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