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How do I rotate a Regular polygon in C#

I need to rotate the regular polygon around a set center by a given degree can somebody help?
Im using this code the generate the regular polygon
private static void DrawRegularPolygon(PointF center, // center Coordinates of circle
int vertexes, // Number of vertices
float radius, // Radius
Graphics graphics)
{
Pen pen;
var angle = Math.PI * 2 / vertexes;
var Rotationangle = (45/180) * Math.PI;
var points = Enumerable.Range(0, vertexes)
.Select(i => PointF.Add(center, new SizeF((float)Math.Sin(i * angle) * radius, (float)Math.Cos(i * angle) * radius )));
if (vertexes%2 == 0)
{
pen = new Pen(Color.Red);
}
else
{
pen = new Pen(Color.Black);
}
graphics.DrawPolygon(pen, points.ToArray());
//graphics.DrawEllipse(Pens.Aqua, new RectangleF(PointF.Subtract(center, new SizeF(radius, radius)), new SizeF(radius * 2, radius * 2)));
}

Try these lines :
graphics.TranslateTransform(center.X, center.Y);
graphics.RotateTransform(180f);
graphics.TranslateTransform(-center.X, -center.Y);
graphics.DrawPolygon(pen, points.ToArray());
I can rotate the polygon 180 degrees, before drawing it.

C# - Rotating polygon randomly

I'm trying to rotate polygon randomly using timer. I got to draw regular polygons and rotate it to one direction. But I'm not sure about how to rotate polygon to random direction using angle or timer interval.
My Code is below:
int sides = 5;
Graphics g = e.Graphics;
nPoints = CalculateVertices(sides, radius, angle, center);
g.DrawPolygon(navypen, nPoints);
g.FillPolygon(BlueBrush, nPoints);
Point center = new Point(ClientSize.Width / 2, ClientSize.Height / 2);
for(int i = 0; i < sides; i++) {
g.DrawLine(new Pen(Color.Navy), center.X, center.Y, nPoints[i].X, nPoints[i].Y);
}
private PointF[] CalculateVertices(int sides, int radius, float startingAngle, Point center)
{
if (sides < 3) {
sides = 3;
}
List<PointF> points = new List<PointF>();
float step = 360.0f / sides;
float angle = startingAngle; //starting angle
for (double i = startingAngle; i < startingAngle + 360.0; i += step) //go in a circle
{
points.Add(DegreesToXY(angle, radius, center));
angle += step;
}
return points.ToArray();
}
private PointF DegreesToXY(float degrees, float radius, Point origin)
{
PointF xy = new PointF();
double radians = degrees * Math.PI / 180.0;
xy.X = (int)(Math.Cos(radians) * radius + origin.X);
xy.Y = (int)(Math.Sin(-radians) * radius + origin.Y);
return xy;
}
private void timer2_Tick(object sender, EventArgs e){
angle += 1;
angle_tri -= 1;
Invalidate();
}

Here is an example of drawing a list of points rotated with varying speeds, both angular and and timing..:
First a few variables:
Random rnd = new Random();
float angle = 0f;
List<Point> points = new List<Point>();
Then a Tick with varying speed and a varying angle:
private void timer1_Tick(object sender, EventArgs e)
{
angle += rnd.Next(0, 33)/ 10f;
timer1.Interval = rnd.Next(100) + 15;
pictureBox5.Invalidate();
}
Here is the Paint event of a PictureBox, which is DoubleBuffered, so it won't flicker..:
private void pictureBox5_Paint(object sender, PaintEventArgs e)
{
if (points.Count > 1)
{
Point center = new Point(
(points.Select(x => x.X).Max() + points.Select(x => x.X).Min()) / 2,
(points.Select(x => x.Y).Max() + points.Select(x => x.Y).Min()) / 2);
e.Graphics.TranslateTransform(center.X, center.Y);
e.Graphics.RotateTransform(angle);
e.Graphics.TranslateTransform(-center.X, -center.Y);
e.Graphics.DrawPolygon(Pens.DarkGreen, points.ToArray());
}
}
Note that due to the weird speed changes this is anything but smooth; you would have to find better algorithms for them than mere randomness..

