TinySpline

TinySpline is a small, yet powerful library for interpolating, transforming, and querying arbitrary NURBS, B-Splines, and Bézier curves. It is implemented in ANSI C (C89) and provides a wrapper for C++ along with auto-generated bindings C#, D, Java, Lua, Octave, PHP, Python, R, and Ruby.

License

MIT License - see the LICENSE file in the source distribution.

Some Features of This Library

• Use a single struct for NURBS, B-Splines, Bézier curves, lines, and points.
• Support for opened and clamped splines.
• Create splines of any degree and dimension.
• Evaluate splines using De Boor's algorithm.
• Interpolate cubic splines using the Thomas algorithm.
• Insert knots and split splines without modifying the shape.
• Derive splines of any degree.
• Subdivide splines into Bézier curves.
• A wrapper for C++ as well as bindings for C#, D, Java, Lua, PHP, Python, and Ruby.
• Easy to use with OpenGL.

Feel free to ask for more features via the issues or to contribute to TinySpline. :)

Getting Started

The following listing uses the C++ wrapper to give a short example of TinySpline:

#include <iostream>
#include "tinysplinecpp.h"

int main(int argc, char **argv)
{
	// Create a cubic spline with 7 control points in 2D using
	// a clamped knot vector. This call is equivalent to:
	// tinyspline::BSpline spline(7, 2, 3, TS_CLAMPED);
	tinyspline::BSpline spline(7);

	// Setup control points.
	std::vector<tinyspline::real> ctrlp = spline.controlPoints();
	ctrlp[0]  = -1.75; // x0
	ctrlp[1]  = -1.0;  // y0
	ctrlp[2]  = -1.5;  // x1
	ctrlp[3]  = -0.5;  // y1
	ctrlp[4]  = -1.5;  // x2
	ctrlp[5]  =  0.0;  // y2
	ctrlp[6]  = -1.25; // x3
	ctrlp[7]  =  0.5;  // y3
	ctrlp[8]  = -0.75; // x4
	ctrlp[9]  =  0.75; // y4
	ctrlp[10] =  0.0;  // x5
	ctrlp[11] =  0.5;  // y5
	ctrlp[12] =  0.5;  // x6
	ctrlp[13] =  0.0;  // y6
	spline.setControlPoints(ctrlp);

	// Stores our evaluation results.
	std::vector<tinyspline::real> result;

	// Evaluate `spline` at u = 0.4 using 'evaluate'.
	result = spline.eval(0.4).result();
	std::cout << "x = " << result[0] << ", y = " << result[1] << std::endl;

	// Derive `spline` and subdivide it into a sequence of Bezier curves.
	tinyspline::BSpline beziers = spline.derive().toBeziers();

	// Evaluate `beziers` at u = 0.3 using '()' instead of 'evaluate'.
	result = beziers(0.3).result();
	std::cout << "x = " << result[0] << ", y = " << result[1] << std::endl;

	return 0;
}

Installation

Compiling From Source

TinySpline uses the CMake build system to compile and package its interfaces. The C interface is implemented in ANSI C (C89) and, thus, should be compatible with almost every compiler. All other features of TinySpline are optional and will be disabled if CMake does not find the corresponding dependencies; however, CMake and an appropriate C/C++ compiler must be available, regardless of the interface you want to build. The following compiler suites are tested: GCC, Clang, and MSVC. In order to create the bindings, Swig (3.0.1 or above) must be available. Each binding may have further dependencies to generate the source code of the target language. The following table gives an overview:

Language	Dependencies to Generate Source	(Relative) Output Directory
C#		csharp
D	-	dlang
Golang	-	go
Java	Java Development Kit	org/tinyspline
Lua	Lua headers	lua
PHP	PHP (Zend) headers *	php
Python	Python headers	python
Ruby	Ruby headers	ruby

• Please note that macOS comes with PHP, but does not provide the Zend headers. It is recommended to use a package manager (such as Homebrew) to obtain the headers.

To simplify the usage of the bindings, the generated source files are compiled and/or packaged if necessary. That is, for instance, the generated Java files are compiled to .class files and packaged into a jar archive. Accordingly, the following tools are required if you want to package the corresponding binding:

Language	Required Tool(s)	Output File
C#	Any of: csc, mcs, dmcs, gmcs	TinySpline.dll
Java	javac and jar (available in JDK)	tinyspline.jar

Now let's start building TinySpline. First of all, checkout the repository and cd into it:

git clone git@github.com:msteinbeck/tinyspline.git tinyspline
cd tinyspline

Afterwards, create a build directory and cd into it:

mkdir build
cd build

Finally, run CMake and build the project:

cmake ..
cmake --build .

You will find the resulting libraries and packages in tinyspline/build/lib.

Python 2 vs. Python 3

While generating the Python binding, Swig needs to distinguish between Python 2 and Python 3. That is, Swig uses the command line parameter -py to generate Python 2 compatible code and -py3 to generate Python 3 compatible code. Accordingly, Swig is configured depending on the Python version found by CMake during initialization. On systems with multiple versions of Python installed, CMake usually chooses the more recent one. If you want to use a specific version of Python instead, set the environment variable 'TINYSPLINE_PYTHON_VERSION' to '2' or '3'.

The following example shows how to force CMake to use Python 2 rather than Python 3:

TINYSPLINE_PYTHON_VERSION=2 cmake ..

Disabling Bindings

For one reason or another, you may have the required packages to build a binding, but you don't want to compile it. You can pass additional arguments to prevent particular bindings from being compiled and packaged:

cmake -DTINYSPLINE_DISABLE_CSHARP=YES ..

Install the C and C++ Libraries

The following command installs TinySpline to your system:

cmake --build . --target install

However, there are several binding-related files that CMake does not install with this command, as some languages use custom tools to install files. Python, for instance, uses Distutils/Setuptools to install files to Python-specific directories that CMake is not aware of. Thus, TinySpline ships further, language-related distribution tools.

Install the Bindings

Depending on your configuration, binding-related distribution files are generated within the root of your build directory. That is, for instance, the file setup.py is generated if support for Python was detected. Currently, the following build tools are supported: Setuptools (Python), Maven (Java), and Luarocks (Lua).

Theoretical Backgrounds

[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.