CPAnimation: cubic bezier curves - the real, working equation

Conflicts:

	AppKit/CPAnimation.j

AppKit/CPAnimation.j

@@ -300,13 +300,47 @@ ACTUAL_FRAME_RATE = 0;
 */
 - (float)currentValue
 {
+    var t = [self currentProgress];
+    
     if ([_delegate respondsToSelector:@selector(animation:valueForProgress:)])
-        return [_delegate animation:self valueForProgress:_progress];
+        return [_delegate animation:self valueForProgress:t];
     
-    if (_animationCurve == CPAnimationLinear)
-        return _progress;
-    
-    alert("IMPLEMENT ANIMATION CURVES!!!");
+    var c1 = [],
+        c2 = [];
+  
+    [_timingFunction getControlPointAtIndex:1 values:c1];
+    [_timingFunction getControlPointAtIndex:2 values:c2];
+ 
+    return CubicBezierAtTime(t,c1[0],c1[1],c2[0],c2[1],_duration);
 }
 
 @end
+
+// currently used function to determine time
+// 1:1 conversion to js from webkit source files
+// UnitBezier.h, WebCore_animation_AnimationBase.cpp
+var CubicBezierAtTime = function CubicBezierAtTime(t,p1x,p1y,p2x,p2y,duration)
+{
+    var ax=0,bx=0,cx=0,ay=0,by=0,cy=0;
+    // `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
+    function sampleCurveX(t) {return ((ax*t+bx)*t+cx)*t;};
+    function sampleCurveY(t) {return ((ay*t+by)*t+cy)*t;};
+    function sampleCurveDerivativeX(t) {return (3.0*ax*t+2.0*bx)*t+cx;};
+    // The epsilon value to pass given that the animation is going to run over |duration| seconds. The longer the animation, the more precision is needed in the timing function result to avoid ugly discontinuities.
+    function solveEpsilon(duration) {return 1.0/(200.0*duration);};
+    function solve(x,epsilon) {return sampleCurveY(solveCurveX(x,epsilon));};
+    // Given an x value, find a parametric value it came from.
+    function solveCurveX(x,epsilon) {var t0,t1,t2,x2,d2,i;
+        function fabs(n) {if(n>=0) {return n;}else {return 0-n;}}; 
+        // First try a few iterations of Newton's method -- normally very fast.
+        for(t2=x, i=0; i<8; i++) {x2=sampleCurveX(t2)-x; if(fabs(x2)<epsilon) {return t2;} d2=sampleCurveDerivativeX(t2); if(fabs(d2)<1e-6) {break;} t2=t2-x2/d2;}
+        // Fall back to the bisection method for reliability.
+        t0=0.0; t1=1.0; t2=x; if(t2<t0) {return t0;} if(t2>t1) {return t1;}
+        while(t0<t1) {x2=sampleCurveX(t2); if(fabs(x2-x)<epsilon) {return t2;} if(x>x2) {t0=t2;}else {t1=t2;} t2=(t1-t0)*.5+t0;}
+        return t2; // Failure.
+    };
+    // Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1).
+    cx=3.0*p1x; bx=3.0*(p2x-p1x)-cx; ax=1.0-cx-bx; cy=3.0*p1y; by=3.0*(p2y-p1y)-cy; ay=1.0-cy-by;
+    // Convert from input time to parametric value in curve, then from that to output time.
+    return solve(t, solveEpsilon(duration));
+};

AppKit/CPWindow/CPWindow.j

@@ -1787,7 +1787,7 @@ CPTexturedBackgroundWindowMask
     [aSheet setFrame:startFrame];
     _sheetContext["opened"] = YES;
 
-    [aSheet _setFrame:endFrame delegate:self duration:0.3 curve:CPAnimationEaseOut];
+    [aSheet _setFrame:endFrame delegate:self duration:0.2 curve:CPAnimationEaseOut];
 
     // Should run the main loop here until _isAnimating = FALSE
     [aSheet becomeKeyWindow];    
@@ -1808,7 +1808,7 @@ CPTexturedBackgroundWindowMask
     [self _setUpMasksForView:sheetContent];
             
     _sheetContext["opened"] = NO;
-    [sheet _setFrame:endFrame delegate:self duration:0.2 curve:CPAnimationLinear];
+    [sheet _setFrame:endFrame delegate:self duration:0.2 curve:CPAnimationEaseIn];
 }
 
 /* @ignore */