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c#computational-geometry
alex
alex

Reputation: 5731

Formula to compute an arcuate segment length

Considering the class:

public class Point3D
{

    public double X;
    public double Y;
    public double Z;

    public Point3D(double x, double y, double z)
    {
        X = x;
        Y = y;
        Z = z;
    }

    public double DistanceTo(Point3D to)
    {
        double dX = Math.Abs(to.X - X);
        double dY = Math.Abs(to.Y - Y);
        double dZ = Math.Abs(to.Z - Z);
        return Math.Sqrt(dX * dX + dY * dY + dZ * dZ);
    }

}

And the class:

public class Segment
{

    public Point3D From;
    public Point3D To;
    public double? Radius;

    public Segment(Point3D from, Point3D to, double? radius)
    {
        From = from;
        To = to;
        Radius = radius;
    }

    public double Length
    {
        get
        {
            double straightLength = From.DistanceTo(To);
            if (Radius == null)
                return straightLength;
            if (Radius < straightLength/ 2d)
                throw new Exception();
            // Compute the arcuate segment length
        }
    }

}

I would like to compute the length of the arc (with Radius) passing through From and To 3D points.

Some help will be welcome!

Upvotes: 2

Views: 934

Answers (2)

Vikranth Inti
Vikranth Inti

Reputation: 111

One more reference: from math.stackexchange

S=length of the arc = r*theta, where r= radius and Cos(theta)=(dotproduct of 2 vectors)/(product of the modulus of those vectors)

Upvotes: 0

Henrik
Henrik

Reputation: 23324

According to http://mathworld.wolfram.com/IsoscelesTriangle.html

straightLength / 2 = Radius * sin( 1/2 * angle)

Therefore:

angle = 2 * arcsin( straightLength / 2 / Radius)

and

arcLength = Radius * angle;

Upvotes: 2

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