[RESOLVED] Elliptical orbit

[Longbottomup]

I have a project, but i can make the square rotate around (circle), not that i want, i want the square rotate like Elipse, can you help me?

[ThomasJohnsen]

Could you post the code here (or the part of the code, that's relevant).

[Longbottomup]

I have attached, so, okay, i will post code.

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Windows.Forms;

namespace Elipse
{
    public partial class Main : Form
    {
        public Main()
        {
            InitializeComponent();
        }
        Graphics g;
        PointF[] p;
        PointF[] cn;
        Pen pen;
        private void Main_Load(object sender, EventArgs e)
        {
            pen = new Pen(Color.AntiqueWhite);
            g = this.CreateGraphics();
            p = new PointF[] { new PointF(200, 150), new PointF(300, 150) };
            cn = new PointF[] { new PointF(300, 150), new PointF(330, 150), new PointF(330, 180), new PointF(300, 180) };
        }

        private void Main_Paint(object sender, PaintEventArgs e)
        {
            //Dagiac(p,Color.AntiqueWhite);
            Dagiac(cn, Color.AntiqueWhite);
        }
        private PointF XoayDiemTamC(PointF p, PointF c, double a)
        {
            PointF Q = new PointF();
            Q.X = p.X * (float)Math.Cos(a) - p.Y * (float)Math.Sin(a) + c.X * (1 - (float)Math.Cos(a)) + c.Y * (float)Math.Sin(a);
            Q.Y = p.X * (float)Math.Sin(a) + (p.Y * (float)Math.Cos(a)) - c.X * (float)Math.Sin(a) + c.Y * (1 - (float)Math.Cos(a));
            return Q;
        }
        private PointF[] XoayDiemTamCDagiac(PointF[] p, PointF c, double a)
        {
            PointF[] Q = new PointF[p.Length];
            for (int i = 0; i < p.Length; i++)
            {
                Q[i] = XoayDiemTamC(p[i], c, a);
            }
            return Q;
        }
        private void MyLine(PointF p1, PointF p2, Color c)
        {           
            g.DrawLine(new Pen(c), p1, p2);
        }
        private void Dagiac(PointF[] p, Color c)
        {
            for (int i = 0; i < p.Length - 1; i++)
            {
                MyLine(p[i], p[i + 1], c);
            }
            MyLine(p[p.Length - 1], p[0], c);
        }

        private void timerxoay_Tick(object sender, EventArgs e)
        {
            //p = XoayDiemTamCDagiac(p, p[0], 1 * Math.PI / 180);
            cn = XoayDiemTamCDagiac(cn, p[0], 1 * Math.PI / 180);
            //g.Clear(BackColor);
            this.Invalidate();
        }

        private void cmdrotate_Click(object sender, EventArgs e)
        {
            timerxoay.Enabled = true;
        }
    }
}

Important here:

Q.X = p.X * (float)Math.Cos(a) - p.Y * (float)Math.Sin(a) + c.X * (1 - (float)Math.Cos(a)) + c.Y * (float)Math.Sin(a);
            Q.Y = p.X * (float)Math.Sin(a) + (p.Y * (float)Math.Cos(a)) - c.X * (float)Math.Sin(a) + c.Y * (1 - (float)Math.Cos(a));

This code is equation of circle orbit, now, i want that is Elipse, can you help me?

[ThomasJohnsen]

I don't quite follow your code exactly. Why create a graphics object on the main form only to use it in the Paint event, in which a graphics object is already passed as a parameter. Also I think you're making this a tad more complicated than it is. Code below to hopefully give you what you need (or at least illustrate the principle):