Drawing triangles on each edge of regular polygon

I've been tried to draw triangles on each edge of regular polygons.
So far I got to make polygons like this:
What I'm trying to make is that small triangle on the each edge of the polygon:
How do I do this?
Code how to draw polygons is below:
int sides = 5;
Graphics g = e.Graphics;
nPoints = CalculateVertices(sides, radius, angle, center);
g.DrawPolygon(navypen, nPoints);
g.FillPolygon(BlueBrush, nPoints);
Point center = new Point(ClientSize.Width / 2, ClientSize.Height / 2);
for(int i = 0; i < sides; i++) {
g.DrawLine(new Pen(Color.Navy), center.X, center.Y, nPoints[i].X, nPoints[i].Y);
}
private PointF[] CalculateVertices(int sides, int radius, float startingAngle, Point center)
{
if (sides < 3) {
sides = 3;
}
//throw new ArgumentException("Polygon must have 3 sides or more.");
List<PointF> points = new List<PointF>();
float step = 360.0f / sides;
float angle = startingAngle; //starting angle
for (double i = startingAngle; i < startingAngle + 360.0; i += step) //go in a circle
{
points.Add(DegreesToXY(angle, radius, center));
angle += step;
}
return points.ToArray();
}
private PointF DegreesToXY(float degrees, float radius, Point origin)
{
PointF xy = new PointF();
double radians = degrees * Math.PI / 180.0;
xy.X = (int)(Math.Cos(radians) * radius + origin.X);
xy.Y = (int)(Math.Sin(-radians) * radius + origin.Y);
return xy;
}

Try this out...instead of calculating absolute points for the triangle, I've instead computed points for a "unit triangle" at the origin (using your function!). Then I simply rotate and move the Graphics surface and draw the unit triangle where I want it:
public partial class Form1 : Form
{
public Form1()
{
InitializeComponent();
}
private PointF[] nPoints;
private PointF[] triangle;
private int sides = 5;
private int angle = 0;
private int radius = 100;
private int triangleLength = 10;
private void Form1_Load(object sender, EventArgs e)
{
triangle = this.CalculateVertices(3, triangleLength, 0, new Point(0, 0)); // this "unit triangle" will get reused!
}
private void Form1_Paint(object sender, PaintEventArgs e)
{
Graphics g = e.Graphics;
Point center = new Point(ClientSize.Width / 2, ClientSize.Height / 2);
nPoints = CalculateVertices(sides, radius, angle, center);
// draw the polygon
g.FillPolygon(Brushes.Blue, nPoints);
g.DrawPolygon(Pens.Black, nPoints);
for (int i = 0; i < sides; i++)
{
g.DrawLine(Pens.Black, center.X, center.Y, nPoints[i].X, nPoints[i].Y);
}
// draw small triangles on each edge:
float step = 360.0f / sides;
float curAngle = angle + step / 2; // start in-between the original angles
for (double i = curAngle; i < angle + (step / 2) + 360.0; i += step) //go in a circle
{
// move to the center and rotate:
g.ResetTransform();
g.TranslateTransform(center.X, center.Y);
g.RotateTransform((float)i);
// move out to where the triangle will be drawn and render it
g.TranslateTransform(radius, 0);
g.FillPolygon(Brushes.LightGreen, triangle);
g.DrawPolygon(Pens.Black, triangle);
}
}
// this is your code unchanged
private PointF[] CalculateVertices(int sides, int radius, float startingAngle, Point center)
{
if (sides < 3)
{
sides = 3;
}
//throw new ArgumentException("Polygon must have 3 sides or more.");
List<PointF> points = new List<PointF>();
float step = 360.0f / sides;
float angle = startingAngle; //starting angle
for (double i = startingAngle; i < startingAngle + 360.0; i += step) //go in a circle
{
points.Add(DegreesToXY(angle, radius, center));
angle += step;
}
return points.ToArray();
}
// this is your code unchanged
private PointF DegreesToXY(float degrees, float radius, Point origin)
{
PointF xy = new PointF();
double radians = degrees * Math.PI / 180.0;
xy.X = (int)(Math.Cos(radians) * radius + origin.X);
xy.Y = (int)(Math.Sin(-radians) * radius + origin.Y);
return xy;
}
}

DrawEllipse from two joint (Point, or rather X and Y coordinates)

