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In drawing tutorials on how to give a drawing the '3d -effect', the concept of vanishing line is brought up. I don't exactly understand it, but it seems so that all parallel lines on the object that we draw intersect at a point on the vanishing line.

Could a more detailed description of what is going on with the vanishing line be given using projective geometry concepts in mathematics? My main doubts is how exactly is it that the vanishing lines allow us to give the 3D effect to the drawings we make. Like what mathematical idea is underlying it?

tryst with freedom
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  • https://en.wikipedia.org/wiki/Projective_plane This might be a good starting point. – Raad Shaikh Mar 27 '22 at 05:59
  • I order to understand it, it's may be very useful to have an algebraic point of view through the general concept of using $n+1$ (homogeneous) coordinates for describing a $n$-dimensional point. Either by having a special status for the $n+1$st coordinate, or by giving them the normalization rule $\sum_{i=1}^{n+1} x_i=1$ ; in this case, you work on barycentric coordinates ; I strongly advise you to work on them (also called tetrahedral coord. in 3D) : you can understand/explain every projective concept within this "theory" with a physical intuition through "weighing' interpretation. – Jean Marie Mar 27 '22 at 08:19
  • Could you more details in the bary centric interpretation? Perhaps some links which extend the idea a bit more? – tryst with freedom Mar 27 '22 at 08:21
  • Here is an interesting document establishing a bridge between the two "worlds" (barycentric coordinates vs. homogeneous coordinates used in projective geometry) – Jean Marie Mar 28 '22 at 08:35

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