I created a Python package that attempts to implement the Kneedle algorithm. To recreate the function above and detect the point of maximum curvature: x = range(1,21) y = [0.065, 0.039, 0.030, 0.024, 0.023, 0.022, 0.019, 0.0185, 0.0187, 0.016, 0.015, 0.016, 0.0135, 0.0130, 0.0125, 0.0120, 0.0117, 0.0115, 0.0112, 0.013] kn = KneeLocator( x, y, curve=”convex”, … Read more
OK, I think I found the answer. First the solution: cov_x*s_sq is simply the covariance of the parameters which is what you want. Taking sqrt of the diagonal elements will give you standard deviation (but be careful about covariances!). Residual variance = reduced chi square = s_sq = sum[(f(x)-y)^2]/(N-n), where N is number of data … Read more
Let P0, P1, P2 be the control points, and Pc be your fixed point you want the curve to pass through. Then the Bezier curve is defined by P(t) = P0*t^2 + P1*2*t*(1-t) + P2*(1-t)^2 …where t goes from zero to 1. There are an infinite number of answers to your question, since it might … Read more
As you’ve discovered, both Quadratic curves and Cubic Bezier curves just connect 2 points with a curve. Since the Cubic curve has more control points, it is more flexible in the path it takes between those 2 points. For example, let’s say you want to draw this letter “R”: Start drawing with the “non-curvey” parts … Read more
You could use an asymmetrical border to make curves with CSS. border-radius: 50%/100px 100px 0 0; VIEW DEMO .box { width: 500px; height: 100px; border: solid 5px #000; border-color: #000 transparent transparent transparent; border-radius: 50%/100px 100px 0 0; } <div class=”box”></div>
I needed to implement this for work as well. The fundamental concept you need to start with is that the main difference between the regular Catmull-Rom implementation and the modified versions is how they treat time. In the unparameterized version from your original Catmull-Rom implementation, t starts at 0 and ends with 1 and calculates … Read more
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
Use the quadratic Bézier formula, found, for instance, on the Wikipedia page for Bézier Curves: In pseudo-code, that’s t = 0.5; // given example value x = (1 – t) * (1 – t) * p[0].x + 2 * (1 – t) * t * p[1].x + t * t * p[2].x; y = (1 … Read more