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Is this nice property of the cubic bezier why it is more frequently used than other bezier curves in computer graphics?


Reply to tacocat: I think the number of constraints and freedom match when we are using cubic bezier.


Why is it that in the image in the slide we have 4 degrees of freedom, but in a closed loop, we have 8 degrees of freedom?


I think I understand the tangent continuity and position continuity argument, and why there are 8 constraints and 8 DOFs for closed loop. But I'm having a hard time matching this argument with the definition given above for the cubic curves. For 2 cubic curves, we have p_{01} p_{11} p_{21} p_{31} and p_{02} p_{12} p_{22} p_{32} as the 8 variables. This seems to be telling me that there are two fixed curves that would form a smooth closed loop. This doesn't seem quite right... what am I missing here?


How would you actually go about calculating the values to make the endpoints and tangents meet? Do you manipulate only one Bezier curve or average the both of them?


After getting seamless curves, could we use the points and their corresponding tangent at each position to give a rough estimate of how the curve looks like?


Why is the joined curve 4DOF but the loop 8DOF? Are we not counting the other endpoints in the first example?


Does this guarantee the curve has a continuous derivative?