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Knots & Tubes

version 1.0 (75.9 KB) by Enrico Bertolazzi
Generate tubes from 3D curves and plot knots from closed curves.

4 Downloads

Updated 04 Oct 2014

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The scripts
- `generate_closed_tube`
- `generate_open_tube`

given a 3d curve as a sequence of points build a mesh of triangles or polygons realizing a tube around the curve.

A closed tube is realized by the commands:

~~~~~~~~~~~~~~~~~~~
[pnts,conn,line1,line2] = generate_closed_tube(typ,R,nr,xyz) ;
[pnts,conn,line1,line2] = generate_closed_tube(typ,R,nr,x,y,z) ;
~~~~~~~~~~~~~~~~~~~

where R is the ray of the tube, nr is the number of edge used to approximate the circle of ray R moving along the curve.
The points on the guiding curve are specified by using xyz a matrix 3 by N whose columns are the points, or by using the vectors x, y and z. `typ` is the kind of polygons are used to describe the tube

- typ = 0 the mesh is composed by rectangles
- typ = 1 to 4 the mesh is composed by triangles

return values are

- pnts the points of the mesh os the tube as a matrix 3 by npts
- conn cell array where each element is a vector of integer with represents the connection of the faces with the points
- line1 and line2 are vectors of integer which represents the equator lines of the tube-torus.

This command assume that the curve is closed, otherwise use

~~~~~~~~~~~~~~~~~~~
[pnts,conn] = generate_open_tube(typ,R,nr,xyz) ;
[pnts,conn] = generate_open_tube(typ,R,nr,x,y,z) ;
~~~~~~~~~~~~~~~~~~~

which generate an open tube. For typ = 0 there are two polygonal faces at the begin and end of the tube, For typ > 0 this polygon is split in triangles.

**Plotting**
to visualize a tube the utility function

~~~~~~~~~~~~~~~~~~~~
plot_tube( pnts, conn, line1, line2, ... ) ;
~~~~~~~~~~~~~~~~~~~~

can be used. As optional parameter you can use

- 'FaceColor', [r,g,b] = color of the faces
- 'EdgeColor', [r,g,b] = color of the edges
- 'Line1Color', [r,g,b] = color of line 1
- 'Line2Color', [r,g,b] = color of line 2

**Input Output**
A tube can be saved in a text file by using

~~~~~~~~~~~~~~~~~~~~
bbox = save_tube(name,pnts,conn) ;
~~~~~~~~~~~~~~~~~~~~

The file name+'.txt' is generated with a simple description of the tube as a list of points followed by face connections.

To read an already saved tube use

~~~~~~~~~~~~~~~~~~~~
[pnts,conn] = read_tube( fname ) ;
~~~~~~~~~~~~~~~~~~~~

with the obvious meaning.

It is possibile to save a tube or a list o tubes to files which can be used by a mesh generator like NETGEN or TETGEN.

For netgen use:

~~~~~~~~~~~~~~~~~~~~
bbox = save_netgen(fileName,name,pnts,conn) ;
~~~~~~~~~~~~~~~~~~~~

For tetgen use:

~~~~~~~~~~~~~~~~~~~~
bbox = save_tetgen(fileName,names,pin,pnts,conn);
~~~~~~~~~~~~~~~~~~~~

tetgen needs the knowledge of an internal point of the tube stored in `pin`.

**Examples**
In the directory `example` many examples shows as to use the library to build knots and plot it.

Cite As

Enrico Bertolazzi (2021). Knots & Tubes (https://www.mathworks.com/matlabcentral/fileexchange/48021-knots-tubes), MATLAB Central File Exchange. Retrieved .

Comments and Ratings (1)

Jorrit M

Works quite well, but I needed to do some editing myself to be able to plot the tube with different widths

MATLAB Release Compatibility
Created with R2014b
Compatible with any release
Platform Compatibility
Windows macOS Linux
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