I'm looking to show skeleton by ellipse and not by line. I have two Point with coordinates for X and Y.
When i want to draw an ellipse i need
public abstract void DrawEllipse(
Brush brush,
Pen pen,
Point center,
double radiusX,
double radiusY
)
so i have tried with this code but there is some error(don't know radiusY):
double centerX = (jointPoints[jointType0].X + jointPoints[jointType1].X) / 2;
double centerY = (jointPoints[jointType0].Y + jointPoints[jointType1].Y) / 2;
double radiusX =Math.Sqrt( (Math.Pow((jointPoints[jointType1].X - jointPoints[jointType0].X), 2)) + (Math.Pow((jointPoints[jointType1].Y - jointPoints[jointType0].Y), 2)));
drawingContext.DrawEllipse(null, drawPen, new Point(centerX, centerY), radiusX, radiusX/5);
Can anyone help me?
private void DrawBone(IReadOnlyDictionary<JointType, Joint> joints, IDictionary<JointType, Point> jointPoints, JointType jointType0, JointType jointType1, DrawingContext drawingContext, Pen drawingPen,List<JointType> badJoint)
{
Joint joint0 = joints[jointType0];
Joint joint1 = joints[jointType1];
// If we can't find either of these joints, exit
if (joint0.TrackingState == TrackingState.NotTracked ||
joint1.TrackingState == TrackingState.NotTracked)
{
return;
}
// We assume all drawn bones are inferred unless BOTH joints are tracked
Pen drawPen = this.inferredBonePen;
if ((joint0.TrackingState == TrackingState.Tracked) && (joint1.TrackingState == TrackingState.Tracked))
{
drawPen = drawingPen;
}
//If a bone makes parts of an one bad angle respect reference angle
if (badJoint.Contains(jointType0) && badJoint.Contains(jointType0))
drawPen = new Pen(Brushes.Red, 6);
drawingContext.DrawLine(drawPen, jointPoints[jointType0], jointPoints[jointType1]);

You cannot (just) use the DrawEllipse method, because that will always draw horizontal or vertical elipses.
Use this code to implement the rotation: https://stackoverflow.com/a/5298921/1974021 and write a method that takes the following input parameters:
Focalpoint1
FocalPoint2
Radius
As an ellipse can be described by both focal points and a (combined) radius. If you use the focal points, the ellipsis will overlap at the joints to create a circle-like pattern at each joint. Is that about what you want? (It is even easier if you only want them to touch at the joint)
Okay, it's actually not the focal point but the center of the osculating circle. Try this method:
private static void DrawEllipse(Pen pen, Graphics g, PointF pointA, PointF pointB, float radius)
{
var center = new PointF((pointA.X + pointB.X) / 2, (pointA.Y + pointB.Y) / 2);
var distance = GetDistance(pointA, pointB);
// The axis are calculated so that the center of the osculating circles are conincident with the points and has the given radius.
var a = radius + distance / 2; // Semi-major axis
var b = (float)Math.Sqrt(radius * a); // Semi-minor axis
// Angle in degrees
float angle = (float)(Math.Atan2(pointA.Y - pointB.Y, pointA.X - pointB.X) * 180 / Math.PI);
using (Matrix rotate = new Matrix())
{
GraphicsContainer container = g.BeginContainer();
rotate.RotateAt(angle, center);
g.Transform = rotate;
g.DrawEllipse(pen, center.X-a, center.Y-b, 2 * a, 2 * b);
g.EndContainer(container);
}
}
private static float GetDistance(PointF a, PointF b)
{
var dx = a.X - b.X;
var dy = a.Y - b.Y;
return (float)Math.Sqrt(dx * dx + dy * dy);
}

Transcribing a polygon on a circle

i am currently try to inscribe diagonals of a decagon inside a circle
like this
in c# my approach would be creating a circle
e.Graphics.DrawEllipse(myPen, 0, 0, 100, 100);
and draw lines inside using
e.Graphics.DrawLine(myPen, 20, 5, 50, 50);
after that i would draw a decagon polygon.
currently im stuck at how to divide the circle into 10 parts/ finding the correct coordiantes of the points on the circumference of the circles because im not good in math,
i want to know how would i know the next point in a circumference of the circle the size of my circle is indicated above.
and also i want also to ask a better approach for my problem.
Thank you :)

