Struct CircleGeometryUtilities

float CircleRadiusAdjustmentFactor (

int

steps

)

Radius factor to adjust for circle approximation errors.

If a circle is approximated by fewer segments, it will be slightly smaller than the original circle. This factor is used to adjust the radius of the circle so that the resulting circle will have roughly the same area as the original circle.

int CircleSteps (

Matrix4x4	matrix
float	radius
float	maxError

)

The number of steps required to get a circle with a maximum error of maxError.

float[] circleRadiusAdjustmentFactors = new float[] { 1.56f, 1.25f, 1.15f, 1.1f, 1.07f, 1.05f, 1.04f, 1.03f, 1.03f, 1.02f, 1.02f, 1.02f, 1.01f, 1.01f, 1.01f, 1.01f, 1.01f, 1.01f, 1.01f, 1.01f, }

Cached values for CircleRadiusAdjustmentFactor.

We can calculate the area of a polygonized circle, and equate that with the area of a unit circle x * cos(math.PI / steps) * sin(math.PI/steps) * steps = pi
Solving for the factor that makes them equal (x) gives the expression below.

Generated using the python code: [math.sqrt(2 * math.pi / (i * math.sin(2 * math.pi / i))) for i in range(3, 23)]


It would be nice to generate this using a static constructor, but that is not supported by Unity's burst compiler.