100, 400, # P3 400, 300, # P4 700, 500 # P5 ], 2) # <- dimensionality of the points # Draw spline as polyline. points = spline.sample(100) x = points[0::2] y = points[1::2] plt.plot(x, y) # Draw point at knot 0.3. vec2 = spline.eval(0.3).result_vec2() plt.plot(vec2.x, vec2.y, 'ro') # Draw tangent at knot 0.7. pos = spline(0.7).result_vec2() # operator () -> eval der = spline.derive()(0.7).result_vec2().normalize() * 200 s = pos - der t = pos + der plt.plot([s.x, t.x], [s.y, t.y]) # Draw 15 normals with equidistant distribution. knots = spline.equidistant_knot_seq(15) frames = spline.compute_rmf(knots) for i in range(frames.size()): pos = frames.at(i).position nor = pos + frames.at(i).normal * 20 # You can also fetch the tangent and binormal: # frames.at(i).tangent # frames.at(i).binormal plt.plot([pos.x, nor.x], [pos.y, nor.y], 'g') plt.show()Result:
The latest Doxygen documentation can be found at: https://msteinbeck.github.io/tinyspline/
The documentation of the C interface (https://msteinbeck.github.io/tinyspline/tinyspline_8h.html) is quite extensive and also serves as an entry point for the C++ interface documentation (as well as the documentation for the bindings created from the C++ interface).
If you use TinySpline in your research, please cite it as below.
@INPROCEEDINGS{Steinbeck:SANER:21, author = {Steinbeck, Marcel and Koschke, Rainer}, booktitle = {2021 IEEE International Conference on Software Analysis, Evolution and Reengineering (SANER)}, title = {TinySpline: A Small, yet Powerful Library for Interpolating, Transforming, and Querying NURBS, B-Splines, and Bézier Curves}, year = {2021}, pages = {572-576}, doi = {10.1109/SANER50967.2021.00068} } Other publications:
@INPROCEEDINGS{Steinbeck:VISSOFT:22, author = {Steinbeck, Marcel and Koschke, Rainer}, booktitle = {2022 Working Conference on Software Visualization (VISSOFT)}, title = {Edge Animation in Software Visualization}, year = {2022}, pages = {63-74}, doi = {10.1109/VISSOFT55257.2022.00015} } [1] is a very good starting point for B-Splines.
[2] explains De Boor's Algorithm and gives some pseudo code.
[3] provides a good overview of NURBS with some mathematical background.
[4] is useful if you want to use NURBS in TinySpline.