envelope.go (1582B)
1 // Copyright (c) 2014 The mathutil Authors. All rights reserved. 2 // Use of this source code is governed by a BSD-style 3 // license that can be found in the LICENSE file. 4 5 package mathutil // import "modernc.org/mathutil" 6 7 import ( 8 "math" 9 ) 10 11 // Approximation type determines approximation methods used by e.g. Envelope. 12 type Approximation int 13 14 // Specific approximation method tags 15 const ( 16 _ Approximation = iota 17 Linear // As named 18 Sinusoidal // Smooth for all derivations 19 ) 20 21 // Envelope is an utility for defining simple curves using a small (usually) 22 // set of data points. Envelope returns a value defined by x, points and 23 // approximation. The value of x must be in [0,1) otherwise the result is 24 // undefined or the function may panic. Points are interpreted as dividing the 25 // [0,1) interval in len(points)-1 sections, so len(points) must be > 1 or the 26 // function may panic. According to the left and right points closing/adjacent 27 // to the section the resulting value is interpolated using the chosen 28 // approximation method. Unsupported values of approximation are silently 29 // interpreted as 'Linear'. 30 func Envelope(x float64, points []float64, approximation Approximation) float64 { 31 step := 1 / float64(len(points)-1) 32 fslot := math.Floor(x / step) 33 mod := x - fslot*step 34 slot := int(fslot) 35 l, r := points[slot], points[slot+1] 36 rmod := mod / step 37 switch approximation { 38 case Sinusoidal: 39 k := (math.Sin(math.Pi*(rmod-0.5)) + 1) / 2 40 return l + (r-l)*k 41 case Linear: 42 fallthrough 43 default: 44 return l + (r-l)*rmod 45 } 46 }