Distance between a point(x,y,z) and a surface(X,Y,Z)

I am trying to calculate the minimum distance between a point(x,y,z) and a surface defined by points (X;Y,Z). I now the normal to the point (x,y,z) from which I want to calculate distance, however I am not able to figure out the way of interpolating my surface so that the minimum distance is obtained, no matter the number of points in my surface.

Right now my option is to calcualte the distance from my point (x,y,z) to all the points in surface (X,Y,Z) and keep just the smallest one. However, I think there must be a better way of doing so.

Thank you very much for your help.

[darova]

Assume blue points are your data. You want closest distance D1 or it should be precise D0?

[Aurea94]

It should be D0 precise. For the moment with the simplification I am doing I know I am calculating D1.

[Ali Grysah]

hi i need matlab 2008 windos7 /.bt32

can you help me,,and thunks

Answer 1

[darova]

THe best idea i have: refine close region using interp2 and just find closest distance (blue)

[Aurea94]

Thank you very much! I think it is the best option I can get!

Answer 2

[David Hill]

Seems like a math question rather than a Matlab question. The minnum distance between a plane and a point is just the absolute value of the dot product between the point and the unit normal vector of the plane. The normal vector of the plane can be easily found with the 3 points given and is just the cross product between two vectors lying in the plane. For example:

p=[1 -2 0;0 -1 2;3 1 4];%three points given on the plane
d=diff(p);%two vectors lying in the plane
N=cross(d(1,:),d(2,:));
n=N/norm(N);%unit normal vector of plane

You do the rest

[Aurea94]

Helo David!

Sorry perhaps I missed that information in my message. My surface has a changing curvature, that is the normal vector at each point of the surface is not constant. That is why I cannot do what you propose. If this was not the case your proposal was a good one, thought.

[Star Strider]

Perhaps the surfnorm functon could be helpful?

[Aurea94]

Thats a good option I didn't knw t obtain surface normals! Thanks