/*
 * Copyright 2006 the original author or authors.
 * 
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 * 
 *      http://www.apache.org/licenses/LICENSE-2.0
 * 
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */ 

package org.wamblee.gps.geometry;

import org.wamblee.general.Pair;

/**
 * Represents a plane. Usually used to represent a tangent plane to the earth surface to
 * locally approximate the earth as flat.  
 *
 * @author Erik Brakkee
 */
public class Plane {
    
    private static final double EPS = 1e-4;
    
    private Coordinates _point; 
    private Coordinates _normal; 
    private Coordinates _north;
    private Coordinates _east;

    /**
     * Constructs a plane. 
     * @param aPoint Point on the plane. 
     * @param aNormal Normal, not necessarily normalized. 
     */
    public Plane(Point aPoint, Point aNormal) {
        _point = aPoint.getReferenceCoordinates(); 
        _normal = aNormal.getReferenceCoordinates().normalize();
        Coordinates north = new Coordinates(0.0, 0.0, 1.0);
        _north = north.subtract(_normal.scale(north.innerProduct(_normal))).normalize();
        _east = _north.outerProduct(_normal);
      
        if (  _normal.innerProduct(_north) > EPS ) {
            throw new IllegalArgumentException("North access is not within the plane");
        }
    }
    
    /**
     * Projects a point onto the plane.  
     * @param aPoint Point to project. 
     * @return Projected point. 
     */
    private Coordinates project(Point aPoint) { 
        Coordinates ref = aPoint.getReferenceCoordinates();
        double lambda = _normal.innerProduct(
                _point.subtract(ref));
        return ref.add(_normal.scale(lambda));
    }
    
    /**
     * Returns normalized coordinates within the plane of the projection of a point. 
     */
    public Pair<Double,Double> normalizedProjection(Point aPoint) { 
        Coordinates projection = project(aPoint);
        Coordinates delta = projection.subtract(_point);
        double x1 = delta.innerProduct(_north);
        double x2 = delta.innerProduct(_east);
        return new Pair<Double,Double>(x1, x2);
    }
}