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!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhucQPtmk4LWWlNrxzA

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/laboratory-project-bezier-curves-part-3

Related Videos:

Laboratory Project: Bezier Curves Part 2: https://youtu.be/HN-xNfncklU
Laboratory Project: Bezier Curves Part 1: https://youtu.be/S7aApca_B04
Parametric Calculus: Surface Area Part 1: https://youtu.be/4bMEIf6WD8M
Parametric Calculus: Arc Length Part 1: https://youtu.be/AWvJDK-m6wQ
Parametric Calculus: Areas: https://youtu.be/XdplYV61xlM
Parametric Calculus: Tangents: https://youtu.be/deQwD2o0Sas
Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE .