I'm trying to compute 2d projections of a 3d mesh from different views using matlab.
The solution I m using now, is to plot the 3d mesh, rotate it, and make a screenshot.
I would like to know if there is any matlab internal functions or any other solution that allow me, given a set of vertices and triangles, to compute the projections without having to plot the 3D mesh
Thanks
You can use the view command to rotate the axes and change the viewpoint. The azimuth and elevation are given in degrees (ref. documentation for more info). Here's a small example:
ha=axes;
[x,y,z]=peaks;
surf(x,y,z);
xlabel('x');ylabel('y');zlabel('z')
%#projection on the X-Z plane
view(ha,[0,0])
%#projection on the Y-Z plane
view(ha,[90,0])
%#projection on the X-Y plane
view(ha,[0,90])
This is what it looks like:
Projections on different 2D planes
X-Z
Y-Z
X-Y
Related
I have a 3D matrix (250x3x7) where the 1st dimension are the data points, 2nd dimension the x,y,z coordinates, and 3rd dimension the slice location. This 3D matrix are the contours at each slice location and these contours are not parallel to each other. I wish to interpolate these contour onto some planes in 3D space. These planes are parallel to each other. I have the x,y,z coordinates of each pixel of these plane. The example in images below will explain it better. I want to interpolates those contours on those grey colour planes.
Image1: contours and plane
Image: The few slices of contours and a few number of plane
I tried using interp3 to interpolate the contours with meshgrid, but I'm not sure how to interpolate it to a specific location (plane) in 3D space. Hope someone can help me with this. Do let me know if my question is not clear. Thanks!
Basically, I have a many irregular circle on the ground in the form of x,y,z coordinates (of 200*3 matrix). but I want to fix a best circle in to the data of x,y,z coordinates (of 200*3 matrix).
Any help will be greatly appreciated.
I would try using the RANSAC algorithm which finds the parameters of your model (in your case a circle) given noisy data. The algorithm is quite easy to understand and robust against outliers.
The wikipedia article has a Matlab example for fitting a line but it shouldn't be too hard to adapt it to fit a circle.
These slides give a good introduction to the RANSAC algorithm (starting from page 42). They even show examples for fitting a circle.
Though this answer is late, I hope this helps others
To fit a circle to 3d points
Find the centroid of the 3d points (nx3 matrix)
Subtract the centroid from the 3D points.
Using RANSAC, fit a plane to the 3D points. You can refer here for the function to fit plane using RANSAC
Apply SVD to the 3d points (nx3 matrix) and get the v matrix
Generate the axes along the RANSAC plane using the axes from SVD. For example, if the plane norm is along the z-direction, then cross product between the 1st column of v matrix and the plane norm will generate the vector along the y-direction, then the cross product between the generated y-vector and plane norm will generate a vector along the x-direction. Using the generated vectors, form a Rotation matrix [x_vector y_vector z_vector]
Multiply the Rotation matrix with the centroid subtracted 3d points so that the points will be parallel to the XY plane.
Project the points to XY plane by simply removing the Z-axes from the 3d points
fit a circle using Least squares circle fit
Rotate the center of the circle using the inverse of the rotation matrix obtained from step 5
Translate back the center to the original location using the centroid
The circle in 3D will have the center, the radius will be the same as the 2D circle we obtained from step 8, the circle plane will be the RANSAC plane we obtained from step 3
I have a set of data in 3D which are in the same plane. I have a Triangle containing those data points in the same plane. But the Area of the Triangle is much larger. I want to find the smallest area triangle (co-ordinate of its 3 points) containing all the data point inside it. There are some concepts available for 2D data points, but I need to find this in 3D dimension.
It looks like Matlab has a function for this, convhull. You want to find the convex hull of the data set. http://www.mathworks.com/help/matlab/ref/convhull.html This function works for points in 2d or 3d space.
I am wondering if there is a way to build a random 3D surface from only one (top-down) 2D image of this surface. The fact is that the 3D surface needs the z-coordinates (the heights and the depths) and the 2D (top-down) image gives only the x and y coordinates.
I believe that the main problem is that we can't get the real ranges of the dimensions (x,y,z) of the surface from one 2D (top-down) image but we can get some kind of normalized scaling which is not the real one (it's just similar).
For example:
If we have an image with a surface (2D) and we want 3D of this surface (x,y,z) we can have easily the x and the y coordinates from the image. We can't have the real range of the amplitude (z coordinate) in each point of the surface but only the gray-tones scaling. Is there any ideas on how could we take the real sizes of the amplitudes of a surface from one 2D (top-down) image?
Left is a sample of 2D top-down image and Right is a surface which created by the 2D
http://www.sendspace.com/file/9wzx0u
p.s.
I can't post an image because of my reputation, so I uploaded one on sedspace.com.
Read in the image:
A = imread(filename)
Plot the surface plot using the magnitude of the value read in for each x and y from the file:
surf(A)
I write my study and is stuck when i try triangulate the contour of surface. When it is in 2D its ok. When it in 3D a have trouble with triangle angle detection, i tried with:
Triange have 3 Vertices v1,v2,v3
I create 2 vectors(vec21, vec23) from v2v1 and v2v3
then vec21 x vec23 and obtain a det of matrix
on the stand which I define Span angle
I also check if edges do not crossing and if any point isnt in area of triangle.
But when it in 3D i choose point around polygon then this metod didn't work
Points of contour i want triangulate to flat polygon: https://docs.google.com/open?id=0Bw5-VXnqutXBckRJMGNJMW9JaXc
Bad resoult: https://docs.google.com/open?id=0Bw5-VXnqutXBMzV5elIxX1FaeDQ
In 2d:
Points on 2D :https://docs.google.com/open?id=0Bw5-VXnqutXBWVE4bWJsZ09mOVk
Good resoults:https://docs.google.com/open?id=0Bw5-VXnqutXBdGFKM2Z4UnFRdXc
Where i made mistake? Can u explain me this?
Greetings!
PS. Im interested in algoithm at 2 last case:http://www.cosy.sbg.ac.at/~held/projects/triang/triang.html
Typically one would use a Delaunay Triangulation for the 2D case. For the 3D case you can project the points to 2D, triangulate and project the triangles back to 3D. This will of course only work if the patch to be triangulated can be projected to 2D (without selfintersections).