polar co-ordinates : Java Glossary

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polar co-ordinates
Many geometric shapes, such as circles, spirals and polygons are easier to describe in polar co-ordinates, 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
poral_coordinates cartesian_coordinates drawing_coordinates

You can convert polar co-ordinates to Cartesian x,y co-ordinates 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 );
To convert to drawing co-ordinates you must round to integers and invert the sign of y, since y grows down in Java rather than up as in mathematics.

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