import javax.vecmath.*;
import javax.media.j3d.*; // Canvas3D etc

class Helix implements Curve3f {
	float r;
	float a;
	double upAngle;

	Helix ( float radius, float aIn ) {
		r = radius;
		a = aIn;
		upAngle = - Math.asin ( a / Math.sqrt ( 4* Math.PI*Math.PI + a*a) );
	}

	public Point3f valueAt ( float t ) {
		return new Point3f ( r * (float) Math.cos ( 2 * t * Math.PI ),
			r * (float) Math.sin ( 2 * t * Math.PI ), a * t );
	}

	public Vector3f Vector3fAt ( float t ) {
		return new Vector3f ( r * (float) Math.cos ( 2 * t * Math.PI ),
			r * (float) Math.sin ( 2 * t * Math.PI ), a * t );
	}

	public Transform3D frameAt ( float t ) {
		Transform3D spin = new Transform3D();
		Transform3D temp1 = new Transform3D();
		Transform3D temp2 = new Transform3D();

		spin.setTranslation ( Vector3fAt ( t ) );
		temp1.rotZ ( 2*Math.PI*t + Math.PI/2 );
		spin.mul ( temp1 );
		temp2.rotY ( upAngle );
		//System.out.println ( upAngle );
		spin.mul ( temp2 );
		// they work backwards  (bottom to top)
		return spin;
	}
}