Bezier curve the maths of the “Pen Tool”


The Bezier Curve is the mathematics behind the “Pen Tool” a graphic designer’s primary drawing tool. A Bezier Curve is a curved line in which its shape is defined by a mathematical equation.  They are used in vector applications such as Adobe Illustrator and Photoshop as well as InDesign and Quark Express. It consists of two anchor points and levers that control the angle at which the curves leaves the end points.  Without Bezier curves it would be almost impossible to produce the multitude of unique and beautiful designs.


Clicking the pen tool creates segments


They are named after the French mathematician Pierre Bezier who invented them, these are mathematically generated non-uniform curves.  When used by a skilled designer they can create complex shapes with a smooth endpoint and they are particularly useful for creating the letterforms of logos, digital art and computer graphics.  However the “Pen Tool,” is not exactly intuitive, and they are difficult to control and take some time to learn.  I remember at Design College the frustration of practicing with the “Pen Tool” by tracing the unreasonable curves of the Coke Cola logo. I was in a constant state of anxiety and a lack of concentration meant pulling stray lines and arcs across my artboard.

Vector Graphics – are primarily designed by using the “Pen Tool”.  The vector image is a representation of Bezier curves.  The vector image has no fixed point a line can have end points at any position within the image.  Vector graphics are images that basically describe shapes and lines that may be easily altered in size and shape using geometric transformations.   Because the objects within a vector image are described by equation the file size is very small  and it is perfect for creating computer generated images.

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