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

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.

[Torsten]

Not possible unless you know the 3d-curve itself by a sequence of points (x(i),y(i),z(i)).

[Hege]

Thanks for the reply. Each curve is modelled by voxels. So, I can get the coordinates of all voxels. for instance, If a curve called ''A'' has 20 voxels, I can get the X,Y,Z coordinates of all voxels in curve A.

[Torsten]

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)

[Hege]

Dear Sir,

Thank you very much for your reply. Really appreciate it. I am working according to your feedback.

[Hege]

Dear Sir,

I am happy with your answer. but there is no 'ICON' accept the answer. Pls advice.

[Torsten]

I changed my comment to an answer.

Thanks for your feedback.

Answer 1

[Torsten]

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)