Calculate the 2d height of the rectangle

• primalvisions
In summary, the speaker is trying to calculate the 2D height of a rectangle rotated in 3D on multiple axes. They are having trouble when rotating on the y-axis and ask for help in calculating the total height from the bottom left corner to the top right corner. The object is for an orthographic view and the speaker defines height as the distance projected back onto the x-y plane. They also mention that the axes of rotation are perpendicular and provide a mathematical solution for calculating the height.
primalvisions
I have a rectangle i am rotating in 3d on multiple axis. i am trying to calculate the 2d height of the rectangle and I am quite lost.

For example, if i rotate the rectangle on the x-axis so the top of the rectangle comes forward and the bottom moves back. i can calculate the height of this fine.

But then i rotate it on the y-axis so the left of the rect moves to the right and the right hand side moves left.

Whats the total height from the bottom left corner to the top right corner extent when rotated on 2 axis?

Its for an orthographic view of the object where you show the front, top and side views of the 3d object.

Any clue how i can calculate this?

Cheers =)

Can you give it a better description as to where the rectangle is (centered on the x-y plane is what it sounds like)? And what is your definition of height here? You mean the distance when you project the rotated rectangle back onto x-y plane? Or the distance when projected onto the z-axis?

yes it is centered on the x-y plane and yes the height when projected back onto the x-y plane.

the total distance from the bottom to the top in a 2d view when rotated in 3d about the x-axis then the y-axis.

=)

Fortunately the axes of rotation are perpendicular, so you have an easy time doing this.

If you start off with a point at (x,y,0) and you rotate about the x-axis by an angle t, the new point you get is

(x,ycos(t),ysin(t)).

Since you know the x coordinate of the point is unchanged, you can see this by just considering the rotation of the point (y,0) in the y-z plane around the origin by an angle of t)

Now for a caveat. When I decided I was going around by an angle t, that's the angle you see when you look at the y-z plane such that y is horizontal, and z is the vertical axis (which is how you defined it).

Next we look at the x-z axis. The point (x,ysin(t)) is rotated by an angle of r - we omit the y coordinate since it's fixed when rotating about the y axis. Now we hit a problem here, since the left of the rectangle moves to the right regardless of which direction you rotate it in. I'll assume the left of the rectangle is being rotated upwards, if it's moving down just use -r here. Then the new point is
(xcos(r)-ysin(t)cos(r),ysin(t)sin(r) + xsin(r)). so going back into three dimensions we get

(xcos(r)-ysin(t)cos(r),ycos(t),ysin(t)sin(r)+xsin(r))

What is a 2d height of a rectangle?

A 2d height of a rectangle refers to the distance between the top and bottom sides of the rectangle when viewed on a flat, two-dimensional plane.

How do you calculate the 2d height of a rectangle?

The formula for calculating the 2d height of a rectangle is: height = length x width. This means you need to multiply the length of one side of the rectangle by the width of the other side.

Can the 2d height of a rectangle be negative?

No, the 2d height of a rectangle cannot be negative. It is a physical measurement and cannot have a negative value.

What units are used to measure the 2d height of a rectangle?

The 2d height of a rectangle can be measured in any unit of length, such as inches, feet, meters, or centimeters.

Can the 2d height of a rectangle be calculated if only the perimeter is known?

No, the 2d height of a rectangle cannot be calculated if only the perimeter is known. The perimeter is the sum of all four sides and does not provide enough information to determine the individual side lengths.

Replies
8
Views
5K
Replies
25
Views
864
Replies
5
Views
5K
Replies
1
Views
2K
Replies
20
Views
3K
Replies
4
Views
1K
Replies
7
Views
2K
Replies
4
Views
866
Replies
1
Views
2K
Replies
1
Views
1K