Difference between revisions of "3D Fundamentals Tutorial 3"
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| − | * | + | * How does sight (the Retina) work? How do we see 3D? [https://youtu.be/cN97hkDrzcc?t=0m26s 0:26] |
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| − | :* . | + | :* The retina is basically a 2D image sensor array |
| + | :* It projects 3D space onto a 2D interpretation | ||
| + | :* There are numerous cues to allow us to perceive 3D. One is rotating an image along various axes | ||
</div> | </div> | ||
| + | * Applying 3D rotation to our cube [https://youtu.be/cN97hkDrzcc?t=1m46s 1:46] | ||
| + | * Deriving the three 3D rotation matrices (around the x,y,z axes) [https://youtu.be/cN97hkDrzcc?t=5m16s 5:16] | ||
| + | * Implementing rotation matrices in the <code>Mat3</code> class [https://youtu.be/cN97hkDrzcc?t=8m25s 8:25] | ||
| + | * How to rotate around any orientation? Concatentate the matrices [https://youtu.be/cN97hkDrzcc?t=14m17s 14:17] | ||
| + | * Switching between multiple 3D interpretations by your brain [https://youtu.be/cN97hkDrzcc?t=16m18s 16:18] | ||
| + | * The order of concatenation in 3D rotation matters [https://youtu.be/cN97hkDrzcc?t=17m29s 17:29] | ||
| + | <div class="mw-collapsible-content"> | ||
| + | :* The transformation is not commutitive and different orders result in different orientations | ||
| + | :* Just pick one order and stich with it. As long as you're consistent, there is no problem | ||
| + | </div> | ||
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Revision as of 01:45, 28 April 2020
In this video we start from the canonical 2D rotation transformation matrix and extend it to 3D to derive rotation around the Z, Y, and X-axes. We also jerk off said axes, using the left-hand rule of course (right hand is busy with the mouse).
Contents
2D Rotation
For an in-depth explanation / derivation of the formula for 2D rotation, check out this video. There is also another video in the same series that deals with encoding transformations in matrices, and it can be found here.
Video
The tutorial video is on YouTube here.
- How does sight (the Retina) work? How do we see 3D? 0:26
- The retina is basically a 2D image sensor array
- It projects 3D space onto a 2D interpretation
- There are numerous cues to allow us to perceive 3D. One is rotating an image along various axes
- Applying 3D rotation to our cube 1:46
- Deriving the three 3D rotation matrices (around the x,y,z axes) 5:16
- Implementing rotation matrices in the
Mat3class 8:25 - How to rotate around any orientation? Concatentate the matrices 14:17
- Switching between multiple 3D interpretations by your brain 16:18
- The order of concatenation in 3D rotation matters 17:29
- The transformation is not commutitive and different orders result in different orientations
- Just pick one order and stich with it. As long as you're consistent, there is no problem
Downloads
The GitHub repository for the tutorial code is here.
