Strategies for drawing space curves?

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SUMMARY

This discussion focuses on effective strategies for drawing and conceptualizing space curves, particularly in the context of Geometry and Calculus courses. Key techniques include starting with an origin point and defining axes for x, y, and z coordinates. The conversation also highlights the importance of using guidelines in axis planes to represent three-dimensional points. Helpful video resources for visual learners are provided, including links to YouTube tutorials that demonstrate these concepts.

PREREQUISITES
  • Understanding of three-dimensional coordinate systems
  • Familiarity with vector functions, specifically r(t) =
  • Basic knowledge of Geometry and Calculus concepts
  • Experience with drawing tools such as Maple or Mathematica
NEXT STEPS
  • Explore advanced techniques for plotting vector curves in Mathematica
  • Learn about the application of parametric equations in space curves
  • Investigate perspective drawing methods applicable to three-dimensional shapes
  • Watch additional tutorials on YouTube focusing on space curves and vector functions
USEFUL FOR

This discussion is beneficial for students in Geometry and Calculus courses, educators teaching these subjects, and anyone interested in mastering the visualization of space curves and vector functions.

vanceEE
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What are some helpful strategies for drawing and conceptualizing space curves? I'm having trouble drawing them and I'm not very artistic! Also, please provide helpful videos on this topic if you can.
Thanks.
 
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Programming, maple, mathematica, stuff like that.
 
vanceEE said:
What are some helpful strategies for drawing and conceptualizing space curves? I'm having trouble drawing them and I'm not very artistic! Also, please provide helpful videos on this topic if you can.
Thanks.

Drawing these manually is supposed to be part of instruction. This will/must/should occur in Geometry and in Calculus 2 and Calculus 3. This is much like perspective drawing, but without forming Vanishing Points.(Maybe the response is inadequate. Difficult to describe through writing on the forum how to do these drawings).If it helps, start with an origin point, draw an axis upward called z, draw an axis to the right called y, draw an axis diagonally downward toward the left and call it x... not sure if these are right since so long ago that I did these. You can represent three-D points and using drawn guidelines in the axis planes.
 
Last edited:
symbolipoint said:
A search yielded these, which should be a very good beginning:

http://youtu.be/IBDiWlXJcUk

http://youtu.be/DI7ofaEgyTQ

Hi, these we're very helpful, but I'm looking for instructions on plotting and conceptualizing space and vector curves rather than single points e.g. ##r(t) = <f(t),g(t),h(t)>##

Thanks.
 

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