// Michael, this is a Request for information on coordinate frame, and how are coordinates
// converted back and forth with the "world coordinate frame?"

var vM = moi.vectorMath;

// P1 is a point in world coordinates, which is to be the temporary origin in coordinate frame.
// P2 to be a suitable point for creating the frame x axis.
// P3 to be a suitable point for creating the frame y axis.
// The next 4 lines are correct, from Mirror script:
var FrameOrigin = vM.createPoint(P1.x, P1.y, P1.z);
var FrameXAxis = vM.createPoint(P2.x, P2.y, P2.z);
var FrameYAxis = vM.createPoint(P3.x, P3.y, P3.z);
var catFrame = vM.createFrame( FrameOrigin, FrameXAxis, FrameYAxis );


// The first question is, given points P4 and P5, in world coordinates, will the
// following code create points Pt4 and Pt5 in catFrame coordinates?

var Pt4 = moi.coordinateFrame.evaluate.catFrame(P4.x, P4.y, P4.z);
var Pt5 = moi.coordinateFrame.evaluate.catFrame(P5.x, P5.y, P5.z;)


// The second question is, having calculated point Pt6, the vertex of parametric catenary
// curve between Pt4 and Pt5, using cosh, which I already know how to do,
// will the following code convert point Pt6 back into world coordinates?


var x = moi.coodinateFrame.distancex(catFrame.Pt6);
var y = moi.coodinateFrame.distancey(catFrame.Pt6);
var z = moi.coodinateFrame.distancez(catFrame.Pt6);
var vertexPt6 = vM.createPoint( x, y, z );

// (next, point vertexPt6 will then become the new origin in a new coordinate frame...)

Thank you.

Hi Brian,

> // P1 is a point in world coordinates, which is to be the temporary origin in coordinate frame.
> // P2 to be a suitable point for creating the frame x axis.
> // P3 to be a suitable point for creating the frame y axis.
> // The next 4 lines are correct, from Mirror script:
> var FrameOrigin = vM.createPoint(P1.x, P1.y, P1.z);
> var FrameXAxis = vM.createPoint(P2.x, P2.y, P2.z);
> var FrameYAxis = vM.createPoint(P3.x, P3.y, P3.z);
> var catFrame = vM.createFrame( FrameOrigin, FrameXAxis, FrameYAxis );

Which one is the "Mirror script" ?

One note is that here P2 and P3 should actually be vectors - meaning that they represent an oriented direction and not a point location.

The way a coordinate frame works is that there is one point for its origin and then 3 vector directions for x, y, and z axes. Often you'll just give it the x and y axis directions because the z axis can be calculated from those automatically by doing a cross product.


> // The first question is, given points P4 and P5, in world coordinates, will the
> // following code create points Pt4 and Pt5 in catFrame coordinates?
>
> var Pt4 = moi.coordinateFrame.evaluate.catFrame(P4.x, P4.y, P4.z);
> var Pt5 = moi.coordinateFrame.evaluate.catFrame(P5.x, P5.y, P5.z;)

The syntax here does not quite look correct - there isn't any coordinateFrame member function off of the root moi object, so doing: moi.coordinateFrame isn't going to do anything. I think you want to call something on catFrame directly, so more like: catFrame.evaluate( x, y, z );

But the .evaluate() method on a coordinate frame is for taking an x,y,z point that is in that coordinate system and converting into a world coordinate point. It basically starts at the frame's origin, then goes along the x axis direction of the frame by the x value that you pass in, and then the same for y and z values. So if for example you passed in just evaluate(0,0,0) that would give you back just the origin point. if you passed evalute(1,0,0) that would give back a point that was 1 unit away from the frame's origin in the x axis direction.


If you want to go the reverse way of getting a world coordinate point in terms of the frame's coordinate system then you would want to use the distance methods, you can do this:

var x = frame.distancex( pt );
var y = frame.distancey( pt );
var z = frame.distancez( pt );

And then that x,y,z point will be a point in that local coordinate system. Each of those calls returns the distance that the passed in point is located at along each frame axis direction, basically a plane that is formed from the origin point and the axis direction.



> // The second question is, having calculated point Pt6, the vertex of parametric catenary
> // curve between Pt4 and Pt5, using cosh, which I already know how to do,
> // will the following code convert point Pt6 back into world coordinates?
>
>
> var x = moi.coodinateFrame.distancex(catFrame.Pt6);
> var y = moi.coodinateFrame.distancey(catFrame.Pt6);
> var z = moi.coodinateFrame.distancez(catFrame.Pt6);
> var vertexPt6 = vM.createPoint( x, y, z );


So if I understand properly, you've got the reverse thing for this part - if you have an x,y,z that is in the local coordinate system of the frame, use the .evaluate() method on the frame to convert to a world coordinate value.

Hope this helps, please let me know if it does not make sense.

- Michael

Thank you very much Michael, for your response.
It is very understandable, and useable. :-)

(The mirror script is the official moi script in its command subdirectory.)
So the x-axis and y-axis direction vectors used to create the new frame would be (or could be) in world coordinate frame.
A new y-axis, parallel to the world coordinate y-axis would have the same vector direction, (0,1,0).
The new x-axis vector direction can be calculated from the two points, mathematically, or with vectorMath...

Hi Brian,

> So the x-axis and y-axis direction vectors used to create the
> new frame would be (or could be) in world coordinate frame.

Yup, normally those direction vectors are in world coordinates. The origin is also in world coordinates - the whole package of data gives the position and orientation of the frame's coordinate system.


> A new y-axis, parallel to the world coordinate y-axis would
> have the same vector direction, (0,1,0).

Yup that's correct.


> The new x-axis vector direction can be calculated from
> the two points, mathematically, or with vectorMath...

Yup, but the x-axis vector should be one that is at a 90 degree angle to the y axis vector. But it can be pivoted around the x-axis, like for example here in red are different possible x-axis lines that would work with the given green y axis:



- Michael

Thank you Michael.
Should have enough now to finish a catenary curve script hanging from two points in 3D, even with different z values, with
gravity in the -y direction. There is plenty of code on the internet.
Yes, the new x-axis "rotates" about the new y-axis, to "zero out" the z values.

Just figured out that a minus sign "-" is not the same as a dash "–".

So cut and paste of formulas with dashes for minus signs, from Microsoft Word to Notepad++, creates parse errors in javascript.