1/*
2 * linear - perform a simple two point 2D linear interpolation
3 *
4 * Copyright (C) 2005-2007,2021  Landon Curt Noll
5 *
6 * Calc is open software; you can redistribute it and/or modify it under
7 * the terms of the version 2.1 of the GNU Lesser General Public License
8 * as published by the Free Software Foundation.
9 *
10 * Calc is distributed in the hope that it will be useful, but WITHOUT
11 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
12 * or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
13 * Public License for more details.
14 *
15 * A copy of version 2.1 of the GNU Lesser General Public License is
16 * distributed with calc under the filename COPYING-LGPL.  You should have
17 * received a copy with calc; if not, write to Free Software Foundation, Inc.
18 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
19 *
20 * Under source code control:	2005/12/12 06:41:50
21 * File existed as early as:	2005
22 *
23 * chongo <was here> /\oo/\	http://www.isthe.com/chongo/
24 * Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
25 */
26
27/*
28 * linear - perform a simple two point 2D linear interpolation
29 *
30 * given:
31 *	x0, y0		first known point on the line
32 *	x1, y1		second known point on the line
33 *	x		a given point to interpolate on
34 *
35 * returns:
36 *	y such that (x,y) is on the line defined by (x0,y0) and (x1,y1)
37 *
38 * NOTE: The line cannot be vertical.  So x0 != y0.
39 */
40define linear(x0, y0, x1, y1, x)
41{
42    /* firewall */
43    if (!isnum(x0) || ! isnum(y0) || !isnum(x1) || ! isnum(y1) || !isnum(x)) {
44	quit "non-numeric argument passed to linear";
45    }
46    if (x0 == x1) {
47	quit "linear given a line with an infinite slope";
48    }
49
50    /* return y = y0 + (delta_Y/delta_X) * (x - x0) */
51    return y0 + (((y1-y0)/(x1-x0)) * (x - x0));
52}
53