I’ve written some quick-and-dirty code that estimates this for Bézier curves of any degree. (Note: this is pseudo-brute force, not a closed-form solution.) Demo: http://phrogz.net/svg/closest-point-on-bezier.html /** Find the ~closest point on a Bézier curve to a point you supply. * out : A vector to modify to be the point on the curve * curve … Read more
I just implemented something similar in a project I am working on. My solution was to use a Catmull-Rom spline instead of using Bezier splines. These provide a very smooth curve THROUGH a set a points rather then a bezier spline ‘around’ points. // Based on code from Erica Sadun #import “UIBezierPath+Smoothing.h” void getPointsFromBezier(void *info, … Read more
You are correct in that UIBezierPath is simply an objective-c wrapper for Core Graphics, and therefore will perform comparably. The difference (and reason for your performance delta) is your CGContext state when drawing your CGPath directly is quite different to that setup by UIBezierPath. If you look at UIBezierPath, it has settings for: lineWidth, lineJoinStyle, … Read more
As already said: there is no exact representation of the circle using Bezier curves. To complete the other answers : for Bezier curve with n segments the optimal distance to the control points, in the sense that the middle of the curve lies on the circle itself, is (4/3)*tan(pi/(2n)). So for 4 points it is … Read more
The problem with joining subsequent sample points together with disjoint “curveTo” type functions, is that where the curves meet is not smooth. This is because the two curves share an end point but are influenced by completely disjoint control points. One solution is to “curve to” the midpoints between the next 2 subsequent sample points. … Read more