Reconstruction of 3D curve from two 2D projections.....

Posted on 1998-12-15
Last Modified: 2010-04-06

      If  I got two 2D projections of a 3D curve in real space how to reconstruct it(3D curve).Assuming that we know the position and orientation of those two image planes on which we got projections.

      where can I get the mathematical background for this and please suggest me the web sites and referrence books I have to refer....

      Respond me quickly.It's a part of my project work...
Urgent please.......

Question by:vijaybrd

Expert Comment

Comment Utility
This will give you links to a number of pages that deal with 3d graphics.  Hope this helps,
LVL 13

Expert Comment

Comment Utility
You can find the x, y and z coordinates of each vertice in the 2 2D curves:
For example x and y in curve 1 and z and y (=same as previous) in curve 2.


Author Comment

Comment Utility
Thanq Epsylon.....

      Yah.... the problem is we will be given 2d points on two image planes which are taken from two different views i.e. two diffrent positions and orientaions.We will be given the position and orientation of two image planes and two sets of 2d points of the curve on two image planes.So,how to construct the 3D curve from these 2D points....

      I think U got my point....

      Try to suggest methods for the above posed problem...

      Thanq for ur answer

LVL 10

Expert Comment

Comment Utility
If the views are just plane (XY) (YZ) and (XZ) views it is quit simple:

XY: (3,4)
YZ: (4,2)

Then the point is (3,4,2) (X,Y,Y)

If the view are more complex the task is somewhat more complex:

First of all I assume no perspective is used in the view, so a view is just a plan (which is defined by two vectors and a point).

The method is as follows:

Known of a point in a view is that it is on a line, orthogonal on the viewing plan through the point on the plane.

The orthogonal vector is calculated easily:
It is the normalized vector constructed of the points where it cuts the individual axes.

If you have constructed the lines for both views,the desired point is on the crossing of these two lines.

Repeat this process for every point of the curve and you 3D curve is constructed.

My math is a bit rusty but I hope it helped.

Regards Jacco
Highfive Gives IT Their Time Back

Highfive is so simple that setting up every meeting room takes just minutes and every employee will be able to start or join a call from any room with ease. Never be called into a meeting just to get it started again. This is how video conferencing should work!


Author Comment

Comment Utility

      Thanq a lot for ur answer.... But it is not clear to me.My Idea is that we can construct 2D curves (best fit) on each of the image planes using the given set of points.

      From these curves we have to select feature points and match them on both the curves and we have to construct 3D curve like that....If u r talking about "Reconstruction of 3D points from two 2D projections",I have already done it.Please suggest methods for curve ( direct methods if any)..


LVL 10

Expert Comment

Comment Utility
Your method will not work and I'll tell you why:

Getting the matching points on the two curves is impossible, because you don't know how far on the 3D curve you are when traveling along one of the 2D curves. Why? Because this information is missing in a 2D curve....

The way I described is the only way.

If you want to construct curves from 3D points you can just use a Splines method. They are very well documented. (I like Bezier curves better but they involve helper points which can't be easily calculated from an existing curve).

Regards Jacco

Accepted Solution

stiff earned 200 total points
Comment Utility
The math for the operations you are describing are given in:
"The VNR Concise Encyclopedia of Mathematics", by Gellert,
Kustner, Hellwich, and Kasther (editors), 1975, Van Nostrand Reinhold (publisher).

Expert Comment

Comment Utility

This question was awarded, but never cleared due to the JSP-500 errors of that time.  It was "stuck" against userID -1 versus the intended expert whom you awarded.  This corrects the problem and the expert will now receive these points; points verified.

Please click on your Member Profile and select "View Question History" to navigate through any open or locked questions you may have to update and finalize them.  If you are an EE Pro user, you can also choose Power Search to find all your open questions.

This is the Community Support link, if help is needed, along with the link to All Topics which reflects many TAs recently added.  Also in the Community Support link is a question on how experts can help, if they wish, on the cleaning of old and abandoned questions.
Thank you,
Moderator @ Experts Exchange

Featured Post

What Is Threat Intelligence?

Threat intelligence is often discussed, but rarely understood. Starting with a precise definition, along with clear business goals, is essential.

Join & Write a Comment

Suggested Solutions

Keep your audience engaged and get the most out of your next presentation with these quick Prezi tips.
Many programs have tried to outwit PowerPoint in terms of technology and skill. These programs, however, still lack several characteristics that PowerPoint has possessed from the start. Here's why PowerPoint replacements won't entirely work for desi…
In this tutorial viewers will learn how to create blended and gradiated shapes in Illustrator using the blend tool Draw two shapes, one of them in a different color: Select both and create a blend by going to Object > Blend > Make: Blends can also b…
HTML5 has deprecated a few of the older ways of showing media as well as offering up a new way to create games and animations. Audio, video, and canvas are just a few of the adjustments made between XHTML and HTML5. As we learned in our last micr…

728 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question

Need Help in Real-Time?

Connect with top rated Experts

8 Experts available now in Live!

Get 1:1 Help Now