Looking for tips on sketching of 3-d graphs?

In summary, the speaker is seeking tips for drawing 3-D graphs accurately in multi-variable calculus. One suggestion is to use "level curves" and draw cross sections in the coordinate planes for different values of the variables. The speaker also mentions a method called the trace method, where one substitutes values for the variables to create 2-D graphs that can be combined to form a complete 3-D graph.
  • #1
maximf
5
0
basically I'm in the last 2 chapters of multi variable calculus (right now in double integrals) and i know how important it is in some exercises to sketch the 3-d graphs accuratley. However all the 3-d graphs that I'm trying to sketch are very off... even a simple shape like a cylinder looks bad.

anyway are there any tips for manual sketching that might help me graph the functions little more accuratley?
 
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  • #2
Drawing "level curves" should help. One thing I like to do is draw cross sections in the coordinate planes: if x= 0, what is the graph in the yz-plane? If y= 0, what is the graph in the xz-plane? If z= 0, what is the graph in the xy-plane? The imagine those graphs place on the coordinate axes.
 
  • #3
how do you properly draw the coordinate axes? what i do is sketch one vertical that will be Z and one horizontal that will be Y. and the X axis i draw diagonally through the squares (i use math paper obviously...)
 
  • #4
HallsofIvy said:
Drawing "level curves" should help. One thing I like to do is draw cross sections in the coordinate planes: if x= 0, what is the graph in the yz-plane? If y= 0, what is the graph in the xz-plane? If z= 0, what is the graph in the xy-plane? The imagine those graphs place on the coordinate axes.

Yes. This is probably the best way to do it. Just substitute different values for the individual variables in the equation. This will give you the 2d graph created with the remaining variables on the plane perpendicular to the point at which you have substituted. Just do this a few times for all of the different variables and you will be able to shade in a complete 3d graph.

My teachers call it the trace method.
 

Related to Looking for tips on sketching of 3-d graphs?

1. How do I start sketching a 3-D graph?

To start sketching a 3-D graph, you will need to have a clear understanding of the equations or data that you want to represent. Begin by plotting the x, y, and z axes and then plot the points for each data point or equation. From there, you can connect the points to create the 3-D graph.

2. What are the key elements to consider when sketching a 3-D graph?

The key elements to consider when sketching a 3-D graph include the axes, labels, scale, and data points or equations. It is important to accurately plot the axes and label them appropriately to provide context for the graph. The scale should also be carefully chosen to accurately represent the data. Additionally, pay attention to the data points or equations and ensure they are accurately represented in the graph.

3. Are there any helpful tips for improving the visual appeal of a 3-D graph?

Yes, there are several tips for improving the visual appeal of a 3-D graph. One tip is to use different colors or textures to represent different data sets or equations. This can make the graph more visually appealing and easier to interpret. Additionally, you can adjust the perspective of the graph to provide a more interesting view. Lastly, make sure to use a clear and legible font for labels and titles.

4. How can I accurately represent curved surfaces in a 3-D graph?

To accurately represent curved surfaces in a 3-D graph, you can use a technique called meshing. This involves breaking the curved surface into smaller, more manageable segments and plotting them individually. You can also use a computer program or software to help with this process.

5. What are some common mistakes to avoid when sketching a 3-D graph?

Some common mistakes to avoid when sketching a 3-D graph include mislabeling axes, inaccurately plotting points, and using an incorrect scale. It is also important to pay attention to the perspective of the graph and make sure it accurately represents the data. Additionally, avoid cluttering the graph with too many data points or equations, as this can make it difficult to interpret.

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