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# Finding inner normal of an edge using C

Posted on 1998-05-28
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Hi,

How can we calculate the inner normal of a linear edge of a polygonal face ?
The data i have is some face data (its surface normal, face center and face boundary) and the vertices of the edge.
The vertices and other data are represented in the Cartesian form.
(only x,y coordinate is of the interest)

I have a routine to calculate the normal vector** to the edge, but no idea how to make sure it
is an inner normal.
** note: edge vector = <x1,y1>
normal vector = <-y1,x1>

thanks,
Sam
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Question by:kutaksama

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Expert Comment

ID: 1251039
What's an inner normal? I mean, AFAIK, a normal is a normal... there should be no concept of direction. Also, since you talk about a face normal, we should be in 3D, so why z-coord in not of interest?

-julio
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Expert Comment

ID: 1251040
How about just traversing the edges counterclockwise?
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Author Comment

ID: 1251041
I am working in a 3D geometric problem, but i reduce the problem into 2D when i just focus my attention to a planar face of a 3D object. This planar face is in the xy plane of the Cartesian space. That's why z-coordinate can be omited.
Inner normal mean a normal vector to the edge in the direction towards the region bounded by the face, instead of directing away from the face region.

-Sam
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Author Comment

ID: 1251042
Edited text of question
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Expert Comment

ID: 1251043
If the face is in the x-y plane, then the normal should be in the z direction, and your only problem is whether it is (0,0,1) or (0,0,-1) - is that correct?
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Accepted Solution

julio011597 earned 400 total points
ID: 1251044
Given the edge P1-P2 where:

P1(x1, y1);
P2(x2, y2);

The slope of the P1-P2 edge is:

m(P1,P2) = (y2 - y1) / (x2 - x1);

and the slope of *the* (ANY) normal is:

m'(P1,P2) = - (1 / m(P1,P2)) = - (x2 - x1) / (y2 - y1);

This is almost all you need to know of a normal... indeed there's a normal direction, not a normal vector.

Let's go a bit further. Now we want the normal straight line passing by the mid-point M of edge P1-P2.

M = M((x2 + x1) / 2, (y2 + y1) / 2);

so we need to work out our particular y=mx+q, by the following system:

{ m = m'(P1,P2) =  - (x2 - x1) / (y2 - y1);
{ (y2 + y1) / 2 = m (x2 + x1) / 2 + q;  (passage through M)

a couple of steps lead to:

{ m =  - (x2 - x1) / (y2 - y1);
{ q = (y2^2 - y1^2 + x2^2 - x1^2) / (2 (y2 - y1));

so the normal straight line to our edge, passing through M, is:

y =  - (x2 - x1) / (y2 - y1) x + (y2^2 - y1^2 + x2^2 - x1^2) / (2 (y2 - y1));

This is almost all analytic geometry has to tell about the problem.
Again, there's no concept of direction, that is, there's no concept of inner or outer normals.

I just wander if your final goal is actually related to analytic geometry...

-julio
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Expert Comment

ID: 1251045
BTW, i say:

> indeed there's a normal direction, not a normal vector

It is hard for me since i don't know the exact English terms, but there's a distinction between "direction" and "way" (orientation?) Geometry tells "direction" is just - to put it *very* simply - the slope of a straight line. A "way" instead means which way you walk the straight line towards, which brings the concept of inner/outer... but, again, analytical geometry does not deal with "ways".

-julio
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Expert Comment

ID: 1251046
So (sorry for so much comments), when i later say:

> Again, there's no concept of direction, that is, there's no concept of inner or outer normals.

i actually mean "there's no concept of way" (or "orientation"...).

Just to tell, we call them "direzione" and "verso".

-julio
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LVL 5

Expert Comment

ID: 1251047
...BTW, i've seen the question you previously posted.

Also, i can give a C code that given P1 and P2 coords, gives back m' or... whatever you're looking for :)

Third, i've seen the answer you refer to, but i cannot understand what it is about. That is, <x,y> is not an edge, unless it means <P1,P2>... and, if so, <P2,-P1> is not its normal, AFAIK.

-julio
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Expert Comment

ID: 1251048
kutaksama, did that help?

-julio
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