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# 3D Rotation in 2D

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I'm trying to render some dots to the screen using just 2D and rotate them when my mouse moves across the screen so it looks like a rotating cube. I'm having issues with the rotation equations, and I am sure I have them wrong somewhere. Here is my program (in C#):

using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Windows.Forms; using System.Drawing; namespace 3DRotation { class Program : Form { Font f; float mouseX, mouseY; float oldMouseX, oldMouseY; Point3D[] points; float pointOffsetX = 50; float pointOffsetY = 50; public Program() { f = new Font("Courier New", 12); points = new Point3D[8]; points[0] = new Point3D(-25, -25, -25); points[1] = new Point3D(-25, 25, -25); points[2] = new Point3D(25, -25, -25); points[3] = new Point3D(25, 25, -25); points[4] = new Point3D(-25, -25, 25); points[5] = new Point3D(25, -25, 25); points[6] = new Point3D(-25, 25, 25); points[7] = new Point3D(25, 25, 25); this.MouseMove += new MouseEventHandler(onMouseUp); this.Paint += new PaintEventHandler(painter); this.DoubleBuffered = true; } public void onMouseUp(object sender, MouseEventArgs e) { oldMouseX = mouseX; oldMouseY = mouseY; mouseX = e.X; mouseY = e.Y; foreach (Point3D point in points) { point.rotateX((oldMouseX - mouseX) / 100); point.rotateY((oldMouseY - mouseY) / 100); } this.Text = "Mouse Position: " + mouseX + ", " + mouseY; this.Invalidate(); } public void painter(object sender, PaintEventArgs e) { Pen p = new Pen(Brushes.Black, 1); foreach (Point3D point in points) { e.Graphics.FillEllipse(Brushes.Black, (float)point.x + pointOffsetX, (float)point.y + pointOffsetY, 5, 5); } } static void Main(string[] args) { Application.Run(new Program()); } class Point3D { public double x, y, z; public Point3D(double x = 0d, double y = 0d, double z = 0d) { this.x = x; this.y = y; this.z = z; } //In rotateX, the point is rotated around the X-axis at 0, 0. //x should remain the same, while y and z rotate. public void rotateX(double radians) { System.Console.WriteLine(radians); y = (y * Math.Cos(radians)) - (z * Math.Sin(radians)); z = (y * Math.Sin(radians)) + (z + Math.Cos(radians)); } //In rotateY, the point is rotated around the Y-axis at 0, 0. //y should remain the same, while x and z rotate. public void rotateY(double radians) { x = (x * Math.Cos(radians)) - (z * Math.Sin(radians)); z = (x * Math.Sin(radians)) + (z + Math.Cos(radians)); } } } } 

I'm using my own 3D point class to hold the x, y, and z values, but when I draw it to the screen I only really use x and y. (I will use z later for scale)

Can someone who knows 3D rotation functions tell me what I am doing wrong?

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Rewrite the 2 occurrences of

 z = (x * Math.Sin(radians)) + (z + Math.Cos(radians)); 
to look like

 z = (x * Math.Sin(radians)) + (z * Math.Cos(radians)); 

Where to use +sine and where to use -sine is a convention. And how to map mouse pointer movement to rotation also. And whether the chosen composition of rotations is what you want in the end has to be investigated, too. Hence, after correcting the above shown mistake the result may still not look at expected.

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Also, notice that you first assign a value to x and you then use x when computing the new value for z, but you really wanted to use the old value of x. This is a common mistake.