How Can I Understand 3D Rotation Matrices Like 2D?

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SUMMARY

The discussion focuses on understanding 3D rotation matrices by drawing parallels with 2D rotation matrices. The user references the 2D rotation formulas and matrix, specifically x' = x cos θ - y sin θ and y' = x sin θ + y cos θ, represented in matrix form as [cos θ -sin θ] [sin θ cos θ]. A request for a similar explanation for 3D rotation matrices is made, with a suggestion to consult the Wikipedia page on Euler angles for further clarification.

PREREQUISITES
  • Understanding of 2D rotation matrices
  • Familiarity with trigonometric functions (sine and cosine)
  • Basic knowledge of 3D coordinate systems
  • Concept of Euler angles in 3D transformations
NEXT STEPS
  • Study 3D rotation matrices and their derivations
  • Learn about Euler angles and their applications in 3D graphics
  • Explore quaternion representation for 3D rotations
  • Investigate the use of rotation matrices in computer graphics libraries like OpenGL
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Students and professionals in computer graphics, robotics, and physics who need to understand 3D transformations and rotations in their work.

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I am having a hard time figuring out 3d rotation matrices expression.
After much search, I got 2D - http://www.siggraph.org/education/materials/HyperGraph/modeling/mod_tran/2drota.htm
With 2d,
x'=xcos t - ysin t
y'=xsin t + ycos t

and the matrix is :
[cos t -sin t]
[sin t cos t]

but where can I find a similar explanation for 3d? Can someone pls explain.
 
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