Projecting distance for Unit Vector

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SUMMARY

The discussion focuses on calculating the unit vector for a non-orthogonal Cartesian grid using the formula Ue = (dy/se)i - (dx/se)j, where Se = sqrt(dx² + dy²). The user seeks clarification on how to project distances onto the i and j axes and inquires about the definition of the inner product in this context. The formula provided is essential for determining the unit vector based on the east face of a cell.

PREREQUISITES
  • Understanding of Cartesian coordinates and non-orthogonal grids
  • Familiarity with vector mathematics and unit vectors
  • Knowledge of surface area calculations in geometry
  • Basic grasp of inner product definitions in linear algebra
NEXT STEPS
  • Research vector projection techniques in non-orthogonal coordinate systems
  • Study the concept of inner products in vector spaces
  • Explore applications of unit vectors in computational geometry
  • Learn about surface area calculations for irregular shapes
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Mathematicians, physicists, computer graphics developers, and anyone involved in computational geometry or vector analysis.

andykol
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Hello,
I am calculating Unit vector for non orthogonal Cartesian grid. To calculate Unit Vector I need to project eg. y and x distance of east face of cell on i and j axis resp. I am using following formula-
Unit vector= Ue
Surface area= Se=sqrt(dx2+dy2)

Ue=(dy/se)i-(dx/se)j

Can anybody please tell me how I can calculate projection?
 
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How are you defining the inner product?
 

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