Java Glossary : polar co-ordinates

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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

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.

co-ordinates ¤ polygon

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