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Laboratory Project: Bezier Curves Part 2





UPDATE: At 10:33 it should be dy/dx and NOT dx/dt. #Typo

In this video I go over Part 2 of the Laboratory Project: Bezier Curves. In this part I look at Question 2 of the project, which asks us to prove that the tangent line at the first control point, from the graph produced in Part 1, extends through to the second control point. Similarly I prove that this is the case for the tangent line at the 4th control point, which passes through to the 3rd control point. To prove this I show that we need to first calculate the derivative dy/dx by using it’s parametric form, i.e. (dy/dt)/(dx/dt), and then showing that it is equal to the slope of the line connecting the two control points. The good thing when calculating the derivative is that the Bezier curves are defined by identical x and y parametric equations, albeit the x/y’s are interchanged, so cuts the effort in calculating dy/dx by half. This is a very interesting video on the nature of Bezier curves, cubic Bezier curves to be exact, so make sure to watch this video, and stay tuned for later parts!

Download the notes in my video:

View Video Notes on Steemit:

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Laboratory Project: Bezier Curves Part 1:
Parametric Calculus: Surface Area Part 1:
Parametric Calculus: Arc Length Part 1:
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Parametric Equations and Curves: .

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2 comments

  1. at the beginning of last line of Questions 2 answer you wrote dydt, but u meant dydx, right?

    Reply
  2. UPDATE: At 10:33 it should be dy/dx and NOT dx/dt. #Typo

    I don’t always draw tangent lines to control points on Bezier Curves but when I do they usually cross into another control point 😉

    View Video Notes on Steemit: https://steemit.com/mathematics/@mes/laboratory-project-bezier-curves-part-2

    #GetOnSteem

    Reply

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