Basic math for drawing a circle #Circle

Radians
Basic:
- Radian is an unit for angles.
- 1 radian is the angle when the arc length is same as the radius
- Circumference is same as radians of 360 degrees = 2π

180 degrees = 3.141592653589793 radians = PI
360 degrees = 6.283185307179586 radians = TWO_PI

1.0 radian = 180 / PI 
           = 57.29577951308232 degrees

Conversions between degrees and radians

DegToRad(degrees){
    radians = degrees * PI / 180
}

RadToDeg(radians){
    degrees = radians * 180 / PI
}

Trigonometry

In some programming languages, sin() or cos() function uses radians, not degrees for its argument.

sin(radians)
cos(radians)

Here are the values of sin or cos when 0, 90, 180, 270, 360 degrees.

//---use "signed long" type to get accurate values to avoid to be rounded

0° = 0 * PI/180 radians
sin(0) = 0
cos(0) = 1

90° = 90 * PI/180 radians
sin(PI / 2) = 1
cos(PI / 2) = 0

180° = 180 * PI/180 radians
sin(PI) = 0
cos(PI) = -1

270° = 270 * PI/180 radians
sin(PI * 3/2) = -1
cos(PI * 3/2) = 0

360° =  360 * PI/180 radians
sin(TWO_PI) = 0
cos(TWO_PI) = 1

Calculate a coordinate on a circle from an angle

x = cos(radians) * r
y = sin(radians) * r

or

x = cos(degrees * PI / 180) * r
y = sin(degrees * PI / 180) * r

Calculate a coordinate on a circle from a percentage
TWO_PI = 360° = 100%. You can calculate radians from a percentage.

percentage = degrees / 360
x = cos(percentage * TWO_PI) * r
y = sin(percentage * TWO_PI) * r

The divisor is a number of vertices you want to set on a circle.
If the vertices is 10, the shape will be a decagon rather than a circle.
It's important when you want to get edges of the circle with for-loop etc.

percentage = i / 10
x = radius * cos(percentage * TWO_PI) * r
y = radius * sin(percentage * TWO_PI) * r

atan2 returns an angle between two points in radians.

atan2(y2-y1, x2-x1)