De Casteljau's algorithm
De Casteljau's algorithm is a special way of drawing curved lines on a computer or piece of paper. It's called an algorithm because it's a set of steps that a computer can follow to make the curved line.
To use de Casteljau's algorithm, you start with four points. These points will be the beginning and end points of the curve, and two other points in between.
Then, you draw a straight line between the first two points, and another straight line between the last two points. These two lines will be the "arms" of the curve.
Next, you divide each "arm" into two parts by finding the middle point. You then draw a straight line between those two middle points.
You keep doing this, dividing each new line into two parts and drawing a straight line between the two middle points, until you have a smooth and curved line.
The important thing to remember is that each new point you add is found by taking two of the previous points, averaging them, and using that average as the new point. It's a bit like playing the guessing game "halfway to the answer" over and over again until you reach the final point.
De Casteljau's algorithm is a very useful tool in computer graphics and design, and it allows us to create some really beautiful and intricate curved lines!
To use de Casteljau's algorithm, you start with four points. These points will be the beginning and end points of the curve, and two other points in between.
Then, you draw a straight line between the first two points, and another straight line between the last two points. These two lines will be the "arms" of the curve.
Next, you divide each "arm" into two parts by finding the middle point. You then draw a straight line between those two middle points.
You keep doing this, dividing each new line into two parts and drawing a straight line between the two middle points, until you have a smooth and curved line.
The important thing to remember is that each new point you add is found by taking two of the previous points, averaging them, and using that average as the new point. It's a bit like playing the guessing game "halfway to the answer" over and over again until you reach the final point.
De Casteljau's algorithm is a very useful tool in computer graphics and design, and it allows us to create some really beautiful and intricate curved lines!