Coding Challenge #113: 4D Hypercube (aka "Tesseract")

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Published on August 22, 2018 1:53:53 PM ● Video Link: https://www.youtube.com/watch?v=XE3YDVdQSPo

Duration: 43:53

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In this coding challenge, I visualize a 4D Hypercube (aka "Tesseract") in Processing (Java). Code: https://thecodingtrain.com/challenges/113-4d-hypercube-aka-tesseract

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References:
🔢 Matrix Multiplication: http://matrixmultiplication.xyz
🗄 Rotation Matrix on Wikipedia: https://en.wikipedia.org/wiki/Rotation_matrix
🗄 3D Projection on Wikipedia: https://en.wikipedia.org/wiki/3D_projection
🗄 Tesseract on Wikipedia: https://en.wikipedia.org/wiki/Tesseract

Videos:
🎥 Understanding 4D -- The Tesseract: https://youtu.be/iGO12Z5Lw8s
🚂 3D Rendering with Rotation and Projection: https://youtu.be/p4Iz0XJY-Qk
🚂 Matrix Math: https://youtu.be/uSzGdfdOoG8
🚂 Matrix Multiplication for 3D Rendering: https://youtu.be/tzsgS19RRc8
🔴 Coding Train Live 148.2: https://youtu.be/M_YNwb7UudI?t=1370s

Related Coding Challenges:
🚂 #112 3D Rendering with Rotation and Projection: https://youtu.be/p4Iz0XJY-Qk

Timestamps:
0:00 Introducing today's topic: rendering a 4D hypercube
7:30 Create a P4Vector class
9:43 Extend the points array to have 16 points
13:06 Create the projection matrix
16:16 Stereographic projection
18:04 Connect the points
22:17 Add an offset to the connect function
26:26 Create rotation in the 4th dimension
29:49 Create a rotationXY matrix
36:52 Rotate around the w axis
40:23 We have now entered the 4th dimension!!
40:58 What dimension could you visualize?

Editing by Mathieu Blanchette
Animations by Jason Heglund
Music from Epidemic Sound

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🔗 Processing: https://processing.org

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#3drendering #orthographicprojection #rotationmatrix #4dhypercube #tesseract #processing