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// Copyright (c) 2014 The mathutil Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package mathutil // import "modernc.org/mathutil"
import (
"math"
)
// Approximation type determines approximation methods used by e.g. Envelope.
type Approximation int
// Specific approximation method tags
const (
_ Approximation = iota
Linear // As named
Sinusoidal // Smooth for all derivations
)
// Envelope is an utility for defining simple curves using a small (usually)
// set of data points. Envelope returns a value defined by x, points and
// approximation. The value of x must be in [0,1) otherwise the result is
// undefined or the function may panic. Points are interpreted as dividing the
// [0,1) interval in len(points)-1 sections, so len(points) must be > 1 or the
// function may panic. According to the left and right points closing/adjacent
// to the section the resulting value is interpolated using the chosen
// approximation method. Unsupported values of approximation are silently
// interpreted as 'Linear'.
func Envelope(x float64, points []float64, approximation Approximation) float64 {
step := 1 / float64(len(points)-1)
fslot := math.Floor(x / step)
mod := x - fslot*step
slot := int(fslot)
l, r := points[slot], points[slot+1]
rmod := mod / step
switch approximation {
case Sinusoidal:
k := (math.Sin(math.Pi*(rmod-0.5)) + 1) / 2
return l + (r-l)*k
case Linear:
fallthrough
default:
return l + (r-l)*rmod
}
}
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