Area2D_F32.java

/*
 * Copyright (C) 2011-2015, Peter Abeles. All Rights Reserved.
 *
 * This file is part of Geometric Regression Library (GeoRegression).
 *
 * 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 georegression.metric;

import georegression.struct.point.Point2D_F32;
import georegression.struct.shapes.Polygon2D_F32;
import georegression.struct.shapes.Quadrilateral_F32;

/**
 * The area contained inside 2D shapes
 *
 * @author Peter Abeles
 */
public class Area2D_F32 {

	/**
	 * Computes the area of an arbitrary triangle from 3-vertices.
	 *
	 * area = | a.x*(b.y - c.y) + b.x*(c.y - a.y) + c.x*(a.y - b.y) | / 2
	 *
	 * @param a Corner point 1
	 * @param b Corner point 2
	 * @param c Corner point 3
	 * @return area
	 */
	public static float triangle( Point2D_F32 a, Point2D_F32 b, Point2D_F32  c ) {
		float inner = a.x*(b.y - c.y) + b.x*(c.y - a.y) + c.x*(a.y - b.y);

		return (float)Math.abs(inner/2.0f);
	}

	/**
	 * Area of a quadrilateral computed from two triangles.
	 *
	 * @param quad quadrilateral
	 * @return area
	 */
	public static float quadrilateral( Quadrilateral_F32 quad ) {
		float bx = quad.b.x-quad.a.x;
		float by = quad.b.y-quad.a.y;
		float cx = quad.c.x-quad.a.x;
		float cy = quad.c.y-quad.a.y;
		float dx = quad.d.x-quad.a.x;
		float dy = quad.d.y-quad.a.y;

		if( (bx * cy - by * cx >= 0) == (cx * dy - cy * dx >= 0)) {
			return triangle(quad.a,quad.b,quad.c) + triangle(quad.a,quad.c,quad.d);
		} else {
			return triangle(quad.a,quad.b,quad.d) + triangle(quad.b,quad.c,quad.d);
		}
	}

	/**
	 * Area of a simple polygon.  Meaning it can be concave or convex, but can't have self intersections
	 * @param poly Simple polygon
	 * @return area
	 */
	public static float polygonSimple( Polygon2D_F32 poly ) {
		float total = 0;

		Point2D_F32 v0 = poly.get(0);
		Point2D_F32 v1 = poly.get(1);
		for (int i = 2; i < poly.size(); i++) {
			Point2D_F32 v2 = poly.get(i);

			total += v1.x*( v2.y - v0.y);

			v0 = v1; v1 = v2;
		}

		Point2D_F32 v2 = poly.get(0);
		total += v1.x*( v2.y - v0.y);
		v0 = v1; v1 = v2;
		v2 = poly.get(1);
		total += v1.x*( v2.y - v0.y);

		return (float)Math.abs(total/2.0f);
	}
}