RevSrf component not accepting vector as axis

I disagree with this definition.

It’s you against the rest of the universe. :wink:

// Rolf

Perhaps the rest of the Rhino universe :slight_smile:

I understand UnitVector like this:

In introductory physics textbooks, the standard basis vectors are often instead denoted {\displaystyle \mathbf {i} ,\mathbf {j} ,\mathbf {k} }athbf {i} ,athbf {j} ,athbf {k} (or {\displaystyle \mathbf {\hat {x}} ,\mathbf {\hat {y}} ,\mathbf {\hat {z}} }athbf {at {x}} ,athbf {at {y}} ,athbf {at {z}}, in which the hat symbol ^ typically denotes unit vectors).

This if from here (Euclidean vector - Wikipedia)

Basis Vectors (Unit Vectors) have starting point Oxyz and direction along the respective axis, as well as the magnitude of 1.

LOL, riddle me this then,

You cannot use unit vectors to define the axis for revolution, but when decomposing a plane you get a point and unit vectors :smiley:

image

It doesn’t make sense.

If unit vector is just a direction and no point, then vectors not starting from the same point cannot create just one plane, they can create infinite number of planes in the possible locations where two vectors’ origin points coincide, or are along the same infinite line (ray)

GH unit vector by it’s description is
image

Assuming it’s a direction and magnitude, no point, so in fact a collection of all vectors with that direction and magnitude. This is a vector field to me. Then it makes sense to not being suitable as axis for RevSrf.

The result of Plane decomposition, however, is described as “Axis Vector” so it has to have a direction according to the respective global axis, magnitude 1 and origin O, then why can’t I use this so called Axis Vector as input to RevSrf. It is not a UnitVector(Field) any more it has a starting point it’s an axis component.

image

Yes it makes sense, since a Plane has an Origin, which is a Point AND Vectors.

Two separate things combined (“bundled”) into a Plane.

So, a Plane is not a Vector.

A Plane only contains vectors, and a Point.

Therefore a Plane (not the Vectors) has a Location in space, whereas the individual Vectors doesn’t.

And this is always true for vectors, they don’t have a Location only a Direction (unless you “force” it to have a Location from “outside” the vector - like the Plane does - since the Vector cannot store a “starting point” in itself, but a Plane can, and a Line can too).

A Vector - by definition - is a Direction. Nothing else.

So a Plane can be Located in space (its Origin), and then Vectors gives the directions from that very Point.

So, again, “Direction only” is always true for vectors. No exceptions. Ever.

// Rolf Lampa

Illustrating vectors, directions, which can be “anyware in space” (because it doesn’t have a specific location constraining it). From Khan academy:

Ref: https://www.khanacademy.org/math/precalculus/vectors-precalc

1 Like

Although I think Rolf has made some very logical and clear points I also find this counter intuitive.

vector
ˈvɛktə/

MATHEMATICSPHYSICS

a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.

I think that when creating a vector from 2 points. Start and End, you should be able to use that as an axis, it makes no sense to requiere the extra step of generating a line. Even Rhino does not draw a line when performing those sort of operations (mirror, revolve, etc) unless in the background it is using a line and deleting it in the blink of an eye…

Not entirely, simply because one point and three vectors do not define just one plane, in the best case they define three planes.
If we have to be exact a decomposition of a plane should be one point and two vectors that lie on that plane, the third vector is a cross product of the other two.

Yes, a vector is an abstract term with meaning of direction, but it has a location in 3d space, along an infinite line that coincides with that vector. Assuming there is a defined point for that vector. Like in the case of Plane Decomposition. That means exactly one thing - that vector is a basis vector, a unit vector located exactly at the origin. It can be considered to be an axis, therefore, no reason for not being allowed when creating revolution, mirror, etc.

No. A vector, or better, multiple similar vectors can be anywhere in space. At the same time. An identical direction (vector) can exist in different places at the same time. Which is the very idea with a vector.

Which is demonstrated in the picture below. If you see more than two unique vectors (directions) you have a serious problem. Well, you do have a serious problem with vectors.

bild

// Rolf

not at all, I have a serious problem with unit vectors not being treated as basis vectors, respectively treated as axes and used in revolution, mirror etc.

Or of course the lack of a separate definition of axes or basis vectors, if unit vectors are to be treated as abstract directions.

For sure, plane decomposition should result in basis vectors, always.