package com.pau101.util;

/**
 * @author Paul Fulham (pau101)
 */
public final class BezierUtils
{
    private BezierUtils()
    {}
    
    /**
     * Compute the value of all nth degree Bernstein polynomials.
     *
     * @param curveDegree : degree of curve
     * @param t : curve parameter on interval [0,1]
     * @param scalars : curveDegree + 1 Bernstein values.
     */
    public static void allBernstein(int curveDegree, float t, float scalars[])
    {
        int j, k;
        float nt = 1 - t;
        float saved;
        scalars[0] = 1;
        for(j = 1; j <= curveDegree; j++){
            saved = 0;
            for(k = 0; k < j; k++){
                float temp = scalars[k];
                scalars[k] = saved + nt * temp;
                saved = t * temp;
            }
            scalars[j] = saved;
        }
    }
    
    /**
     * Compute point of nth degree Bezier curve.
     *
     * @param controlPoints : curveDegree + 1 control points
     * @param curveDegree : degree of curve
     * @param t : curve parameter on interval [0,1]
     * @param point : resulting point
     */
    public static void pointOnBezierCurve(float controlPoints[][], int curveDegree, float t, float point[])
    {
        float scalars[] = new float[curveDegree + 1];
        int k;
        allBernstein(curveDegree, t, scalars);
        point[0] = point[1] = point[2] = 0;
        for(k = 0; k <= curveDegree; k++){
            point[0] += scalars[k] * controlPoints[k][0];
            point[1] += scalars[k] * controlPoints[k][1];
            point[2] += scalars[k] * controlPoints[k][2];
        }
    }
    
    /**
     * Compute an approximate length of a Bezier curve given the control points.
     *
     * @param controlPoints : control points of a Bezier curve
     * @return the approximate length
     */
    public static float approximateLength(float controlPoints[][])
    {
        float length = 0;
        for(int i = 0; i < controlPoints.length - 1; i++){
            float xDif = controlPoints[i + 1][0] - controlPoints[i][0];
            float yDif = controlPoints[i + 1][1] - controlPoints[i][1];
            float zDif = controlPoints[i + 1][2] - controlPoints[i][2];
            length += Math.sqrt(xDif * xDif + yDif * yDif + zDif * zDif);
        }
        return length;
    }
    
    public static int tesselationSegementsForLength(float length, float scale)
    {
        float noLessThan = 10 * scale;
        float segs = length * scale / 30F;
        return (int)Math.ceil(Math.sqrt(segs * segs * 0.6 + noLessThan * noLessThan));
    }
    
    public static float[][] curve(float controlPoints[][])
    {
        return curve(controlPoints, 1);
    }
    
    public static float[][] curve(float controlPoints[][], float scale)
    {
        int count = tesselationSegementsForLength(approximateLength(controlPoints), scale);
        float[][] points = new float[count][3];
        for(int i = 0; i < count; i++){
            float t = i / (float)(count - 1);
            float[] point = new float[3];
            pointOnBezierCurve(controlPoints, controlPoints.length - 1, t, point);
            points[i] = point;
        }
        return points;
    }
}