How to count rotated image coordinates in C#?

Question

I'm making program to draw some lines by using x y coordinates to image in picturebox. The image will be adjustable so can be resized or rotated but I want the drawn lines to follow the image along not staying on the picturebox coordinates. When zoomed in or out the lines still following the images but when rotated it jumps randomly not following the image.

Default program with 3 lines drawn

Zoomed image with lines still in place

Rotated image by 10 degrees. the lines jumps to random location.

I'm currently using this one with 2 coordinates to form a line but it makes the coordinates jumping everywhere randomly not rotated along with the image. this is the code for the black line 1.

---Edit---

this is the code to rotate clockwise but somehow it moves counter clockwise. the angle2 value is still unknown and that 32 is the closest position possible by trying one by one with rotating it counter clockwise. the coordinate didnt jump as random as before now it rotates along with the pic but the rotated location is still incorrect. after rotate it 360 degrees the coordinate location is slightly moved from original. and every rotation goes counter clockwise.

Original before rotating with 32 value in angle 2

After rotating 360 degrees

float x = (float)bmp.Width / 2;
float y = (float)bmp.Height / 2;
ang = ang + 10;
double ang2 = 32;
double newLine1X1 =  (line1X1 - x) * Math.Cos(ang2 /180) + (line1Y1 - y) * Math.Sin(ang2 /180) + x;
double newLine1Y1 = -(line1X1 - x) * Math.Sin(ang2 /180) + (line1Y1 - y) * Math.Cos(ang2 /180) + y;
double newLine1X2 =  (line1X2 - x) * Math.Cos(ang2 /180) + (line1Y2 - y) * Math.Sin(ang2 /180) + x;
double newLine1Y2 = -(line1X2 - x) * Math.Sin(ang2 /180) + (line1Y2 - y) * Math.Cos(ang2 /180) + y;
line1X1 = (int)newLine1X1;
line1Y1 = (int)newLine1Y1;
line1X2 = (int)newLine1X2;
line1Y2 = (int)newLine1Y2;

Clockwise Rotation Code

float x = (float)bmp.Width / 2;
float y = (float)bmp.Height / 2;
ang = ang - 10;
double ang2 = -32;
double newLine1X1 = (line1X1 - x) * Math.Cos(ang2 /180) - (line1Y1 - y) * Math.Sin(ang2 /180) + x;
double newLine1Y1 = (line1X1 - x) * Math.Sin(ang2 /180) + (line1Y1 - y) * Math.Cos(ang2 /180) + y;
double newLine1X2 = (line1X2 - x) * Math.Cos(ang2 /180) - (line1Y2 - y) * Math.Sin(ang2 /180) + x;
double newLine1Y2 = (line1X2 - x) * Math.Sin(ang2 /180) + (line1Y2 - y) * Math.Cos(ang2 /180) + y;
line1X1 = (int)newLine1X1;
line1Y1 = (int)newLine1Y1;
line1X2 = (int)newLine1X2;
line1Y2 = (int)newLine1Y2;

Counter Clockwise Rotation Code

can anyone tell me how to fix this rotation error? Thank you very much.

Answer 1

what you are asking for is a transformation matrix and an offset vector

https://en.wikipedia.org/wiki/Transformation_matrix#Rotation

P_x shall be the x coordinate of a point P, while P_y shall be its y coordinate

PT_x and PT_y shall be the transformed coorinates

O_x and O_y shall be the offset point (the point the picture is rotated around)

d shall be the rotation angle ...

PT_x =  (P_x - O_x) * cos(d) + (P_y - O_y) * sin(d) + O_x
PT_y = -(P_x - O_x) * sin(d) + (P_y - O_y) * cos(d) + O_y

---

Example: A rotating Box with a line that points to the same spot while the box rotates

using System;
using System.Drawing;
using System.Windows.Forms;

namespace SoExamples.Rotation
{
    public  class Form1 : Form
    {
        Bitmap bmp = new Bitmap(100, 100); //placeholder... our rotating box
        Point p1 = new Point(80,5);//a point in our rotating box
        int deg = 0;//the current rotation of the box in degrees 0...359
        Point start;//a point to start drawing a line...


        public Form1()
        {
            InitializeComponent();

