I have a couple of plugins where I create either an arc or a circle to use as a path, collect the vertices, and then abort the operation…
it’s fine when only needed once, but I now only need three points, recalculated many times,
given points A, B, what is the best formula to find C and D?
I also know the distance between C, B, D…
A and B could be anywhere in 3D space…
john
My first thoughts…
clone pointB as pointC
make a rotation transformation [tr] about pointA using the Z_AXIS and the desired angle
pointC.transform!(tr)
repeat for pointD with a negative rotation angle.
If you want an ‘offset’ dimension rather than an angle, you can get the flat-radius using Pythag.
Using the flat-radius and desired ‘offset’ you can get the angle for the transformation rotation, OR calculate the new point directly…
Although you could try some basic 2D trigonometry, I would recommend using 3D transformations instead. Point A can be projected onto the X-Y plane as point E. Since it is the main X-Y plane through the origin, its coordinates would be <A.x, B.y, and zero>. Given A and B as Point3d variables “point_A” and “point_B”, expanding upon what @TIG said:
point_E = Geom::Point3d.new( point_A.x, point_A.y, 0.0)
angle = 360.0 / 24.0
rotation_EZ = Geom::Transformation.rotation( point_E, Z_AXIS, angle.degrees)
point_C = point_B.transform( rotation_EZ )
point_D = point_B.transform( rotation_EZ.inverse )
I don’t know how to determine the angle from the default circle segment, but I hard coded it to 360/24. You will want to come up with your own value.
@BruceYoung
I don’t think you need to project point_A onto the ground.
So then you don’t need point_E, because the rotation is around a vector [Z_AXIS] and any point sets the rotation’s transformation around itself using that vector - so point_A works fine as it is.
Otherwise your code is fine…
Since the OP didn’t specify the actual angle through which to rotate the new two points [or how else we might determine the two points’ locations], your idea to take the default circle segmentation at 360/24.0 seems OK for now…
But if the ‘offset’ of the points is a fixed distance from point_B then your earlier approach to project point_A onto the ‘ground’ could be adjusted to take account of point_B’s z value:
point_E = Geom::Point3d.new( point_A.x, point_A.y, point_B.z)
Then the radius of the ‘circle of rotation’ is:
radius = point_E.distance(point_B)
That can then be used to calculate a perpendicular offset from point_B for point_C & D
cheers both for the input…
I did use rotation of the cloned point in the end…
the segment length is a variable that I calculate based on the view and model widths…
angle = (360/segments).degrees rescue 1.degrees
also as it may not be at z == 0 I used [point_A.x, point_A,y, point_B.z] as my second point for the radius…
I also needed to calculate the vector as Z_axis failed in some scenario’s…
I’ll add a gif when I advance it a bit more…
john
You also do not need the flattened point_E in this scenario as Array has been extended with an API #distance method.
radius = [ point_A.x, point_A.y, point_B.z ].distance(point_B)
For the angles, this is simple trigo geometry. If dBC and dBD are equal, you can use the transformation to build the whole arc.
#Given <ptA>, <ptB> and the chord distances <dBC> and <dBD>
normal = Z_AXIS
center = ptA.project_to_plane([ptB, normal])
radius = center.distance(ptB)
angleBC = 2 * Math.asin(0.5 * dBC / radius) #isocele triangle
angleBD = 2 * Math.asin(0.5 * dBD / radius) #isocele triangle
ptC = Geom::Transformation.rotation(center, normal, angleBC) * ptB
ptD = Geom::Transformation.rotation(center, normal, -angleBD) * ptB