// This is Free Software under GNU Affero General Public License v >= 3.0
// without warranty, see README.md and license for details.
//
// SPDX-License-Identifier: AGPL-3.0-or-later
// License-Filename: LICENSES/AGPL-3.0.txt
//
// Copyright (C) 2019 by via donau
//   – Österreichische Wasserstraßen-Gesellschaft mbH
// Software engineering by Intevation GmbH
//
// Author(s):
//  * Sascha L. Teichmann <sascha.teichmann@intevation.de>

package common

// Linear constructs a function which maps x1 to y1 and x2 to y2.
// All other values are interpolated linearly.
func Linear(x1, y1, x2, y2 float64) func(float64) float64 {
	// f(x1) = y1
	// f(x2) = y2
	// y1 = x1*a + b <=> b = y1 - x1*a
	// y2 = x2*a + b

	// y1 - y2 = a*(x1 - x2)
	// a = (y1-y2)/(x1 - x2) for x1 != x2

	if x1 == x2 {
		return func(float64) float64 {
			return 0.5 * (y1 + y2)
		}
	}
	a := (y1 - y2) / (x1 - x2)
	b := y1 - x1*a
	return func(x float64) float64 {
		return x*a + b
	}
}