github.com/acrespo/mobile@v0.0.0-20190107162257-dc0771356504/exp/sprite/clock/tween.go (about) 1 // Copyright 2014 The Go 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 clock 6 7 // Standard tween functions. 8 // 9 // Easing means a slowing near the timing boundary, as defined by 10 // a cubic bezier curve. Exact parameters match the CSS properties. 11 var ( 12 EaseIn = CubicBezier(0.42, 0, 1, 1) 13 EaseOut = CubicBezier(0, 0, 0.58, 1) 14 EaseInOut = CubicBezier(0.42, 0, 0.58, 1) 15 ) 16 17 // Linear computes the fraction [0,1] that t lies between [t0,t1]. 18 func Linear(t0, t1, t Time) float32 { 19 if t >= t1 { 20 return 1 21 } 22 if t <= t0 { 23 return 0 24 } 25 return float32(t-t0) / float32(t1-t0) 26 } 27 28 // CubicBezier generates a tween function determined by a Cubic Bézier curve. 29 // 30 // The parameters are cubic control parameters. The curve starts at (0,0) 31 // going toward (x0,y0), and arrives at (1,1) coming from (x1,y1). 32 func CubicBezier(x0, y0, x1, y1 float32) func(t0, t1, t Time) float32 { 33 return func(start, end, now Time) float32 { 34 // A Cubic-Bezier curve restricted to starting at (0,0) and 35 // ending at (1,1) is defined as 36 // 37 // B(t) = 3*(1-t)^2*t*P0 + 3*(1-t)*t^2*P1 + t^3 38 // 39 // with derivative 40 // 41 // B'(t) = 3*(1-t)^2*P0 + 6*(1-t)*t*(P1-P0) + 3*t^2*(1-P1) 42 // 43 // Given a value x ∈ [0,1], we solve for t using Newton's 44 // method and solve for y using t. 45 46 x := Linear(start, end, now) 47 48 // Solve for t using x. 49 t := x 50 for i := 0; i < 5; i++ { 51 t2 := t * t 52 t3 := t2 * t 53 d := 1 - t 54 d2 := d * d 55 56 nx := 3*d2*t*x0 + 3*d*t2*x1 + t3 57 dxdt := 3*d2*x0 + 6*d*t*(x1-x0) + 3*t2*(1-x1) 58 if dxdt == 0 { 59 break 60 } 61 62 t -= (nx - x) / dxdt 63 if t <= 0 || t >= 1 { 64 break 65 } 66 } 67 if t < 0 { 68 t = 0 69 } 70 if t > 1 { 71 t = 1 72 } 73 74 // Solve for y using t. 75 t2 := t * t 76 t3 := t2 * t 77 d := 1 - t 78 d2 := d * d 79 y := 3*d2*t*y0 + 3*d*t2*y1 + t3 80 81 return y 82 } 83 }