polar coordinates : Java Glossary

polar coordinates

Many geometric shapes, such as circles, spirals and polygons are easier to describe in polar coordinates, with an angle and radius instead of x,y. You have a central point and you measure the angle in radians counter clockwise from due east. You measure the radius as the distance from the centre.

Polar	Cartesian	Java Drawing

You can convert polar coordinates to Cartesian x,y coordinates with:

// polar to Cartesian
double x = Math.cos( angleInRadians ) * radius;
double y = Math.sin( angleInRadians ) * radius;

// Cartesian to polar.
double radius = Math.sqrt( x * x + y * y );
double angleInRadians = Math.acos( x / radius );

If your angles are in degrees, to see how to convert them to radians, see the radians entry. To convert to drawing coordinates you must round to integers and invert the sign of y, since y grows down in Java rather than up as in mathematics.

AffineTransform
coordinate systems
gore
Math gotchas
pi/π
polygon
radian
trigonometry

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