IbrahimMajdi / Basic-Spline

Spline package for unity

Basic-Spline

An intuitive and lightweight path for Unity.

This package was built with two goals in mind. The first is to keep everything simple by keeping a clean UI and a simple API that only implements the basic spline functionality. The second goal is to implement analytical methods for curve sampling to avoid point caching.

Features

• Simple, intuitive user interface.
• Using analytical methods for closest point finding and arc-length spline sampling without point caching.
• Multi-point selection, twist control, and scene geometry projection.
• Easy, intuitive API that offers a great range of flexibility.

Complete C# source code is provided.

Usage

to create a path, go to GameObject/Path/Path. By coding, you can either use the Path class or the Spline class, the Path is a MonoBehaviour and it's only a wrapper for the Spline class.

	//generating spline

        ControlPoint[] controlPoints = new ControlPoint[]
        {
            new ControlPoint(new Vector3(0,0,0),new Vector3(0,0,-1),new Vector3(0,0,1)),
            new ControlPoint(new Vector3(1,0,0),new Vector3(0,0,1),new Vector3(0,0,-1))
        };
        Spline spline = new Spline(controlPoints);

        //operating on control points

        spline.AddControlPoint(new ControlPoint(new Vector3(2, 1, -1), new Vector3(-1, 0, 0), new Vector3(1, 0, 0)));
        spline.InsertControlPoint(1, new ControlPoint(new Vector3(1, 1, 0), new Vector3(0, 0, 1), new Vector3(0, 0, -1)));
        spline.RemoveControlPoint(1);
        //shifting all points to the right
        for (int i = 0; i < spline.ControlPointsCount; i++)
        {
            var cpoint = spline.GetControlPoint(i);
            cpoint.Move(new Vector3(1, 0, 0));
            spline.SetControlPoint(i, cpoint);
        }

        //operating on segments

        for (int i = 0; i < spline.SegmentCount; i++)
        {
            var segment = spline[i];
            //Iterate over the segment points in fixed parametric steps.
            segment.Iterate(excute: (point) =>
            {
                //do something with point ..
            }, 30);
        }

sampling the curve using arc length

you can sample the curve by the arc length using Spline.GetPoint, you can also go from the arc length to the curve parameter or the other way around using Segment.EvaluateParameter and Segment.EvaluateLength.

• To approximate the arc length, this package uses [Approximate Arc Length Parametrization MARCELO WALTER ,AND ALAIN FOURNIER]
• I tried to find the inverse for arc length approximation, but the error margin was too big, so I stuck to root-finding on [Arc Length Approximation] using hybrid Newton's method.
• This package also implements other more accurate methods to find the arc length, such as different adaptive subdivision.

finding the closest point

to get the closest point on the spline to the given point, use Spline.GetClosestLength. This method will return the arc length from the beginning of the spline to the closest point. You can use it with conjunction Spline.GetPoint to get the closest point.

• To find the closest point, this package uses [ Xiao-Diao Chen, Yin Zhou, Zhenyu Shu, Hua Su, Jean-Claude Paul. Improved Algebraic Algorithm On Point Projection For Bézier Curves. HAL, 2007 ]
• And for roots finding, it uses the hybrid Newton's method.