First of all, I am not a mathematician so my terminology might not be correct. Also English is not my first language so I might make some spelling mistakes.
The context
I am wondering if I can use an existing 2d Bézier curve implementation (in code) to calculate 3d Bézier curves given the relevant 3d Bézier point coordinates.
It is not an option to implement an "correct" 3d curve function. Because of various reasons.
Some background
I have found the answer of Cesareo in the following post [1] and the image there [2] shows me that Bézier curves could be "reconstructed" using two of the three possible flat representations (two of the colored lines in the image)
The expanded question
What I need someone to confirm is that when I convert the 3d Bézier curve points to the 2d plane coordinates and have two 2d Bézier curves generated (on two different 2d planes) for say the "top down view" and "side view" and I "(re)construct" the points of the two planes back into 3 dimensional space by sampling the two planes (use the "top down view" coordinates with the height of the "side view") will I get the same 3d curve as with a "conventional" Bézier curve implementation?
Or maybe I have to add the two curves together in a different way? Maybe the average of the two/three 2d lines?
Hopefully someone can help me with this as I don't know how to solve or check the correctness of my hypothesis.
[1]: https://math.stackexchange.com/questions/2816117/how-to-convert-3d-b%C3%A9zier-curve-to-separate-curves
[2]:
The context
I am wondering if I can use an existing 2d Bézier curve implementation (in code) to calculate 3d Bézier curves given the relevant 3d Bézier point coordinates.
It is not an option to implement an "correct" 3d curve function. Because of various reasons.
Some background
I have found the answer of Cesareo in the following post [1] and the image there [2] shows me that Bézier curves could be "reconstructed" using two of the three possible flat representations (two of the colored lines in the image)
The expanded question
What I need someone to confirm is that when I convert the 3d Bézier curve points to the 2d plane coordinates and have two 2d Bézier curves generated (on two different 2d planes) for say the "top down view" and "side view" and I "(re)construct" the points of the two planes back into 3 dimensional space by sampling the two planes (use the "top down view" coordinates with the height of the "side view") will I get the same 3d curve as with a "conventional" Bézier curve implementation?
Or maybe I have to add the two curves together in a different way? Maybe the average of the two/three 2d lines?
Hopefully someone can help me with this as I don't know how to solve or check the correctness of my hypothesis.
[1]: https://math.stackexchange.com/questions/2816117/how-to-convert-3d-b%C3%A9zier-curve-to-separate-curves
[2]: