Virtual Reconstruction

2D Transformations Applet


  • This applet lets you explore the math behind object transformations in a plane.
  • The plane is shown in the left frame (grid width: 10 units). At the outset, an object (a square or a mandible) is centered at the coordinate origin.
  • The middle panel contains input fields for translation, rotation and scaling and the matrix stack ("Initial Scene")
  • The right panel contains two 3x3 matrices, the Current Transformation Matrix, and the Total Transformation Matrix.
  • Here is an example how to use the applet:
    • translate the object by 10 units in x-directions and by 20 units in y-direction (input the respective values in the transformation fields, then press apply translation).
    • the object will be moved correspondingly; the matrix stack will show the corresponding transformation, and the Current Transformation Matrix will show how your input values appear in the matrix that will be multiplied with previous tranformations.
    • apply a rotation by 30 degrees (proceed in analogy to the first step).
    • the current transformation matrix shows how this rotation looks like as a matrix multiplication
    • the new transformation is added to the matrix stack; these transformations are concatenated to obtain their combined effect of translation and rotation
    • the total transformation matrix now contains the multiplication of the translation and the rotation matrices.
    • as you apply additional transformations, the matrix stack will grow steadily.
  • And here are some additional hints:
    • you can step through the stack to review the temporal sequence of transformations applied to the object (a simple animation!) and delete selected transformations.
    • you may modify any transformation by typing into the input fields of the Current Transformation Matrix (use the return key on your keyboard to input values; note: only the first two rows can be modified; the last row contains characteristic values of homogeneous transformation matrices).
    • Explore rotation about a specified point (use the x and y fields in the rotation panel)
    • Try to simulate taphonomic compression of a fossil mandible and its virtual correction (see Ch.6)
0. Introduction
1. Virtual Reconstruction
2. Data Representation
Data Format Applet
Color Applet
3. Data Acquisition
4. Image Data Processing
Filter Applet
5. Visualization and Interaction
Transformation Applet
Software Hints
6. Virtual Fossil Reconstruction
Software Hints
7. From VR to RV
8. Morphometric analysis
Figure 8.23 (color)

Available from John Wiley & Sons

Virtual Reconstruction:
A Primer in Computer-Assisted Paleontology and Biomedicine

Virtual Reconstruction: A Primer in Computer-Assisted Paleontology and Biomedicine

Christoph P. Zollikofer,
Marcia Ponce de Leon

ISBN: 0-471-20507-9
333 pages
June 2005

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