Just for grits and shins, here's a generic implementation that will inscribe an X-sided polygon into the Rectangle you pass it. Note that in this approach I'm not actually calculating any absolute points. Instead, I am translating the origin, rotating the surface, and drawing the lines only with respect to the origin using a fixed length and an angle. This is repeated in a loop to achieve the end result below, and is very similar to commanding the Turtle in Logo:
public partial class Form1 : Form
{
PictureBox pb = new PictureBox();
NumericUpDown nud = new NumericUpDown();
public Form1()
{
InitializeComponent();
this.Text = "Inscribed Polygon Demo";
TableLayoutPanel tlp = new TableLayoutPanel();
tlp.RowCount = 2;
tlp.RowStyles.Clear();
tlp.RowStyles.Add(new RowStyle(SizeType.AutoSize));
tlp.RowStyles.Add(new RowStyle(SizeType.Percent, 100));
tlp.ColumnCount = 2;
tlp.ColumnStyles.Clear();
tlp.ColumnStyles.Add(new ColumnStyle(SizeType.AutoSize));
tlp.ColumnStyles.Add(new ColumnStyle(SizeType.AutoSize));
tlp.Dock = DockStyle.Fill;
this.Controls.Add(tlp);
Label lbl = new Label();
lbl.Text = "Number of Sides:";
lbl.TextAlign = ContentAlignment.MiddleRight;
tlp.Controls.Add(lbl, 0, 0);
nud.Minimum = 3;
nud.Maximum = 20;
nud.AutoSize = true;
nud.ValueChanged += new EventHandler(nud_ValueChanged);
tlp.Controls.Add(nud, 1, 0);
pb.Dock = DockStyle.Fill;
pb.Paint += new PaintEventHandler(pb_Paint);
pb.SizeChanged += new EventHandler(pb_SizeChanged);
tlp.SetColumnSpan(pb, 2);
tlp.Controls.Add(pb, 0, 1);
}
void nud_ValueChanged(object sender, EventArgs e)
{
pb.Refresh();
}
void pb_SizeChanged(object sender, EventArgs e)
{
pb.Refresh();
}
void pb_Paint(object sender, PaintEventArgs e)
{
// make circle centered and 90% of PictureBox size:
int Radius = (int)((double)Math.Min(pb.ClientRectangle.Width, pb.ClientRectangle.Height) / (double)2.0 * (double).9);
Point Center = new Point((int)((double)pb.ClientRectangle.Width / (double)2.0), (int)((double)pb.ClientRectangle.Height / (double)2.0));
Rectangle rc = new Rectangle(Center, new Size(1, 1));
rc.Inflate(Radius, Radius);
InscribePolygon(e.Graphics, rc, (int)nud.Value);
}
private void InscribePolygon(Graphics G, Rectangle rc, int numSides)
{
if (numSides < 3)
throw new Exception("Number of sides must be greater than or equal to 3!");
float Radius = (float)((double)Math.Min(rc.Width, rc.Height) / 2.0);
PointF Center = new PointF((float)(rc.Location.X + rc.Width / 2.0), (float)(rc.Location.Y + rc.Height / 2.0));
RectangleF rcF = new RectangleF(Center, new SizeF(1, 1));
rcF.Inflate(Radius, Radius);
G.DrawEllipse(Pens.Black, rcF);
float Sides = (float)numSides;
float ExteriorAngle = (float)360 / Sides;
float InteriorAngle = (Sides - (float)2) / Sides * (float)180;
float SideLength = (float)2 * Radius * (float)Math.Sin(Math.PI / (double)Sides);
for (int i = 1; i <= Sides; i++)
{
G.ResetTransform();
G.TranslateTransform(Center.X, Center.Y);
G.RotateTransform((i - 1) * ExteriorAngle);
G.DrawLine(Pens.Black, new PointF(0, 0), new PointF(0, -Radius));
G.TranslateTransform(0, -Radius);
G.RotateTransform(180 - InteriorAngle / 2);
G.DrawLine(Pens.Black, new PointF(0, 0), new PointF(0, -SideLength));
}
}
}
I got the formula for the length of the side here at Regular Polygon Calculator.

One way of dealing with this is using trigonometric functions sin and cos. Pass them the desired angle, in radians, in a loop (you need a multiple of 2*π/10, i.e. a = i*π/5 for i between 0 and 9, inclusive). R*sin(a) will give you the vertical offset from the origin; R*cos(a) will give you the horizontal offset.
Note that sin and cos are in the range from -1 to 1, so you will see both positive and negative results. You will need to add an offset for the center of your circle to make the points appear at the right spots.
Once you've generated a list of points, connect point i to point i+1. When you reach the ninth point, connect it to the initial point to complete the polygon.

I don't test it, but i think it is ok.
#define DegreeToRadian(d) d * (Pi / 180)
float r = 1; // radius
float cX = 0; // centerX
float cY = 0; // centerY
int numSegment = 10;
float angleOffset = 360.0 / numSegment;
float currentAngle = 0;
for (int i = 0; i < numSegment; i++)
{
float startAngle = DegreeToRadian(currentAngle);
float endAngle = DegreeToRadian(fmod(currentAngle + angleOffset, 360));
float x1 = r * cos(startAngle) + cX;
float y1 = r * sin(startAngle) + cY;
float x2 = r * cos(endAngle) + cX;
float y2 = r * sin(endAngle) + cY;
currentAngle += angleOffset;
// [cX, cY][x1, y1][x2, y2]
}
(fmod is c++ function equals to floatNumber % floatNumber)