- 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)