Drawing Surfaces & Space Curves

In summary, the conversation discusses drawing surface curves and the struggles with this topic. The person asks for resources to help with understanding this fundamental concept in Multivariate and Vector Calculus. The other person suggests using old lecture notes that review 2D conics and their graphs and give examples of drawing 3D conic surfaces. These notes are available as PDF files at math.asu.edu/~kurtz/LectureNotes/Lecture7.pdf and math.asu.edu/~kurtz/LectureNotes/Lecture8.pdf.
  • #1
vanceEE
109
2

Homework Statement


Drawing surface ##f(x,y) = ...## or ##r(t) = <f(t),g(t)>## etc.

The Attempt at a Solution


I've been working on drawing space curves lately, by breaking into separate planes and by level curves. I'm struggling w/ this topic. (1) If I'm not mistaken, this is fundamental in order to grasp the other topics within Multivariate and Vector Calculus, correct? (2) Are there any resources recommended for this topic, ANY help will be highly appreciated. Thank you.
 
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  • #2
vanceEE said:

Homework Statement


Drawing surface ##f(x,y) = ...## or ##r(t) = <f(t),g(t)>## etc.

The Attempt at a Solution


I've been working on drawing space curves lately, by breaking into separate planes and by level curves. I'm struggling w/ this topic. (1) If I'm not mistaken, this is fundamental in order to grasp the other topics within Multivariate and Vector Calculus, correct? (2) Are there any resources recommended for this topic, ANY help will be highly appreciated. Thank you.

I have some old lecture notes of mine that review 2d conics and their graphs and give examples of how to use that to draw 3d conic surfaces. These were for my own use during my lectures so they aren't that polished for publication. They are handwritten and my handwriting isn't that great, but you might find them useful if you work through the examples. They are pdf files and you can find them at:

math.asu.edu/~kurtz/LectureNotes/Lecture7.pdf [Broken]
math.asu.edu/~kurtz/LectureNotes/Lecture8.pdf [Broken]
 
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What is the difference between a drawing surface and a space curve?

A drawing surface refers to a two-dimensional space where an image can be created, such as a canvas or paper. A space curve, on the other hand, is a three-dimensional curve that exists in space and can be represented on a drawing surface through techniques like perspective drawing.

How can drawing surfaces be manipulated to create the illusion of depth?

Drawing surfaces can be manipulated through techniques such as shading, perspective, and foreshortening to create the illusion of depth. These techniques involve adjusting the size, angle, and placement of objects on the surface to create a sense of distance and dimension.

What is the role of mathematics in drawing surfaces and space curves?

Mathematics plays a crucial role in understanding and creating drawing surfaces and space curves. Concepts such as geometry, perspective, and projection are essential in accurately representing three-dimensional objects on a two-dimensional surface. Additionally, mathematical equations and formulas can be used to create complex space curves.

What are some common techniques for drawing space curves?

Some common techniques for drawing space curves include using isometric projection, orthographic projection, and perspective drawing. These techniques involve creating a three-dimensional representation of the curve on a two-dimensional surface by adjusting the angles and proportions of the curve.

How can drawing surfaces and space curves be used in scientific research?

Drawing surfaces and space curves can be used in scientific research to visually represent complex data and concepts. For example, space curves can be used to graphically represent the motion of objects in physics, while drawing surfaces can be used to create diagrams and illustrations in biology and chemistry. Additionally, these techniques can be used to create accurate models and simulations in various scientific fields.

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