Plane Normals

You know when you make a change to something before a sketch and the sketch
completely flips to its mirrored position? Or maybe an extrude or a cut
just changes directions? I just ran into this and was able to figure out
what's going on.

The change I made was to change the value of a sketch fillet. It didn't
cause any sketch errors, change the number of edges, vertices or faces, it
was just a size change. A plane was defined based on this face (3 pt
plane), and it lost one of its references. When I reselected the
reference, the sketch that was on it flipped position. Obviously a plane
normal problem, but SW gives you no control over the plane normal.

It turns out that the solution was to go back into the feature and reselect
the vertices in the original order. So with a 3 pt plane, the order in
which you pick the vertices determines the plane normal direction, and if
you reselect the vertices without paying attention, you may flip your plane
and everything dependent on it.

This would be a good thing if there was some way for users to know about
the functionality. Maybe a reorder button in the dialog like in the loft
section dialog? Maybe something in the help that says that's how it works?
Maybe an indicator and a switch to help the user understand the
significance of and how to control plane normals?

Anyway, I know I sometimes lose a lot of work when I'm not willing to stop
and figure out why things like that happen. Just thought I'd pass on that
info.

matt

 

One of the things SW could stand to do as well as Pro/E: control of
plane and sketchorientation.

 

Thanks for the heads-up, Matt

I've struck this occasionally and never got to the bottom of it.

Quite agree about the frustrations of not being able to specify or lock down
the plane normal direction

Sometimes "dumbing down" the toolset makes things harder rather than easier.

 

Thanks for the heads-up, Matt

I've struck this occasionally and never got to the bottom of it.

Quite agree about the frustrations of not being able to specify or lock down
the plane normal direction

Sometimes "dumbing down" the toolset makes things harder rather than easier.

 

So is it right hand rule or left hand rule.


If picking in clockwise order orients the Z axis pointing out of the
screen it is righthand rule.

 

I did some experiments with planes defined normal to a curve. Got
control over plane normal while reorienting defining geometry past 180
degrees, but still flippy w.r.t. sketch horizontal definition.

 

For a 3 pt plane it's right hand rule.

For a line and a point, it seems to try to align itself with the X, Y or Z
positive direction.

A couple years ago I posted the bit about moving a sketch from one plane or
face to another perpendicular plane or face and then back flips the
directon the sketch will extrude. Not that it's really useful, it's just
interesting.

matt

 

Thanks Matt. I never took the time to figure out why it did that.


Rocky


www.dzynsource.com

 

The crossproduct of any two non-colinear vectors
*on a plane* is a vector normal to it.

(Beware vectors that are not on the same plane as
you will get a different result ... best that they have
a point in common).

Each plane can have two such vectors, in opposite
directions, depending on the order of the crossproduct
of the vectors IIRC. A*B <> B*A. Both are valid normals.

Any three non-colinear points can define two
such vectors.

http://mathworld.wolfram.com/CrossProduct.html

I don't know if that helps any ....

 

Co linear vectors don't have a cross product! ie, zero by def.

Best that they have a plane in common!!

But ackshooly, iffin the program is doin it's job, "planarity" (ie, a
convenient xyz type plane) shouldn't matter. Alls you need are the
"direction cosines" for each line (vector), and the direction cosines of the
cross product just pop right out--of the right formula, of course. A decent
program should spit these out automatically.

If said program is not giving you direction cosines (and you need them), you
can do it quite expediently in a spread sheet. W/ the three direction
cosines, you can actually visualize the line in space, w/ a little
familiarity.
Ackshooly, you could have the spread sheet graph it as well!
Jes in case you have suspicions of the resultant vectors in yer $37,000
Saladworks package.

Ackshooly, the cross product is written A X B ( = -B X A). The algebraic
sign can be very important--esp. on final exams!

An asterisk is perilously close to a dot, which represents, well, the "dot"
product.
Ito *magnitudes*, the cross product is simply ABsin angle
The dot product is ABcos angle; included angle.
Which are other thumbnail "checks" of yer program. IOW, the *maximum*
length of *either* the cross or dot product is the straight multiplication
of original vector lengths. (sin, cos =1)

or a plane!

The cross product is in fact the quantity called "torque", if said vectors
are a distance and a force.
The direction of the torque vector follows the "right-hand screw rule" which
is the translation of a rh screw as you twist it.
In fact, I can't think of any *mechanical quantity* that is a cross product,
other than torque! Some shit in E&M uses cross products.

