Updated tutorial_transforms (markdown)
@ -57,14 +57,14 @@ Doing this to the selected point will move it back to the center:
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This was expected, but then let's do something more interesting. Use the dot product of X and the point, and add it to the dot product of Y and the point:
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```python
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var final_pos = x.dot(new_pos) + y.dot(final_pos)
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var final_pos = x.dot(new_pos) + y.dot(new_pos)
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```
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Then what we have is.. wait a minute, it's the ship in it's design position!
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<p align="center"><img src="images/tutomat9.png"></p>
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How did this black magic happen? The ship was lost in space, and now it's back home!
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It might seem strange, but it does have plenty of logic. Remember, as we have seen in the [previous tutorial](tutorial_vector_math#distance-to-plane), what happened is that the distance to X axis, and the distance to Y axis were computed. This was enough to obtain back the design coordinates for every point in the ship.
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It might seem strange, but it does have plenty of logic. Remember, as we have seen in the [previous tutorial](tutorial_vector_math#distance-to-plane), what happened is that the distance to X axis, and the distance to Y axis were computed. Calculating distance in a direction or plane was one of the uses for the dot product. This was enough to obtain back the design coordinates for every point in the ship.
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So, what he have been working with so far (with X, Y and Origin) is an **Oriented Coordinate System**. X an Y are the **Basis**, and **Origin** is the offset.
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