How to Visualize 3D Surfaces for a PVT Diagram

In summary, the conversation discusses the steps to fold a piece of paper in half both long ways and short ways, as well as how to visualize a 3D PVT diagram. The visualization can be achieved by drawing traces of the given surface in the coordinate-planes and setting z=0 in the xy-plane to get 2x+2y=6.
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benorin
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How to visualize 3-d surfaces in a test friendly manor
1. Fold in half the long way
8C3B63F5-0397-4C14-B408-AF0C7B8C5B47.jpeg

2. Fold in half the short way

53BE26D0-C33C-4FEE-86DD-29C59E96FA10.jpeg

3. Unfold paper, grasping the left side horizontal crease, bend the paper as shown by making the left crease flush with the bottom vertical crease and crease along the -45 degree bend (not shown)

46A766D2-4969-4B6C-A39C-9150D956FC83.jpeg


4. This is the visualization for the plane
2x+2y+z=6, made by drawing traces of the given surface in the coordinate-planes. For example, in the xy-plane set z=0 to get 2x+2y=6.
DFD72ACE-D5AC-4430-A283-778E68A88464.jpeg
 
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  • #2
Vague question. What are you looking for?
 
  • #3
mathman said:
Vague question. What are you looking for?
It’s a how to post, not a question
 
  • #4

1. What is the purpose of visualizing 3-d surfaces in science?

Visualizing 3-d surfaces allows scientists to better understand complex data and relationships between variables. It also helps in identifying patterns and trends that may not be apparent in 2-dimensional representations.

2. What tools or software can be used to visualize 3-d surfaces?

There are various tools and software available for visualizing 3-d surfaces, such as MATLAB, Python, and R. There are also specialized software specifically designed for 3-d surface visualization, such as ParaView and VisIt.

3. How do you interpret a 3-d surface plot?

A 3-d surface plot typically shows the relationship between three variables, with the x and y axes representing the two independent variables and the z-axis representing the dependent variable. The height or color of the surface indicates the value of the dependent variable at a particular combination of the independent variables.

4. What are some common challenges when visualizing 3-d surfaces?

Some common challenges when visualizing 3-d surfaces include choosing the appropriate visualization technique, selecting the right variables to plot, and dealing with large datasets that may slow down the rendering process. It is also important to properly scale and label the axes to accurately interpret the plot.

5. Can 3-d surface visualization be used for any type of data?

Yes, 3-d surface visualization can be used for a wide range of data, including scientific, engineering, and financial data. However, it is most effective when visualizing continuous data with three or more variables. Categorical data can also be visualized using techniques such as stacked bar charts or parallel coordinates plots.

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