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mathpointcurvequadratic

Quadratic Bézier Curve: Calculate Points

I'd like to calculate a point on a quadratic curve. To use it with the canvas element of HTML5.

When I use the quadraticCurveTo() function in JavaScript, I have a source point, a target point and a control point.

How can I calculate a point on the created quadratic curve at let's say t=0.5 with "only" knowing this three points?

Solution

  • Use the quadratic Bézier formula, found, for instance, on the Wikipedia page for Bézier Curves:

    quadratic Bezier formula

    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 - t) * (1 - t) * p[0].y + 2 * (1 - t) * t * p[1].y + t * t * p[2].y;

    p[0] is the start point, p[1] is the control point, and p[2] is the end point. t is the parameter, which goes from 0 to 1.