/*
 * linear - perform a simple two point 2D linear interpolation
 *
 * Copyright (C) 2005-2007  Landon Curt Noll
 *
 * Calc is open software; you can redistribute it and/or modify it under
 * the terms of the version 2.1 of the GNU Lesser General Public License
 * as published by the Free Software Foundation.
 *
 * Calc 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 Lesser General
 * Public License for more details.
 *
 * A copy of version 2.1 of the GNU Lesser General Public License is
 * distributed with calc under the filename COPYING-LGPL.  You should have
 * received a copy with calc; if not, write to Free Software Foundation, Inc.
 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 *
 * @(#) $Revision: 30.2 $
 * @(#) $Id: linear.cal,v 30.2 2007/03/17 05:57:42 chongo Exp $
 * @(#) $Source: /usr/local/src/cmd/calc/cal/RCS/linear.cal,v $
 *
 * Under source code control:	2005/12/12 06:41:50
 * File existed as early as:	2005
 *
 * chongo <was here> /\oo/\	http://www.isthe.com/chongo/
 * Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
 */

/*
 * linear - perform a simple two point 2D linear interpolation
 *
 * given:
 *	x0, y0		first known point on the line
 *	x1, y1		second knonw point on the line
 *	x		a given point to interpolate on
 *
 * returns:
 *	y such that (x,y) is on the line defined by (x0,y0) and (x1,y1)
 *
 * NOTE: The line cannot be vertical.  So x0 != y0.
 */
define linear(x0, y0, x1, y1, x)
{
    /* firewall */
    if (!isnum(x0) || ! isnum(y0) || !isnum(x1) || ! isnum(y1) || !isnum(x)) {
	quit "non-numeric argument passed to linear";
    }
    if (x0 == x1) {
	quit "linear given a line with an infinite slope";
    }

    /* return y = y0 + (delta_Y/delta_X) * (x - x0) */
    return y0 + (((y1-y0)/(x1-x0)) * (x - x0));
}