RectangleF myrect = new RectangleF(300.0f, 150.0f, 30.0f, 30.0f);
        RectangleF myorbit = new RectangleF(200.0f, 100.0f, 115.0f, 65.0f);
        float ellipse_angle = 0.0f;
        float rotation_angle = 0.0f;
 
        private void Main_Paint(object sender, PaintEventArgs e)
        {
            e.Graphics.DrawEllipse(Pens.Red, myorbit.X, myorbit.Y, myorbit.Width, myorbit.Height);
 
            using (System.Drawing.Drawing2D.Matrix transformation = new System.Drawing.Drawing2D.Matrix() { })
            {
                transformation.Translate(myrect.X, myrect.Y);
                transformation.Rotate(rotation_angle);
                transformation.Translate(-myrect.X, -myrect.Y);
 
                e.Graphics.Transform = transformation;
            }
 
            e.Graphics.DrawRectangle(Pens.AntiqueWhite, myrect.X, myrect.Y, myrect.Width, myrect.Height);
        }
 
        private void timerxoay_Tick(object sender, EventArgs e)
        {
            ellipse_angle += (float)(Math.PI / 40.0);
            rotation_angle += (float)(Math.PI / 10.0);
            myrect.Location = new PointF(myorbit.X + (float)((Math.Cos(ellipse_angle) + 1.0) * myorbit.Width / 2.0),
                                         myorbit.Y + (float)((Math.Sin(ellipse_angle) + 1.0) * myorbit.Height / 2.0));
            this.Invalidate();
        }
 
        private void cmdrotate_Click(object sender, EventArgs e)
        {
            timerxoay.Enabled = !timerxoay.Enabled;
        }

Regards Tom

[Longbottomup]

I don't quite follow your code exactly. Why create a graphics object on the main form only to use it in the Paint event, in which a graphics object is already passed as a parameter. Also I think you're making this a tad more complicated than it is. Code below to hopefully give you what you need (or at least illustrate the principle):

RectangleF myrect = new RectangleF(300.0f, 150.0f, 30.0f, 30.0f);
        RectangleF myorbit = new RectangleF(200.0f, 100.0f, 115.0f, 65.0f);
        float ellipse_angle = 0.0f;
        float rotation_angle = 0.0f;
 
        private void Main_Paint(object sender, PaintEventArgs e)
        {
            e.Graphics.DrawEllipse(Pens.Red, myorbit.X, myorbit.Y, myorbit.Width, myorbit.Height);
 
            using (System.Drawing.Drawing2D.Matrix transformation = new System.Drawing.Drawing2D.Matrix() { })
            {
                transformation.Translate(myrect.X, myrect.Y);
                transformation.Rotate(rotation_angle);
                transformation.Translate(-myrect.X, -myrect.Y);
 
                e.Graphics.Transform = transformation;
            }
 
            e.Graphics.DrawRectangle(Pens.AntiqueWhite, myrect.X, myrect.Y, myrect.Width, myrect.Height);
        }
 
        private void timerxoay_Tick(object sender, EventArgs e)
        {
            ellipse_angle += (float)(Math.PI / 40.0);
            rotation_angle += (float)(Math.PI / 10.0);
            myrect.Location = new PointF(myorbit.X + (float)((Math.Cos(ellipse_angle) + 1.0) * myorbit.Width / 2.0),
                                         myorbit.Y + (float)((Math.Sin(ellipse_angle) + 1.0) * myorbit.Height / 2.0));
            this.Invalidate();
        }
 
        private void cmdrotate_Click(object sender, EventArgs e)
        {
            timerxoay.Enabled = !timerxoay.Enabled;
        }

Regards Tom

Thanks for your help, it work, but i still question, we can't edit this function to get my elipse?????

private PointF XoayDiemTamC(PointF p, PointF c, double a)
        {
            PointF Q = new PointF();
            Q.X = p.X * (float)Math.Cos(a) - p.Y * (float)Math.Sin(a) + c.X * (1 - (float)Math.Cos(a)) + c.Y * (float)Math.Sin(a);
            Q.Y = p.X * (float)Math.Sin(a) + (p.Y * (float)Math.Cos(a)) - c.X * (float)Math.Sin(a) + (c.Y * (1 - (float)Math.Cos(a)));
            return Q;
        }

We can get it on this code????
In addition, in your code, how to change the coordinate axis. In this form, the coordinate axis of your elips is:

How to custum the tilt of elip by my favourite?
Thanks again, nice help, thank you.

