Examples with QuadraticCurve com.xenoage.utils.math.QuadraticCurve used on opensource projects

Example 1 with QuadraticCurve

use of com.xenoage.utils.math.QuadraticCurve in project Zong by Xenoage.

the class DefaultCurvedLineStrategy method computeCurvedLine.

@Override
public CubicBezierCurve computeCurvedLine(List<Point2f> points, VSide side) {
    ConvexHull convexHull = ConvexHull.create(points, side);
    List<QuadraticCurve> quadCurves = QuadraticCurvesTools.computeOverConvexHull(convexHull, ENDPOINT_TOLERANCE_LP, ENDPOINT_TOLERANCE_LP);
    QuadraticCurve bestQuadCurve = QuadraticCurvesTools.getBestCurve(quadCurves, convexHull);
    CubicBezierCurve bestBezierCurve = BezierCurveTools.computeBezierFrom(bestQuadCurve, points.get(0).x, points.get(points.size() - 1).x);
    bestBezierCurve = BezierCurveTools.correctBezier(bestBezierCurve, side);
    return bestBezierCurve;
}

Example 2 with QuadraticCurve

use of com.xenoage.utils.math.QuadraticCurve in project Zong by Xenoage.

the class QuadraticCurvesTools method computeOverConvexHull.

/**
 * Computes a list of possible quadratic curves over the given {@link ConvexHull},
 * that start at the first point of the hull and end at the last point of the hull,
 * but may also start and end further away according to the given parameters. The curve
 * will not cross the area of the convex hull.
 * @param convexHull  the convex hull
 * @param leftArea    the tolerance of the distance of the start point
 *                    (between 0 and this value). always positive or 0.
 * @param rightArea   the tolerance of the distance of the end point
 *                    (between 0 and this value). always positive or 0.
 * @return  a list of possible quadratic curves
 */
public static List<QuadraticCurve> computeOverConvexHull(ConvexHull convexHull, float leftArea, float rightArea) {
    LinkedList<QuadraticCurve> ret = new LinkedList<>();
    ArrayList<Point2f> points = convexHull.getPoints();
    VSide side = convexHull.getSide();
    int sideDir = side.getDir();
    int n = points.size();
    // compute the possible start and endpoints
    Point2f[] startPoints = new Point2f[] { points.get(0), points.get(0).add(0, sideDir * leftArea) };
    Point2f[] endPoints = new Point2f[] { points.get(n - 1), points.get(n - 1).add(0, sideDir * rightArea) };
    // the quadratic expression {a, b, c} for ax² + bx + c = 0
    // equations:
    // - (2): must start at startPoints[0] or startPoints[1] (between is never optimal!)
    // - (2): must end at endPoints[0] or endPoints[1] (between is never optimal!)
    // inequations:
    // - (0): a must be <=/>= 0 (parabola is open on the bottom/top side, dependent
    // on the side of the convex hull) - not used in SLE, checked later
    // - (m): curve must be above/below each of the m = n-2 middle points (dependent on the side)
    int m = n - 2;
    Point2f[] eq = new Point2f[2 + 2 + m];
    eq[0] = startPoints[0];
    eq[1] = startPoints[1];
    eq[2] = endPoints[0];
    eq[3] = endPoints[1];
    for (int i = 0; i < m; i++) {
        eq[4 + i] = points.get(1 + i);
    }
    // strategy, based on the simplex algorithm for linear optimization:
    // for each possible combination of 3 equations (optimum is always at the corner of the simplex,
    // so we can use the inequations like equations), solve the SLE, test, if the curve is
    // valid for all inequations, and if so, compute the area between the curve and the convex hull.
    // take the curve which has the smallest area.
    // there are ((m+4) choose 3) possible SLEs, but we have to ignore those where eq[0] AND eq[1]
    // are used and those where eq[2] AND eq[3] are used.
    int[][] subsets = getAllCombinationsOf3(m + 4);
    for (int[] eqIndices : subsets) {
        // not useable: {0,1,?}, {2,3,?} and {?,2,3}
        if (eqIndices[0] == 0 && eqIndices[1] == 1 || eqIndices[0] == 2 && eqIndices[1] == 3 || eqIndices[1] == 2 && eqIndices[2] == 3) {
        // ignore
        } else {
            // usable. solve SLE
            double[][] A = new double[3][3];
            double[] b = new double[3];
            for (int iy = 0; iy < 3; iy++) {
                Point2f p = eq[eqIndices[iy]];
                A[iy][0] = p.x * p.x;
                A[iy][1] = p.x;
                A[iy][2] = 1;
                b[iy] = p.y;
            }
            double[] params = Gauss.solve(A, b);
            // parameters ok for all equations?
            boolean ok = true;
            ok &= sideDir * getY(startPoints[0].x, params) >= sideDir * startPoints[0].y;
            ok &= sideDir * getY(startPoints[1].x, params) <= sideDir * startPoints[1].y;
            ok &= sideDir * getY(endPoints[0].x, params) >= sideDir * endPoints[0].y;
            ok &= sideDir * getY(endPoints[1].x, params) <= sideDir * endPoints[1].y;
            // parabole is open on the bottom/top side
            ok &= sideDir * params[0] <= 0;
            for (int im = 0; ok && im < m; im++) {
                ok &= sideDir * getY(points.get(1 + im).x, params) >= sideDir * points.get(1 + im).y;
            }
            if (ok) {
                // remember this equation
                ret.add(new QuadraticCurve((float) params[0], (float) params[1], (float) params[2]));
            }
        }
    }
    if (ret.size() == 0) {
        // no curve found. use direct line between first and last point.
        double[][] A = new double[][] { { points.get(0).x, 1 }, { points.get(n - 1).x, 1 } };
        double[] b = new double[] { points.get(0).y, points.get(n - 1).y };
        double[] params = Gauss.solve(A, b);
        ret.add(new QuadraticCurve(0f, (float) params[0], (float) params[1]));
    }
    // return result
    return ret;
}