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Laboratory Project: Bezier Curves Part 3

In this video I go over Part 3 of the Laboratory Project: Bezier Curves. In this part I look at Question 3 of the project, which looks at moving the second control point in hopes of obtaining a loop within the Bezier curve. I test out different values for the second control point and after experimenting, it appears that in general moving the right of the third control point creates a looped Bezier Curve. What’s also interesting is that the findings of Part 2 hold true for this looped curve, in that the tangent lines at the first control points still pass through the second control point; and like-wise the tangent line at the fourth control point passes through the third control point. This is a great video to understand how manipulating the control points changes the resulting curve in a controlled way, hence the name “control”. This behavior is why the Bezier Curves are used in many computer-aided design technologies, including simply printing letters. I will illustrate this even further in later parts, so stay tuned!

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Related Videos:

Laboratory Project: Bezier Curves Part 2:
Laboratory Project: Bezier Curves Part 1:
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Parametric Calculus: Tangents:
Parametric Equations and Curves: .



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1 comment

  1. I don’t always manipulate the control points of a Bezier Curve but when I do it’s usually to create a loop 😉

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