Intersection between Bezier curve and line. How can I insure that this intersection is smooth?

Question

I am trying to use Bezier curves to plot a path. After conducting some research, I decided to use Bezier curves. I have both the starting point and endpoint as a given. However, the endpoint is a corner point of a line. Thus, I am technically connecting a given starting point to a line that intersects it at the given endpoint. The problem I am facing is that the intersection between the Bezier curve and the line is not smooth.

Note: I am using a cubic polynomial.

For the Bezier curve to smoothly join the line segment, the first control point must lie on the extension of that line segment. — jasonharper, Sep 26 '20 at 15:22
Please remember that Stackoverflow only works if you _accept answers_. — Mike 'Pomax' Kamermans, Sep 30 '20 at 17:47

score 3 · Answer 1 · answered Sep 26 '20 at 15:22

3

A bezier curve is tangent to the line between the control points and endpoints. In other words, if you put your control point on the extension of the horizontal line, the curve will be tangent to it at the endpoint and you'll have a smooth result.

Tangent:

Not tangent:

answered Sep 26 '20 at 15:22

dominicm00

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Thank you very much for the clarification. – Sep 26 '20 at 22:32

Intersection between Bezier curve and line. How can I insure that this intersection is smooth?

1 Answers1