Overview

This experiment demonstrates 3D transformations including translation, rotation, and scaling in a 3D space. The simulation allows you to manipulate 3D shapes (Cube, Tetrahedron, and Octahedron) using various transformation controls.

Step-by-Step Procedure

1. Initial Setup

• The simulation starts with three default shapes: a Cube, a Tetrahedron, and an Octahedron
• Each shape is positioned at different coordinates in 3D space
• The coordinate system is displayed with colored axes (Red for X, Yellow for Y, Blue for Z)

2. Shape Selection

1. Click the "Select" button next to any shape in the shape list
2. The selected shape will be highlighted with a yellow outline
3. Only one shape can be selected at a time
4. The shape's current position will be displayed in the edit modal

3. Rotation Transformation

1. Select a shape using the "Select" button
2. In the Rotation Controls section:
   • Choose the rotation axis (X, Y, or Z) from the dropdown menu
   • Enter the desired rotation angle ($\theta$) in degrees
   • Click "Change Axis" to set the rotation axis
3. Use the slider to control the rotation:
   • Moving the slider from 0 to 1000 will rotate the shape from 0° to the specified angle
   • The rotation will be smooth and continuous
   • The transformation matrix will update in real-time
4. The rotation follows the right-hand rule:
   • X-axis rotation: Counter-clockwise when looking from positive X
   • Y-axis rotation: Counter-clockwise when looking from positive Y
   • Z-axis rotation: Counter-clockwise when looking from positive Z

4. Translation Transformation

1. Select a shape using the "Select" button
2. In the Translation Vector section:
   • Enter the desired X, Y, and Z translation values
   • Click "Apply Translation" to set the translation vector
3. Use the slider to control the translation:
   • Moving the slider from 0 to 1000 will move the shape from its original position to the target position
   • The movement will be smooth and continuous
   • The transformation matrix will update in real-time

5. Scaling Transformation

1. Select a shape using the "Select" button
2. In the Scaling Controls section:
   • Enter the desired X, Y, and Z scaling factors
   • Click "Apply Scaling" to set the scaling factors
3. Use the slider to control the scaling:
   • Moving the slider from 0 to 1000 will scale the shape from its original size to the target size
   • The scaling will be smooth and continuous
   • The transformation matrix will update in real-time

6. Additional Controls

• Use the grid checkboxes to toggle the visibility of XY, YZ, and XZ grids
• Use the lock options to restrict mouse interactions:
  • Lock Graph: Prevents translation
  • Lock Zoom: Prevents zooming
  • Lock Rotate: Prevents rotation
• Click "Reset All" to return all shapes to their initial positions and reset all transformations

7. Transformation Matrix

• The 4x4 transformation matrix is displayed in real-time
• It shows the current transformation being applied to the selected shape
• The matrix updates as you move the slider
• The matrix components represent:
  • Top 3x3: Rotation and scaling
  • Last column: Translation
  • Last row: [0, 0, 0, 1] for affine transformations

Notes

• Always ensure the slider is at zero before making new transformations
• The shape must be selected before applying any transformation
• The transformation matrix helps visualize the mathematical representation of the transformations
• The right-hand rule is used for rotation directions to maintain consistency