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### Highlights from 3D Bresenham's line generation

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# 3D Bresenham's line generation

12 Aug 2008 (Updated )

Generate X Y Z coordinates of a 3D Bresenham's line between two given points

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Description

This program will generate the coordinates of a 3D Bresenham's raster line between two given points.

A very useful application of this algorithm can be found in the implementation of Fischer's Bresenham interpolation method in my another program that can rotate three dimensional image volume with an affine matrix:
http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=21080

Usage: [X Y Z] = bresenham_line3d(P1, P2);

P1 - vector for Point1, where P1 = [x1 y1 z1]

P2 - vector for Point2, where P2 = [x2 y2 z2]

precision (optional) - Although according to Bresenham's line algorithm, point coordinates x1 y1 z1 and x2 y2 z2 should be integer numbers, this program extends its limit to all real numbers. If any of them are floating numbers, you should specify how many digits of decimal that you would like to preserve. Be aware that the length of output X Y Z coordinates will increase in 10 times for each decimal digit that you want to preserve. By default, the precision is 0, which means that they will be rounded to the nearest integer.

X - a set of x coordinates on Bresenham's line

Y - a set of y coordinates on Bresenham's line

Z - a set of z coordinates on Bresenham's line

Therefore, all points in XYZ set (i.e. P(i) = [X(i) Y(i) Z(i)]) will constitute the Bresenham's line between P1 and P1.

Example:

P1 = [12 37 6]; P2 = [46 3 35];
[X Y Z] = bresenham_line3d(P1, P2);
figure; plot3(X,Y,Z,'s','markerface','b');

This program is ported to MATLAB from:

B.Pendleton. line3d - 3D Bresenham's (a 3D line drawing algorithm), 1992.
ftp://ftp.isc.org/pub/usenet/comp.sources.unix/volume26/line3d

Which is also referenced by:

Fischer, J., A. del Rio (2004). A Fast Method for Applying Rigid Transformations to Volume Data, WSCG2004 Conference.
http://wscg.zcu.cz/wscg2004/Papers_2004_Short/M19.pdf

MATLAB release MATLAB 5.2 (R10)
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Comments and Ratings (1)
14 Aug 2008

Using real valued input coordinates (yes, there are applications for that) results in an infinite loop. Apart from that it works well. Good job!

Updates
15 Aug 2008

According to Bresenham's line algorithm, two input points' coordinates should be integer. The program now rounds up any float input coordinates to the nearest integer to prevent the infinite loop.

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