17/03/2020 - Cone and Sections

On this class we learnt how to:

- draw a Cone
- mirror the Cone to reverse
- create Section Plans
- draw Sections on the Cones using the Section Plans

First, we drew a cone which center is located at the x,y coordinates 30, 30, with 10 units of radius and 10 units of height.

The cone that we just created is solid, and we want it to be empty, having just some thickness.

For that, we copied the previous cone down with a tiny distance of 1 unit.

After that, we use Boolean Operations.

There are 3:

- Union, that joins both cones into one piece;
- Intersect, to create an inbetween solid created by the intersection of both cones;
- Subtract, to subtract the space ocuppied by one cone on the other.

For the purpose that we want, we used the Subtract operation.

Then, we mirrored the cone adding one more above the previous one. For that, we use the command 3DMirror.

To be easier to distinguish all the shapes and figures that we are going to create, we use 3 layers, a cyan one for the cone, a yellow one with 45 units of transparency for the section plans and a red one for the sections.

The next step we did was to create 4 different Section Plans:

- 2 perpendicular to the base of the cone;
- 1 to create an elliptical shape, oblique to the cones;
- 1 to create a parabolic shape, paralell to the base;
- 1 to create a hiperbolic shape, also oblique to the cones.

To draw the plans, we draw a rectangular polyline (Pline) paralell to the base and use a half-transparent hatch. Then Copy this plan 3 more times.

Then Move all the plans to the base of the cone.

To rotate all the different plans to different angles, we have to use two types of Rotation, since we are on the 3D model space.

The first one is to create one of the oblique plans, with a 30º angle. For that, we use the 3DRotation using the green axis.

For the second oblique one (45º angle) and the perpendicular, we use the Rotate3D.

Then Copy the perpendicular plan to the center of the cone and Move the paralell plan a bit upper.

Now, to create all the Sections we use the command Section.

Selecting both cones and 3 points of the plan we wish to cut the solids, we create the corresponding sections, now in red.

Then we separate the cones from the plans and sections.

And consecutively, until we have everything separated.

And what if we want to create a Revolution Surface from one of this Sections?

We have to explode the section, just because AutoCad doesn't allow us to RevSurf sections.

And this was the 17th of March class.