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Ruled surfaces: cloak

We have already shown three-dimensional surfaces twice, so this time we will show some special examples: Ruled surfaces. There are not too many rules for this kind of surface. We only need to find two arbitrary curves, whatever they look like, and then connect them to get a surface. Sometimes it may feel like seeing their surfaces directly. No, but if you look for it carefully, you can find that the entire surface is composed of straight lines.

Ruled surfaces can often be seen in life. Because of its particularity, it makes it look a little "artistic". If you are good at observing, you may find that some strange sculptures are part of it. There are many common examples, such as a water cup, which can be seen as a circle on the top and bottom, and then connected to the line. Or the very classic DNA spiral also belongs to the figure formed by clicking straight lines between two curves.
This looks amazing, but we can still find the straight line easily. Then I hope that the two curves are not the same type. For example, one is closed, and the other is just a section of the curve. What would it look like?

Since it is a curve, the cos function will reflect its value very well. We select an interval (0, 2pi) of it so that we have to display the part that will repeat itself, and then translate its position, and then position A little further down, we can get an edge.
Well, it looks good. Let's choose another curve. Since it is a closed curve, the most common one is a circle, and it is also very easy to express. However, when I made the figure, I always felt that something was lacking, that is, since it is a three-dimensional figure, then our curve should also involve the third unknown, then we will take its position on the basis of a circle. Change, change the height of the entire garden in the air to cos (x^2). In this case, this (park) seems to have some ripples.
Aha, then the next step is elementary. we use a straight line to connect the two curves together and then make some height and position adjustments. In this way, we can get the ruled surfaces we want.
It looks good, although I want the lower part of the cloak to belong to a three-dimensional curve, then I set its height-cosx so that it is more like a cloak!
After the final adjustment, the equation of the upper curve and the equation of the lower curve are
Overall, it will look more attractive because, in order to make a cloak-like model, the two curves are located far away, so the curves can be clearly seen (of course, if you use curved surfaces to link the two curves, they are still not easy to find that straight lines connect them) The more special place is at the position of the two sides. Its surface looks the most confusing, and it is also the place that best reflects the special features of Ruled surfaces. One last mention: the size of it is: x=37.4, y=11, z=32.86

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