CVT_MOVIE4
Animated CVT Algorithm

CVT_MOVIE4 is a MATLAB program which animates the generation of a Centroidal Voronoi Tessellation (CVT) dataset.

The action takes place in a square; however, a nonuniform density function is applied, which effectively increases the "weight" of regions in the corners; for this iterative algorithm, the effect of the density function is that many more sample points will come from the corners than from the center. The CVT cells will correspondingly tend to migrate away from the center.

The data that the user may set includes:

• N, the number of points to generate, (100 to 300 is reasonable)
• SAMPLE_NUM, the number of sampling points (10,000 to 100,000 might be reasonable):
• FRAME_NUM, the number of frames to create (5 or 10 might be reasonable to start with, 100 is usually plenty).

The program proceeds to create a series of JPG files, each containing one frame of the animation. It is possible to create an animation by using software such as Apple QuickTime.

Animations:

One version of a sample animation file is stored in the MPEG-4 format. You can see the MP4 animation.

Reference:

1. Franz Aurenhammer,
   Voronoi diagrams - a study of a fundamental geometric data structure,
   ACM Computing Surveys,
   Volume 23, Number 3, pages 345-405, September 1991,
   ../../pdf/aurenhammer.pdf
2. Qiang Du, Vance Faber and Max Gunzburger,
   Centroidal Voronoi Tessellations: Applications and Algorithms,
   SIAM Review, Volume 41, 1999, pages 637-676.

Source Code:

• ch_is_digit.m is TRUE if a character represents a digit.
• cvt_movie4.m the main program for the creation of the movie.
• digit_inc.m increments a character that represents a digit.
• file_name_inc.m "increments" a file name that has numeric characters in it.
• s_len_trim.m returns the length of a string to the last nonblank.
• timestamp.m prints the current YMDHMS date as a timestamp.
• voronoi_new.m an improved version of the voronoi command, draws a Voronoi diagram of a given set of points.

You can go up one level to the MATLAB source codes.