Get vector position projected on line

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SUMMARY

The discussion focuses on projecting a point from the minimum bounds of a rectangle onto a line defined by connected points. The goal is to achieve a general solution that remains valid even if the shapes are rotated, specifically by 45 degrees. Participants suggest using vector mathematics, particularly cross products, to determine the projection accurately. The conversation clarifies the definitions of "maxs and mins" in the context of a rectangle and emphasizes the need for a robust mathematical approach to handle geometric transformations.

PREREQUISITES
  • Understanding of vector mathematics and projections
  • Familiarity with geometric transformations, including rotation
  • Knowledge of cross products in vector calculus
  • Basic concepts of coordinate systems and their applications
NEXT STEPS
  • Research vector projection techniques in computational geometry
  • Learn about cross products and their applications in 2D and 3D space
  • Explore geometric transformations, focusing on rotation matrices
  • Study algorithms for point-line distance calculations in graphics programming
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This discussion benefits mathematicians, computer graphics developers, and engineers working on geometric algorithms or spatial transformations in applications such as CAD software or game development.

twoski
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Let's say i have a set of lines (denoted in the image as connected at the blue dots) and a rectangle with maxs and mins known (denoted with orange dots).

I want to project from the mins of my rectangle such that i get a point on the line below it (the green dot). Furthermore, this needs to be a general solution (ie if the shapes were all rotated 45 degrees i'd still get the same results).

There must be some trick with cross products or something that I'm not seeing here, any insights?

Here is the picture to help make it clear.

ShmKXMo.png
 
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What are the "maxs and mins" of a rectangle? How do the two orange dots define these? How would this work if "the shapes were all rotated 45 degrees"?

This is nothing to do with differential geometry.
 

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