 

Ackshooly, there are some wild-assed cross products in some angular
momentum/moments of inertia problems, but they almost don't count.

 

I did a lot of automotive "in-car position" modeling on my last job. I
quickly got away from using horizontal and vertical constraints in 2D
sketches.

Instead of using sketch horizontal and vertical, I created base axes
for my working X, Y, and Z. Each sketch would have two base
construction lines to form a "working CSYS" constrained
parallel/perpendicular/angle to those axes. Subsequent sketch elements
were constrained parallel/perpendicular/etc. w.r.t. the working CSYS
curves.

A bit cumbersome at first, but it became habit quickly. Saved a lot of
time in the long run. Sketches were more robust and weathered
frame-of-reference changes better. Also makes it easier to relocate
entire sketches.

 

Usually with a unit vector as a surface normal for the correct
projection values.

True, but BB's a fish <G>. He'd want to know what "X" is.
And I have problems showing the dot in ASCII.
Hence the explicit "crossproduct" mention.

The area subsumed by the vectors if they both start at the
same point is equal to it's magnitude.

Don't forget that these vectors are 3D so using trig & computing
unit vectors & transforms first is the hard way indeed.

You don't have to have unit length vectors to start with
to find a normal.

Which is what they want the normal to.

 

There is no reason to state the "on a plane" or "point in common"
since any two arbitrary vectors can be resolved into "coplanar"
component vectors and the cross products of those vectors can be
computed.

To quote the site you listed above:

"Since vectors remain unchanged under translation, it is often
convenient to consider the tail A as located at the origin when, for
example, defining vector addition and scalar multiplication."
http://mathworld.wolfram.com/Vector.html


The cross product of any two vectors is a vector normal to the plane
defined by those vectors.

Consider a vector F and any point O in space. If we draw a vector R
from O to any point on F or on the line of action of F then R x F is a
moment vector M about O perpendicular to the plane containing R and F.

Thus M = R x F = (FR sin theta)1

The moment vector will be independent of where R terminates on F or on
its line of action.


Also, in response to your assertion that mass is a vector:

http://mathworld.wolfram.com/Scalar.html
"A scalar is a one-component quantity that is invariant under
rotations of the coordinate system. "

http://en.wikipedia.org/wiki/Vector_(spatial)
"Vectors can be contrasted with scalar quantities such as distance,
speed, energy, time, temperature, charge, power, work, and mass, which
have magnitude, but no direction (they are invariant under coordinate
rotations). The magnitude of any vector is a scalar."

 

True, any two vectors determine a plane, but if the plane formed by the
vectors is other than cartesian, yer direction cosines are not as simple.
But if you want "real" direction numbers rel to the cartesian coord system,
then it proly is best to leave the vectors as is, and deal w/ the result as
is.
But indeed no big deal.
All solvable in sed spreadsheet...

 

If they are not coplanar I think that the result is called a couple
<G>.

We are speaking of 3D CAD systems too .....

"*Might* be considered" .... do YOU have a good GUT handy?

That's a bit open .... I can, as an example, rotate something
about the X axis unit vector .... does that make the X axis unit
vector a scalar?

Not quite the subject ...
I'm beginning to dislike Wickipedia and those that rely on it.
In 4-space & much of Physics, time is a vector.

 

Oh yeah, I dint catch the beginning of the thread, but iffin alls you need
is normals to a plane, you no need no stinkin cross product!

Planes have equations, like lines, and perpendiculars to the plane (normal
unit vectors) are just simple ops on that equation, sorta like a line w/
slope m, whose perpendicular is -1/m.
Fergot the details fer planes, but it's a similar deal, found in most solid
geometry/calculus texts.
Or so I think....

But $37,000 saladworks should have *alladis*, and then some.
Saladworks should give goddamm *lap dances*.... at least...

 

correct me if I'm wrong, but my recollection from math class is that two
vectors form a plane if and only if they cross at some point... non
crossing vectors in 3d do not define a plane

 

(0,0,0) ==> (1,1,1)
(1,.5,3) ==> (1,.5,.5)

??

 

A*X+B*Y+C*Z+D=0 would be the general form for a plane.
Now, about a 3D line ....