Plane Normals

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.

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.

"TOP" wrote in news:1116207926.143748.178090 @f14g2000cwb.googlegroups.com:

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

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.

---------------------------- Mr. P.V.'d formerly Droll Troll

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.

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."

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:

"A scalar is a one-component quantity that is invariant under rotations of the coordinate system. "

"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."

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

Very true--but then they don't have a meaningful cross product, either.

Now yer axin me to solve the problem!! Don't you know the rules on Usenet, Cliff? We don't really *do* anything useful here, we just talk *about* doin sumpn useful... If you continue to violate the rules....

IIRC, a plane is actually defined by a normal vector to it, passing thru the cartesian origin. This in fact represents the minimum distance between the plane and the origin. So the question is in fact answered! This representation of a plane IS its normal, albeit at a very specific location. Again, std formulas, which should be in $37.... :)

There's other stuff you can do, I th>

IIRC, and indeed I may not, the D in your ax+by+cz+d=0 IS that perpendicular distance to origin!! Or proportional. So this line is not infinite in length. When you think about it, it makes sense, in that only ONE of these perpendiculars exist for a given plane. IOW, the point and vector you mention below, but a very specific point.

What happens is... I believe.... is that x, y, and z are *actually your direction cosines* cos alpha, cos beta, cos gamma.. Now, these three angles are *variables*, and vary such that any line from the origin *must* terminate somewhere on the plane, according to the constraining coefficients a, b, c, and.... d, the distance from the origin.

So a plane is not defined by all the lines (their infinity) *contained in the plane*, but rather by the single normal line connecting the plane to the origin, OR the *collection of lines* satisfying a cos alpha + b cos beta + c cos gamma + d = 0!

You might then ask, well, then what are the *specific* alpha, beta, gamma for the perpendicular line *itself*, going to the origin?? Good Q! Don't know!!!! I'll post to sci.math or sumpn.

True, but I think that "form" is the equation fer dat perp. line! I think...

And, I wouldn't bet the farm on the above, but it's sorta what has stuck around...

Which is why that particular normal, to the origin, defines, or can define, the plane.

Actually, no big deal, iffin you got a spreadsheet, and know the analytic form of the surface. In analogy, consider a crazy curve, a cubic, quartic, whatever. Jes take the derivative at the point of interest, which gives you the slope of the tangent line (m), and its perpendicular is then just -1/m! Done!

*Same goddamm thing* for surfaces and tangent planes/normals, ceptin more of a pita.

Ackshooly, I"m incapable of having fun, because I carry around a shoulder-stooping *angst* over whether or not hiphop and rap are going to make it on my easy-listenin music station any time soon...... If that happens, I think you'll be reading about me in yer local newspaper....

---------------------------- Mr. P.V.'d formerly Droll Troll

Dat's cuz those are "fake" surfaces.

If people used "real" surfaces, ie, like the planes you gave, or parts of spheres, ellipses, etc, which have clear unambiguous algebra "at their root" (couldn't resist), then you wouldn't even *need* a lot of this contouring stuff, which cranks out millions of bytes of data points. Instead, construct a 10-line macro for the analytic curves, blends, whatever, and bang, the machine itself does it, from le macro.

IOW, instead of a goddamm swoopy line from someone's creative innerfuknself, approximate that creation w/ blended portions of *analytic* curves, and bang, no digitizing, no contouring, no nurbs necessary.

Now, the machine itself will still have to increment along to make fashion the curve, w/ stepovers 'n' alladat, but *programming* part would be a whole lot simpler.

Well, I dint make a complete part yet, but enough chips done flew around, she might be happy....

Iffin I unnerstand nurbs correctly, nurbs is kinda cheatin--yeah, you wind up w/ analytic bits and pieces (fwiu), but not nearly as "neat" as if the analytic form had been there to begin with.

For example, sposin yer "mold" was a bowl, *exactly* hemispherical. But instead of inputting the algebraic form, you just scanned the picture, for the program to figger out.. Do you think the software would say, "Oh shit, I no need no stinkin nurbs'n'shit, they jes gave me a g-d hemisphere!" ??

Or would it grind and grind away, curve fittin&splicin, 'til it got what it thought was an acceptable approx. to the drawing?

I myself don't know--ahm jes askin. If the program could do this, then it's pretty hot!

If not, then it might behoove the designer to make geometries as algebraic/analytic as possible.