Hi, everyone.
Kinda noob question here but I’m having trouble figuring this out.
I have a triangle object that I need to rotate such that all points ends up having the same z values with respect to one of its points. Or in other words I keep one of its points fixed and pivot the other points around it till they have the same z value as the pivot point. For simplicity lets just say the triangle needs to end up with all of its z value equating to zero. I need to maintain the shape so I can’t project and deform the triangle.

My initial attempt:
//I’m pivoting about point2 so all point vectors have been sub(point2)
//For simplicity sake I made point1 and point3 have the same non zero Z value

triangle = new Triangle(point1, point2, point3);
normal = new Vector3();
triangle.getNormal(normal);

This doesn’t seem to work for me, the rotation axis is correct but the angle seems to be wrong. The resulting rotation does not end up with same z values.
In reality the triangle has random z valies, point1 and point3 don’t have the same Z so I need to do multiple rotations. Would appreciate it if someone can help with the full function for this.

You can use the points to define 2 edges… b-a and c-b… Then .cross those 2 vectors to get the face normal, and then… find the angle between 0,0,1 and that face normal. and then … construct a 3rd vector as the cross between 0,0,1 and the face normal… This vector is the axis, and the angle is
What we computed… and you construct a quaternion from that axis vector and the angle via quaterniom.fromAxisAngle… and .applyquaternion that rotation quaternion on each of the original points.

Isn’t that the same as the example function I provided?
Three.Triangle.getNormal(normal) //gets the face normal
rotationAxis = zPlane.cross(normal);
rotationAngle = Math.acos(zPlane.dot(normal));

And three.Vector3 has applyAxisAngle() which is more direct than creating a quaternion and applying that to the vector3. I assume its the same.

Here is an exceptionally ugly illustration of the idea - do not rotate the triangle, just recreate it by knowing point B, the lengths of AB and BC, and the angle at B:

I can use this method tho it seems it doesn’t preserve symmetry for symmetrical triangles
For example for the triangle
Vector3(-1,2,3) , Vector3(0,0,0), Vector3(1,2,3)
I would like the resultant triangle pivoting about (0,0,0) to be
Vector3(-1,0,0) , Vector3(0,0,0), Vector3(1,0,0)

Also wondering why the code I used didn’t work as intended.

I didn’t know there is an extra requirements like symmetry.

Also, most likely I misunderstand the issue, because I cannot imagine what rotation will transform triangle [(-1,2,3) , (0,0,0), (1,2,3)] into segment [(-1,0,0) , (0,0,0), (1,0,0)].

Yeah it worked. I didn’t think about having to normalize the axis.
Thanks a lot again. I will look into both solutions and see which is more appropriate.

You calculate the red angle. But the rotation must use the blue angle. The blue angle is the same as the green angle, which is 180°-red; thus the rotation should be 180°-red ( blue = π-red )

I didn’t notice yr code since it wasn’t in code markdown. Creating a quat is more efficient that recomputing axis/angle for each point. what you’re doing does look conceptually similar to what I described though. And if you’re doing this to align an object to the ground plane then you want the quaternion anyway… but it wasn’t clear from your post why you wanted to do this very specific sort of operation.
Any background on what the higher level goal is?

Thanks for the illustration. I did originally have the correct angle as you described, but since I didn’t normalize the axis it still gave me the wrong answer.

Yeah sorry. I’m new to all of this and my math is very basic. I saw examples where you create a quat and then apply the quat to the vector, but then I saw that vector3 has an applyaxisangle function which seemed more direct and less code. I assumed it was faster to do just that since it gave the same result anyway. I didn’t benchmark as its just a handful of triangles.

I get a bunch of triangles that are oriented randomly and goal was to just ensure the triangles I get are transformed such that they all have the same z value, with one point of the triangle acting as the pivot.

Oo i overlooked that bit of context about one of the points being the rotation origin. I guess you would want to subtract that point from the other points first, before applying this rotation, effectively making that point be 0,0,0, apply the rotation, then add that original point back to all of them.

r.e. making the quaternion being faster… creating a axis angle rotation does calls to Math.sin and Math.cos…

but once you have the quaternion, transforming a point by it is just a bunch of multiplies and adds/subs:

Honestly… its possible that the difference is negligible in your case, now that I look at the code.

Anyway… if you put the problem setup into a glitch of a codepen, i bet that would bait some users into solving it. these problems can be like catnip.

Had already subtracted the pivot point vectors. Simple oversight of not normalizing the axis gave me the error which PavelBoytchev pointed out. Thanks for the replies anyways.