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Blazingly fast Minecraft world manipulation for artists, builders and everyone else.
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/*
 * WorldEdit, a Minecraft world manipulation toolkit
 * Copyright (C) sk89q 
 * Copyright (C) WorldEdit team and contributors
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see .
 */

// $Id$

package com.sk89q.worldedit.math.interpolation;

import com.sk89q.worldedit.internal.util.LogManagerCompat;
import com.sk89q.worldedit.math.Vector3;
import org.apache.logging.log4j.Logger;

import java.util.List;
import java.util.Map.Entry;
import java.util.TreeMap;

import static com.google.common.base.Preconditions.checkNotNull;

/**
 * Reparametrises another interpolation function by arc length.
 *
 * This is done so entities travel at roughly the same speed across
 * the whole route.
 */
public class ReparametrisingInterpolation implements Interpolation {

    private static final Logger LOGGER = LogManagerCompat.getLogger();

    private final Interpolation baseInterpolation;
    private double totalArcLength;
    private final TreeMap cache = new TreeMap<>();

    public ReparametrisingInterpolation(Interpolation baseInterpolation) {
        checkNotNull(baseInterpolation);

        this.baseInterpolation = baseInterpolation;
    }

    @Override
    public void setNodes(List nodes) {
        checkNotNull(nodes);

        baseInterpolation.setNodes(nodes);
        cache.clear();
        cache.put(0.0, 0.0);
        cache.put(totalArcLength = baseInterpolation.arcLength(0.0, 1.0), 1.0);
    }

    public Interpolation getBaseInterpolation() {
        return baseInterpolation;
    }

    @Override
    public Vector3 getPosition(double position) {
        if (position > 1) {
            return null;
        }

        return baseInterpolation.getPosition(arcToParameter(position));
    }

    @Override
    public Vector3 get1stDerivative(double position) {
        if (position > 1) {
            return null;
        }

        return baseInterpolation.get1stDerivative(arcToParameter(position)).normalize().multiply(totalArcLength);
    }

    @Override
    public double arcLength(double positionA, double positionB) {
        return baseInterpolation.arcLength(arcToParameter(positionA), arcToParameter(positionB));
    }

    private double arcToParameter(double arc) {
        if (cache.isEmpty()) {
            throw new IllegalStateException("Must call setNodes first.");
        }

        if (arc > 1) {
            arc = 1;
        }
        arc *= totalArcLength;

        Entry floorEntry = cache.floorEntry(arc);
        final double leftArc = floorEntry.getKey();
        final double leftParameter = floorEntry.getValue();

        if (leftArc == arc) {
            return leftParameter;
        }

        Entry ceilingEntry = cache.ceilingEntry(arc);
        if (ceilingEntry == null) {
            LOGGER.warn("Error in arcToParameter: no ceiling entry for " + arc + " found!");
            return 0;
        }
        final double rightArc = ceilingEntry.getKey();
        final double rightParameter = ceilingEntry.getValue();

        if (rightArc == arc) {
            return rightParameter;
        }

        return evaluate(arc, leftArc, leftParameter, rightArc, rightParameter);
    }

    private double evaluate(double arc, double leftArc, double leftParameter, double rightArc, double rightParameter) {
        double midParameter = 0;
        for (int i = 0; i < 10; ++i) {
            midParameter = (leftParameter + rightParameter) * 0.5;
            //final double midArc = leftArc + baseInterpolation.arcLength(leftParameter, midParameter);
            final double midArc = baseInterpolation.arcLength(0, midParameter);
            cache.put(midArc, midParameter);

            if (midArc < leftArc) {
                return leftParameter;
            }

            if (midArc > rightArc) {
                return rightParameter;
            }

            if (Math.abs(midArc - arc) < 0.01) {
                return midParameter;
            }

            if (arc < midArc) {
                // search between left and mid
                rightArc = midArc;
                rightParameter = midParameter;
            } else {
                // search between mid and right
                leftArc = midArc;
                leftParameter = midParameter;
            }
        }
        return midParameter;
    }

    @Override
    public int getSegment(double position) {
        if (position > 1) {
            return Integer.MAX_VALUE;
        }

        return baseInterpolation.getSegment(arcToParameter(position));
    }

}