Mapping 3D point to cone surface using perpendicular line

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SUMMARY

The discussion focuses on mapping a 3D point to a cone surface using perpendicular lines, specifically addressing the calculation of the gradient m3. The solution involves solving simultaneous equations of the straight line functions m1 and m2, which are perpendicular to each other. The bottom diagram presented in the discussion does not accurately represent the solution process. This clarification is crucial for understanding the geometric relationships involved in the mapping process.

PREREQUISITES
  • Understanding of 3D geometry and coordinate systems
  • Knowledge of simultaneous equations and their applications
  • Familiarity with gradients and their geometric interpretations
  • Basic skills in visualizing geometric diagrams and relationships
NEXT STEPS
  • Study the principles of 3D geometry and coordinate transformations
  • Learn how to solve simultaneous equations in multiple dimensions
  • Explore the concept of gradients in vector calculus
  • Investigate geometric interpretations of perpendicular lines in 3D space
USEFUL FOR

Mathematicians, engineers, computer graphics developers, and anyone involved in 3D modeling or geometric computations will benefit from this discussion.

mamort
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Can someone please look at the diagram below and tell me how u1 is obtained. If it is through the use of m3 please explain how the gradient m3 is obtained.

Geometric Problem (v1.3).jpg
 
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Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
Thanks for monitoring this problem, I have now found the solution which is achieved by solving simultaneous equations of both straight line functions (m1 and m2) that are perpendicular in the top diagram above. The bottom diagram is NOT how the solution is achieved.
 

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