Combining two Bezier curves

Question

i have two Bezier curves located at a distance from each other in space. curve 1 has control points A0, A1, A2, A3. A0 and A3 lie on the curve and are its end points. Curve 2 has control points C0, C1, C2, C3. C0 and C3 lie on the curve and are its end points

I want to join two curves A and C with an intermediate Bezier curve B. The intermediate curve B has control points A3 and C0 that lie on the curve and are its end points. intermediate control points B1 and B2 are unknown to me. also the connection should be smooth enough. please help how to proceed. We read a lot about beziers, but don’t know how to do it. thanks and greetings gauri

Answer 1

B1 will be: B1x = 2 * A3x - A2x; B1y = 2 * A3y - A2y;

B2 will be: B2x = 2 * C0x - C1x; B2y = 2 * C0y - C1y;

This should give you a perfectly smooth connection.

Answer 2

@Arty

You are right, but it will provide only a “smooth” connection.

To achieve a better search for these two curves, you must also have a 2nd derivative equal to the junction. I put it here for those who may need this information.