Finding the path between two points

Hi all,

I have two x y z coordinates and I need the path between these two points. It does not necessarily need to be the shortest distance path. I am working with a (3x30) position matrix. The first row represents x, the second row is y and the third row is z.

 Point 1: (x1,y1,z1)
 Point 30: (x30,y30,z30)
 Position matrix: [x1 .......... x30
                   y1 .......... y30
                   z1 .......... z30]

Point 1 and point 30 are given. I need something simple that will give me the remaining 28 points within the matrix.

Thanks in advance!

[James Tursa]

Any restrictions on the path? E.g., is a diagonal jump (two indexes changing at the same time) OK? Can indexes only change a max of 1 for each point?

[Zena Assaad]

No, there are no restrictions on the path.

Answer 1

[James Tursa]

E.g., a somewhat "linear" path allowing "diagonal" jumps (more than one index can change at a time):

Point1 = whatever;
Point30 = whatever;
Pmatrix = [round(linspace(Point1(1),Point30(1),30));
           round(linspace(Point1(2),Point30(2),30));
           round(linspace(Point1(3),Point30(3),30))];

If the points do not need to be integers, then skip the rounding.

[Zena Assaad]

This works well for x and y but it gives zero for all the z values even though the z for point 1 and point 30 are non-zero.

[James Tursa]

It works for me. Probably a typo at your end either for the code above or for the points used. Can you post your Point1 and Point30?

[Zena Assaad]

point 1: (-2600529.46, 379356.01, 0.004)

Point 30: (6025274.59, 2064061.77, 0.132)

Do you think it's spitting out zero because the z values are so close to zero?

[James Tursa]

Values are not integers, so get rid of the round function as stated above. E.g.,

Pmatrix = [linspace(Point1(1),Point30(1),30);
           linspace(Point1(2),Point30(2),30);
           linspace(Point1(3),Point30(3),30)];

[Zena Assaad]

I did get rid of the round from the beginning the values are still coming up as zero.

[James Tursa]

They are not zero ... they are just displaying as zero because of the display format you are using (probably short) and the wide range of values in the result. Try this:

format long g

Then display the result again.

Or just look at the last row by itself:

Pmatrix(3,:)

[Zena Assaad]

That worked perfectly. Thank you very much for all your help.

Answer 2

[Image Analyst]

See Steve's 5 part blog series on it: http://blogs.mathworks.com/steve/2011/11/01/exploring-shortest-paths-part-1/