Transformations: Scaling

Step 1: Understanding Controls and Features

  • Familiarize yourself with the mouse and touch controls listed under Mouse Controls and Mobile Touch Controls. Understand how left-click, right-click, scrolling, and touch gestures translate, rotate, and zoom the simulation.
  • Learn about locking options such as Lock Graph, Lock Zoom, and Lock Rotate to understand how they restrict specific functionalities in the simulation.

Step 2: Shape Manipulation

  • Explore the Shape Controls section. Practice adding, selecting, editing, and deleting shapes using the corresponding buttons (Add, Edit, Delete). Note the instructions regarding shape placement and the warnings about avoiding overlapping coordinates.

Step 3: Understanding Default Scaling

  • Note that shapes in the simulation start with default scaling values:
    • X-axis: 3 (width is 3 times the base size)
    • Y-axis: 2 (height is 2 times the base size)
    • Z-axis: 2 (depth is 2 times the base size)
  • Use the Reset button to return to these default values at any time.

Step 4: Scaling and Transformation

  • In the Scaling Controls section, you can adjust the scaling factors for X, Y, and Z axes:
    • Values > 1: Increase the size from the base size
    • Values = 1: Return to base size for that dimension
    • Values < 1: Decrease the size from the base size
  • Examples of what to expect:
    • X=3, Y=2, Z=2: Default size (3× wider, 2× taller, 2× deeper than base)
    • X=1, Y=1, Z=1: Base size (smaller than default)
    • X=6, Y=4, Z=4: Double the default size
    • X=1.5, Y=1, Z=1: 1.5× wider than base size

Step 5: Using the Slider for Smooth Scaling

  • Important: The slider is used to smoothly transition between the current size and the target size
  • Critical Steps:
    1. First, set your desired X, Y, Z values in the input fields
    2. Click Apply Scaling to set these as your target values
    3. Only then use the slider to see the smooth transition
  • The slider will:
    • Start at 0 (current size)
    • End at 1000 (target size you set)
    • Show smooth scaling animation as you move it
  • Warning: Moving the slider before clicking Apply Scaling will not show the correct scaling effect

Step 6: Grid Options and Visualization

  • Use the Grid Options section to toggle:
    • XY-grid: Shows the horizontal plane
    • YZ-grid: Shows the vertical plane on the right
    • XZ-grid: Shows the vertical plane on the left
  • These grids help visualize the scaling effects in 3D space

Step 7: Best Practices

  • Always follow this sequence:
    1. Set your desired X, Y, Z values
    2. Click Apply Scaling
    3. Then use the slider to see the transition
  • Use the Reset button to return to default values
  • Ensure the slider is at zero before making new adjustments
  • Observe how the shape's proportions change relative to the grid lines
  • Compare the visual changes with the values in the transformation matrix

Step 8: Experimentation

  • Try these exercises to understand scaling:
    1. Reset to defaults (X=3, Y=2, Z=2)
    2. Set X=1, Y=1, Z=1 and click Apply Scaling
    3. Move the slider to see the transition to base size
    4. Set X=2, Y=2, Z=2 and click Apply Scaling
    5. Move the slider to see uniform scaling
    6. Experiment with different values for each axis:
      • Set new values
      • Click Apply Scaling
      • Use the slider to observe the transition
    7. Try the slider at different speeds to understand the animation