Projected curve lengths (XY,XZ,YZ) of 3D arcs

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Hege
Hege 2022-6-7
评论： Torsten 2022-6-30
Hello All,
I have a set of 3D curves as shown in attached image which was was extracted from X-ray Micro-CT system. I know the 3D curve length of each arcs by voxels. Also, using regionprops3 command, I found the coordinates of end points of each curve.
I would like to know the projected curve length of each curve in all three different planes (x-y,x-z,y-z).
Appreciate your comments.
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Hege
Hege 2022-6-30
Dear Sir,
I am happy with your answer. but there is no 'ICON' accept the answer. Pls advice.
Torsten
Torsten 2022-6-30
I changed my comment to an answer.
Thanks for your feedback.

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采纳的回答

Torsten
Torsten 2022-6-30
Then just set the coordinate of the plane you project on to 0 and calculate the arc length of the resulting projected curve.
An approximation for an XY-projected curve is e.g.
sum_{i=1}^{i=n-1} sqrt((x(i+1)-x(i))^2 + (y(i+1)-y(i))^2)
if it is represented in 3d by the points
P1 = (x1,y1,z1), P2=(x2,y2,z2),..., Pn = (xn,yn,zn)

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