03/03/2020 - Parabolic Surface
In the 3rd of March class we started using AutoCAD to create 2D and 3D surfaces.
To be possible to create a Parabolic Revolution Surface it´s mandatory to draw, at first, a parabola.
And what is a Parabola?
Is a curved line, without a rigorous determination, usually the result from a plannar section in a cone, where the section plan has to be paralell to the cone geratrix.
It is mainly composed by an axis, a guideline, a focus and a vertex.
To start the parabola, we drew a vertical line, starting at the point of x,y coordinates 50, 50 and ending ate the point 50, 200. This vertical line will be the guideline of the parabola.
Then, we drew another line, perpendicular to the first one, from the point 50, 125 to the point 300, 125. This one will be the axis of the parabola.
On this second line, whit a distance of 50 units from the guideline, we marked the focus of the parabola.
And, between the guideline and the focus point, we marked the vertex of the future parabola.
The next step was to draw a line paralell to the guideline, with a distance of 30 units of the vertex point and a circunference with center in the focus point and with a radius of, also 30 units.
This 2 elements are essential to determine the first two points that give us the direction of the parabola.
The intersection of the circunference with the vertical line (on the image above) determine, with the vertex, the first 3 points of the parabola.
Then, with the Offset command, giving a distance of 10 units, we created 2 equidistant lines to the former ones.
After this, we had to repeat the previous step to determine all the points of the parabola.
The intersection of this lines is always the position of the next 2 points of our parabola.
We can see the points in the image above with red marks.
If we unite all the points in a sequential and consecutive way, we will be able to see our parabola determined.
To link all the points, we use the command Spline.
Now, with our parabola already drawn, we are finally able to create our Parabolic Surface.
The parabola axis will be used as the rotation axis of the parabolic surface.
For this, we will use the command RevSurf.
First we have to change our AutoCad model space to 3D.
The surface of our figure is constructed by a certain number of lines, called meridians and paralells.
For our Revolution Surface to be more round, we have to change the amount of lines. For that, we use the command Surftab 1 and Surftab 2 and change the amount number to 30.
Now, we activate the RevSurf command.
Then: - select the parabola line
- select the axis
- starts at 0º degrees
- ends at 360º
And, by following this steps, our Parabolic Surface is created.
If we want a better visualization of the surface, we can activate the command Shade. With this command, our surface gains volume and shade.
If we want to give our surface some thickness, all we have to do is an Offset to create an outer parabola to the previous one with a distance of 2 units.
And, after that, close this lines with 2 semi-circunferences.
Then, do, again, RevSurf to both parabolas.
Using a different axis, we can also create some different surfaces, like this one.
And this was our first class of 3D modeling.
To be possible to create a Parabolic Revolution Surface it´s mandatory to draw, at first, a parabola.
And what is a Parabola?
Is a curved line, without a rigorous determination, usually the result from a plannar section in a cone, where the section plan has to be paralell to the cone geratrix.
It is mainly composed by an axis, a guideline, a focus and a vertex.
To start the parabola, we drew a vertical line, starting at the point of x,y coordinates 50, 50 and ending ate the point 50, 200. This vertical line will be the guideline of the parabola.
Then, we drew another line, perpendicular to the first one, from the point 50, 125 to the point 300, 125. This one will be the axis of the parabola.
On this second line, whit a distance of 50 units from the guideline, we marked the focus of the parabola.
And, between the guideline and the focus point, we marked the vertex of the future parabola.
The next step was to draw a line paralell to the guideline, with a distance of 30 units of the vertex point and a circunference with center in the focus point and with a radius of, also 30 units.
This 2 elements are essential to determine the first two points that give us the direction of the parabola.
The intersection of the circunference with the vertical line (on the image above) determine, with the vertex, the first 3 points of the parabola.
Then, with the Offset command, giving a distance of 10 units, we created 2 equidistant lines to the former ones.
After this, we had to repeat the previous step to determine all the points of the parabola.
The intersection of this lines is always the position of the next 2 points of our parabola.
We can see the points in the image above with red marks.
If we unite all the points in a sequential and consecutive way, we will be able to see our parabola determined.
To link all the points, we use the command Spline.
Now, with our parabola already drawn, we are finally able to create our Parabolic Surface.
The parabola axis will be used as the rotation axis of the parabolic surface.
For this, we will use the command RevSurf.
First we have to change our AutoCad model space to 3D.
The surface of our figure is constructed by a certain number of lines, called meridians and paralells.
For our Revolution Surface to be more round, we have to change the amount of lines. For that, we use the command Surftab 1 and Surftab 2 and change the amount number to 30.
Now, we activate the RevSurf command.
Then: - select the parabola line
- select the axis
- starts at 0º degrees
- ends at 360º
And, by following this steps, our Parabolic Surface is created.
If we want a better visualization of the surface, we can activate the command Shade. With this command, our surface gains volume and shade.
If we want to give our surface some thickness, all we have to do is an Offset to create an outer parabola to the previous one with a distance of 2 units.
And, after that, close this lines with 2 semi-circunferences.
Then, do, again, RevSurf to both parabolas.
Using a different axis, we can also create some different surfaces, like this one.
And this was our first class of 3D modeling.
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