shannoga - 9 months ago 109

iOS Question

I have many UIBezierPath that I am animating with CALyerAnimation @"StrokeStart" and @"strokeEnd".

I wish that the animation will have the same speed for all the paths so I thougt I might use the length of the path in :

DISTANCE / TIME = SPEED

Is there a way to calculate the path "length" ?

Thanks

Shani

Answer

While you can calculate Bezier path's length by integrating it numerically, it can be done much easier by dividing path into linear segments. If the segments are small enough the approximation error should be neglectable, especially that you are just trying to animate it.

I'll show you function for quad curves, but you can easily incorporate the solution for cubic curves as well:

```
- (float) bezierCurveLengthFromStartPoint: (CGPoint) start toEndPoint: (CGPoint) end withControlPoint: (CGPoint) control
{
const int kSubdivisions = 50;
const float step = 1.0f/(float)kSubdivisions;
float totalLength = 0.0f;
CGPoint prevPoint = start;
// starting from i = 1, since for i = 0 calulated point is equal to start point
for (int i = 1; i <= kSubdivisions; i++)
{
float t = i*step;
float x = (1.0 - t)*(1.0 - t)*start.x + 2.0*(1.0 - t)*t*control.x + t*t*end.x;
float y = (1.0 - t)*(1.0 - t)*start.y + 2.0*(1.0 - t)*t*control.y + t*t*end.y;
CGPoint diff = CGPointMake(x - prevPoint.x, y - prevPoint.y);
totalLength += sqrtf(diff.x*diff.x + diff.y*diff.y); // Pythagorean
prevPoint = CGPointMake(x, y);
}
return totalLength;
}
```

**EDIT**

If you don't have access to path control points (say you created path using arcs) you can always access underlying Bezier curves using `CGPathApply`

function:

```
- (void) testPath
{
UIBezierPath *path = [UIBezierPath bezierPath];
[path moveToPoint:CGPointZero];
[path addQuadCurveToPoint:CGPointMake(1, 1) controlPoint:CGPointMake(-2, 2)];
CGPathRef p = path.CGPath;
CGPathApply(p, nil, pathFunction);
}
void pathFunction(void *info, const CGPathElement *element)
{
if (element->type == kCGPathElementAddQuadCurveToPoint)
{
CGPoint p;
p = element->points[0]; // control point
NSLog(@"%lg %lg", p.x, p.y);
p = element->points[1]; // end point
NSLog(@"%lg %lg", p.x, p.y);
}
// check other cases as well!
}
```

Note that it doesn't provide the path's start point, but it's easy to keep track of it on your own.