I have a point cloud data in x,y,z co-ordinates. I want to generate surface with rectangular mesh of defined mesh size (i.e. length and breadth specified).

I have a point cloud data in x,y,z co-ordinates. I want to generate surface with rectangular mesh element of defined mesh size (i.e. length and breadth specified). Its not necessary to use available points as vertices. I just need rectangular grid and coordinates of its vertices.

Can anyone help me with this.?

Thanks.

Answer 1

[Ameer Hamza]

You can use the griddata() to convert the linear vectors x, y, and z into a grid. Try this example

X = rand(100,3); % random points

x = X(:,1); % seperate them into x, y, and z variables
y = X(:,2);
z = X(:,3);

xg = linspace(min(x), max(x), 100); % coordinates of grid
yg = linspace(min(x), max(x), 100); % coordinates of grid
[Xg, Yg] = meshgrid(xg, yg); % X and Y grids

Zg = griddata(x, y, z, Xg, Yg);

surf(Xg, Yg, Zg);

griddata() can output NaN at the edge of the grid because actual data is unavailable there. If you want to interpolate to the edges(), then you can try: https://www.mathworks.com/help/matlab/ref/scatteredinterpolant.html

[Kaustubh Tiwarekar]

I tried using this method. Thats not what I need. With this we get a grid surface in X-Y plane and when that actually fits on data grid becomes distorted as per data. I need rectangular grid of spacific size after after it fits the data points in the x-y-z domain (not only in x -y plane).

Also griddata finds duplicate points when I try to apply this on close objects. For eg. I tried using this on a point cloud data of a sphere and while executing griddata function for same x and y there are two z values available. Hence it takes the average of z vales and eliminates one of the values. How to tackle that?

[Ameer Hamza]

Ok, I get your idea. But how do you want to represent the points on the 3D grid? Do you want the points in the elements in the 3D matrix to be 1 if it lies close to a point in your point-cloud and all the other grid points to be 0.

[Kaustubh Tiwarekar]

For my use it doesnt matter if the point from point cloud data lies on the grid or not. I just want rectangular grid with specified dimensions fitting the surface generated by point cloud data and then I need the co-ordintes of the vertices of the grid along with a matrix ' t ' are points id contained in rectangle, nx4 array.

[Ameer Hamza]

Following will create a 3D grid fitting the point cloud

X = rand(100,3); % random points

x = X(:,1); % seperate them into x, y, and z variables
y = X(:,2);
z = X(:,3);

xg = linspace(min(x), max(x), 100); % coordinates of grid
yg = linspace(min(y), max(y), 100);
zg = linspace(min(z), max(z), 100);

[Xg, Yg, Zg] = meshgrid(xg, yg, zg); % X and Y grids

Xg, Yg, and Zg are 3D arrays. If you want to get the coordinates of grid in a linear form, then run this

coordinate_grid = [Xg(:) Yg(:) Zg(:)];

I am not sure about the 4-th column about point id. Can you explain it further?