Geometric formulas of linear perspective

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SUMMARY

The discussion centers on the challenge of translating three-dimensional Cartesian coordinates onto a two-dimensional surface using geometric formulas for linear perspective. The original poster has identified three specific formulas applicable to different viewpoints but expresses frustration over the incomplete nature of linear perspective since the Renaissance. They seek assistance from mathematicians to derive the algebraic foundations behind these geometric formulations. Relevant resources include personal notes shared online and a raytraced image example illustrating the concept.

PREREQUISITES
  • Understanding of three-dimensional Cartesian coordinates
  • Familiarity with geometric principles of linear perspective
  • Basic knowledge of algebraic formulations
  • Experience with ray tracing techniques in computer graphics
NEXT STEPS
  • Research the mathematical foundations of linear perspective
  • Explore the relationship between geometry and algebra in 3D to 2D translations
  • Study ray tracing algorithms and their application in visualizing perspective
  • Investigate historical developments in perspective techniques since the Renaissance
USEFUL FOR

Artists, mathematicians, and computer graphics professionals interested in the principles of linear perspective and its mathematical underpinnings.

theophoretos
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10 years ago i tried (as an artist) to solve the problem of how to translate the 3 dimensional cartesian coordinate onto the 2 dimensional surface with the precise foreshortening. I've only ever figured out 3 formulas for 3 different standpoints... then i gave up. now i recollected my notes, and put them on line.

http://www.geocities.com/easternhistory/perspective.html

the linear perspective developed since the renaissance has never been complete. these 3 formulas are the only completed one i know of. can any math persons figure out the algebraic situation behind this geometric formulation of the translation of 3 d onto the 2 d?

:frown:
 
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