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length of a Bezier curve in 3D

Posted: Sat Jul 01, 2023 10:18 pm
by Yoshi
Any idea how to calculate the length of a Bezier curve in 3D? Suppose I know three control points [x1,y1,z1] , [x2,y2,z2] and [x3,y3,z3]...

Re: length of a Bezier curve in 3D

Posted: Tue Jul 04, 2023 6:59 am
by venhard
hi, there is a book about it. This is full with math and examples. I have a PDF copy. I send this to you.

Re: length of a Bezier curve in 3D

Posted: Wed Jul 05, 2023 7:08 am
by rector
There exists 3d Bezier.class in PHP which is defined by three points and returns curve length. I am unable to attach the file here. Send PM.

Re: length of a Bezier curve in 3D

Posted: Fri Jul 07, 2023 6:12 pm
by tamagotchi
yoshi, check this on wikipedia: https://en.wikipedia.org/wiki/Composite ... zier_curve Now, assume the control points of Eight-segment quadratic polybezier have different "Z"-coordinates. This results in flat curved circle. The question is, how to calculate the perimeter and area from eight control points, each defined by three coordinates {x1, y1, z1] .... [x8, y8, z8]

Re: length of a Bezier curve in 3D

Posted: Sun Jul 09, 2023 6:12 am
by Yoshi
venhard, thank you for book posting