            //preparing our dummy box
            using (var graphics = Graphics.FromImage(bmp))
            {
                graphics.Clear(Color.LightBlue);// a background color...
                graphics.DrawString("X", DefaultFont, Brushes.White, p1);
            }

            //calculating the start point for a line...
            start = new Point(label1.Location.X + label1.Width / 2, label1.Location.Y + label1.Height); //in the middle under the label
        }
        /// <summary>
        /// timer handler, executed every time the timer is ellapsed ... every 100ms
        /// </summary>
        private void timer1_Tick(object sender, EventArgs e)
        {
            deg++;//let's rotate...
            deg %= 360;//0...359
            Invalidate(true);//queue for re-drawing
        }

        /// <summary>
        /// custom painting for the Form ... called every time the form is re-drawn
        /// </summary>
        private void Form1_Paint(object sender, PaintEventArgs e)
        {
            var g = e.Graphics;

            g.Clear(BackColor);

            Point drawTo = new Point(Width / 2, Height / 2);//we want to draw the box in the center of the form
            drawTo.Offset(-bmp.Width / 2, -bmp.Height / 2);//...but we need to specify the upper left corner

            Point rotateAround = new Point(Width / 2, Height / 2);//we want to rotate the box around the center

            g.TranslateTransform(-rotateAround.X, -rotateAround.Y); //translate the rotateAround point as 0,0
            g.RotateTransform(-deg, System.Drawing.Drawing2D.MatrixOrder.Append);//rotate
            g.TranslateTransform(rotateAround.X, rotateAround.Y, System.Drawing.Drawing2D.MatrixOrder.Append);//translate back

            g.DrawImageUnscaled(bmp, drawTo);//draw the box with respect to current transforms... 

            g.ResetTransform();//now back to our original coordinate-space

            var P = new Point(drawTo.X + p1.X, drawTo.Y + p1.Y); //the point we want to point to in the original coordinate-space (before rotation)

            var O = rotateAround;
            var rad = deg * Math.PI / 180d; //System.Math want's our angle in radians 

            //coordinate calculation for a rotation around O
            //PT_x = (P_x - O_x) * cos(d) + (P_y - O_y) * sin(d) + O_x
            //PT_y = -(P_x - O_x) * sin(d) + (P_y - O_y) * cos(d) + O_y

            var PT_x = (P.X - O.X) * Math.Cos(rad) + (P.Y - O.Y) * Math.Sin(rad) + O.X;
            var PT_y = -(P.X - O.X) * Math.Sin(rad) + (P.Y - O.Y) * Math.Cos(rad) + O.Y;

            drawTo = new Point((int)PT_x, (int)PT_y);

            g.DrawLine(Pens.Black, start, drawTo); // draw a line to the calculated point

        }

        //boiler plate code follows...

        private System.ComponentModel.IContainer components = null;
        protected override void Dispose(bool disposing)
        {
            if (disposing && (components != null))
            {
                components.Dispose();
            }
            base.Dispose(disposing);
        }

        private void InitializeComponent()
        {
            this.components = new System.ComponentModel.Container();
            this.label1 = new System.Windows.Forms.Label();
            this.timer1 = new System.Windows.Forms.Timer(this.components);
            this.SuspendLayout();
            // 
            // label1
            // 
            this.label1.AutoSize = true;
            this.label1.Location = new System.Drawing.Point(41, 43);
            this.label1.Name = "label1";
            this.label1.Size = new System.Drawing.Size(197, 13);
            this.label1.TabIndex = 1;
            this.label1.Text = "Some fixed point to start drawing a line to the top left corner of a 'X' in a rotating box...";
            // 
            // timer1
            // 
            this.timer1.Enabled = true;
            this.timer1.Tick += new System.EventHandler(this.timer1_Tick);
            // 
            // Form1
            // 
            this.AutoScaleDimensions = new System.Drawing.SizeF(6F, 13F);
            this.AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
            this.ClientSize = new System.Drawing.Size(800, 450);
            this.Controls.Add(this.label1);
            this.Name = "Form1";
            this.Text = "Form1";
            this.Paint += new System.Windows.Forms.PaintEventHandler(this.Form1_Paint);
            this.ResumeLayout(false);
            this.PerformLayout();

        }
        private System.Windows.Forms.Label label1;
        private System.Windows.Forms.Timer timer1;
    }
}