3D to 2D Projection Formula: PROOF
In this video I derive the formula for projecting 3D coordinates onto a 2D screen using similar triangles. First I plot out the coordinates in 3D and then draw a straight line from the point where we are projecting the coordinates and onto the x = 0 plane. The point of projection can be thought of as the point at which our camera or eyes are located at, thus the resulting 2D projection maintains 3D perspective from that specific point. Drawing a second line passing through the z coordinates of the 3D line, we can see two similar triangles. Either of the similar triangles can be used to obtain identical formulas for the y and z projection coordinates. Note that in this projection derivation, I project the x coordinates to x = 0 and the camera or eyes location is at x = 1000. Epic stuff!
The timestamps of key parts of the video are listed below:
- Projecting 3D coordinates to 2D coordinates: 0:00
- Two Similar Triangles: 2:45
- Determining the formula for the y and z projection: 4:41
- 3D to 2D projection formula: 8:53
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
Related Videos:
Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
------------------------------------------------------
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
Like, Subscribe, Favorite, and Comment Below!
Follow us on:
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
MORE Links: https://linktr.ee/matheasy
Email me: contact@mes.fm
Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
-
13:39
Math Easy Solutions
17 days ago $0.06 earnedCell Theory: Introduction and Fertilization
1802 -
18:44
We Profit with Stock Curry
6 days agoUltimate Advice for Teens & Young Adults
37.2K13 -
LIVE
Lofi Girl
1 year agoSynthwave Radio 🌌 - beats to chill/game to
183 watching -
21:00
Mr. Build It
23 days ago3 Ways to Build Garden Beds
33.6K14 -
1:42:14
Jewels Jones Live
1 day agoDETRANS w/ special guest Mary Margaret Olohan | A Political Rendezvous - Ep. 78
39.7K21 -
1:36:46
Roseanne Barr
1 day ago $73.82 earnedFor Love of Country with Tulsi Gabbard | The Roseanne Barr Podcast #50
155K431 -
6:28:15
CHiLi XDD
14 hours ago[D2] Rumble Featured!! Lets Go!!! #RumbleTakeOver
47.5K7 -
2:45
Chicks in the Office
12 hours agoHolly Madison Talks Reconciliation with Kendra Wilkinson
61K38 -
7:58:23
Di bear
14 hours agoFinal Season Mission, Pantheon | Destiny 2
64.7K7 -
6:54:43
SquallRush
16 hours agoAthenian Rhapsody!
56.4K8