[Longbottomup]

All right, this problem solved. Thanks

[ThomasJohnsen]

It's really not that complex linear algebra.
An ellipse in 2d at origin is determined by

e(phi) = (r1 * cos(phi), r2 * sin(phi))

Change in coordinate matrices are simply rotations around the origin (without mirroring), and can be described as:

           [ cos(theta) -sin(theta) ]
R(theta) = [ sin(theta)  cos(theta) ]

,
so the formula for a rotated ellipse at origin would be:

e(phi)R(theta) = (r1 cos(phi)cos(theta) + r2 sin(phi)sin(theta), r2 sin(phi)cos(theta) - r1 cos(phi)sin(theta))

The example below should illustrate this (though you should know, that using trigonometry to draw arcs is highly inefficient):

// This sub can be made many many times more efficient by using properties of the ellipse equation
        // sqr(x/a) + sqr(y/b) = 1 (using derivatives and the fact, that there are 4 identical quadrants).
        // There are plenty of highly efficient circle/ellipse algorithm to be found online.
        // I decided to keep this simple, using trigonometry, since speed is obviously not your primary concern.
        private void draw_rotated_ellipse(Graphics g, float theta, RectangleF ellipse)
        {
            PointF xaxis = new PointF((float)Math.Cos(theta), (float)Math.Sin(theta));
            PointF yaxis = new PointF(-(float)Math.Sin(theta), (float)Math.Cos(theta));
            PointF ellipse_point;
            PointF current;
            PointF previous = PointF.Empty;
 
            float delta_phi = (float)(Math.PI / 20.0);
 
            for (float phi = 0.0f; phi <= (float)(2.0 * Math.PI); phi += delta_phi)
            {
                // Ellipse equation for an ellipse at origin.
                ellipse_point = new PointF((float)(ellipse.Width * Math.Cos(phi)), (float)(ellipse.Height * Math.Sin(phi)));
 
                // Apply the rotation transformation and translate to new center.
                current = new PointF(ellipse.Left + (ellipse_point.X * xaxis.X + ellipse_point.Y * xaxis.Y),
                                     ellipse.Top + (ellipse_point.X * yaxis.X + ellipse_point.Y * yaxis.Y));
 
                if (previous != PointF.Empty) g.DrawLine(Pens.Red, previous, current);
 
                previous = current;
            }
        }
 
        // This sub is pretty much identical to the one above, so not much explanation needed.
        private void draw_rect_at_ellipse(Graphics g, float theta, RectangleF ellipse, float phi, RectangleF rect)
        {
            PointF xaxis = new PointF((float)Math.Cos(theta), (float)Math.Sin(theta));
            PointF yaxis = new PointF(-(float)Math.Sin(theta), (float)Math.Cos(theta));
            PointF ellipse_point;
 
            // Ellipse equation for an ellipse at origin.
            ellipse_point = new PointF((float)(ellipse.Width * Math.Cos(phi)), (float)(ellipse.Height * Math.Sin(phi)));
 
            // Apply the rotation transformation and translate to new center.
            rect.Location = new PointF(ellipse.Left + (ellipse_point.X * xaxis.X + ellipse_point.Y * xaxis.Y),
                                       ellipse.Top + (ellipse_point.X * yaxis.X + ellipse_point.Y * yaxis.Y));
 
            g.DrawRectangle(Pens.AntiqueWhite, rect.X, rect.Y, rect.Width, rect.Height);
        }

and replace the paint event handler with:

            draw_rotated_ellipse(e.Graphics, ellipse_angle, myorbit);
            draw_rect_at_ellipse(e.Graphics, ellipse_angle, myorbit, rotation_angle, myrect);

Tom

[Longbottomup]

Yeah, thanks, you are thoughtful, my problem solved, ^_^