Strategies for drawing space curves?

In summary, drawing and conceptualizing space curves can be challenging, especially for those who are not artistically inclined. However, there are helpful strategies that can be learned through instruction, particularly in Geometry and Calculus courses. It involves drawing an origin point and three axes, and representing three-dimensional points using guidelines in the axis planes. Additionally, there are helpful videos available online for further guidance.
  • #1
vanceEE
109
2
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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  • #2
Programming, maple, mathematica, stuff like that.
 
  • #3
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.
 
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  • #5
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.
 

1. What are space curves?

Space curves are three-dimensional curves that exist in space, as opposed to curves on a flat surface. They are defined by parametric equations and can represent various shapes and movements in three-dimensional space.

2. What are some common strategies for drawing space curves?

Some common strategies for drawing space curves include using parametric equations to plot points, using computer software to create 3D models, and projecting the curve onto a two-dimensional plane for easier visualization.

3. How do you determine the shape of a space curve?

The shape of a space curve is determined by its parametric equations, which dictate the x, y, and z coordinates of points along the curve. By manipulating these equations, you can change the shape of the curve.

4. Can space curves be used in real-life applications?

Yes, space curves have many real-life applications, including in engineering, architecture, and animation. They can be used to represent the paths of objects in motion, such as the trajectory of a satellite or the movement of a rollercoaster.

5. Are there any challenges in drawing space curves?

One of the main challenges in drawing space curves is visualizing them in three-dimensional space. This can be overcome by using computer software or projecting the curve onto a two-dimensional plane. Additionally, complex space curves may require advanced mathematical skills to create accurate representations.

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