Bézier curve

High school (ages 12+)
Art & Creativity

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/b-zier-curve

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. Who discovered Bézier curve?Popularized by Pierre Bézier in the 1960s, building on earlier work
2. What is the mathematical formulation?Defined by Bernstein polynomials, forming parametric polynomial curves
3. Why do designers use Bézier curves in cars and cartoons?Designers use Bézier curves because they let them make smooth, flowing shapes easily. In cars, they help create the sleek curves of the body. In cartoons and games, they make characters and objects look nice.
4. How do control points shape a Bézier curve?The dots called control points act like handles. Moving a handle pulls the curve toward it, changing how the line bends. The curve itself does not always go through every dot, but the dots decide its shape.

Parametric Polynomial: A curve defined by equations where coordinates are polynomials of a parameter, typically ranging from 0 to 1.
Bernstein Basis Polynomials: The specific polynomials used to define Bézier curves, ensuring desirable mathematical properties.
Convex Hull Property: The property that a Bézier curve always lies within the smallest convex polygon that encloses its control points.
Bézier Spline: A curve formed by connecting multiple Bézier curves smoothly.