Putting 3D in Perspective Question 2: Projecting a 3D Line to 2D

about 1 year ago

In this video I first derive the formula for projecting a 3D point to a 2D screen and then apply that formula to the 3D line from the previous question. To project a 3D image onto a 2D screen, we just have to draw a line extending from the camera or viewpoint that intersects our desired point and extends to the screen. Then applying similar triangles, we can derive the projected coordinates for the y and z coordinates; note that the x-coordinates in this case all get projected to x = 0. Next we apply the derived formula to the clipped 3D line points from Question 1 to obtain the projected coordinates on the 2D screen. And as always, I graph this all out using the amazing GeoGebra 3D graphing calculator: https://www.geogebra.org/calculator/twezjbu5

The timestamps of key parts of the video are listed below:

Question 1: Projecting Clipped 3D Line to 2D: 0:00
Solution: Deriving 3D to 2D projection equation: 0:12
Applying similar triangles: 7:18
Projecting the clipped points of the 3D line: 10:51
Graphing with GeoGebra: 14:31

This video was taken from my earlier video listed below:

Laboratory Project: Putting 3D in Perspective: https://youtu.be/3txedAqdtkQ
HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective
Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK