Putting 3D in Perspective: Projecting a 3D Rectangle to 2D
In this video I project a 3D rectangle onto a 2D screen, while also removing a segment of a line that is behind the rectangle so that it maintains its 3D perspective. I first project the given 3D rectangle coordinates using the 3D to 2D projection equation I derived earlier. Then, I determine the point of intersection of the 3D rectangle and 3D line. The next point that is needed is the point of intersection of the projected 2D line and the bottom portion of the projected 2D rectangle. Once I solve for these, I use GeoGebra to plot the projected line while removing the portion that is behind the rectangle. The resulting 3D chart is truly amazing! https://www.geogebra.org/calculator/twezjbu5
The timestamps of key parts of the video are listed below:
- Question 4: Projecting a 3D rectangle to 2D: 0:00
- Solution: Graphing out the rectangle and its projection in GeoGebra: 1:04
- Remove the portion of the line behind the rectangle: 6:12
- Find point of intersection of the 3D line and rectangle: 7:15
- Determining the equation of the plane of the rectangle: 7:47
- Cross product to get the plane normal vector: 15:48
- Calculating the equation of the plane: 21:12
- Plugging in the line equation into the rectangle equation: 27:03
- Graphing the intersection point in GeoGebra: 32:18
- Finding the point of intersection of the projected line and rectangle: 35:03
- Vector equation of bottom right portion of projected rectangle: 38:08
- Equating the projected line equation with the bottom right rectangle line equation: 41:07
- Calculating the point of intersection of projected line and rectangle: 47:10
- Graphing it all out in GeoGebra: 50:30
This video was taken from my earlier video listed below:
p
- 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
-
11:28
Math Easy Solutions
4 days ago $0.03 earnedLaboratory Project: Taylor Polynomials: Question 1: Quadratic Approximation
1141 -
7:03
Chris Jericho
1 day agoTalk Is Jericho Highlight: Alien Encounters With Mitch Horowitz
9.38K3 -
3:01:45
SNEAKO
8 hours agoSUMMER IS HERE… SPECIAL GUEST
77.8K43 -
1:07:00
Russell Brand
1 day ago“Something BIG is about to happen” - EXCLUSIVE Alex Jones Interview on INFOWARS shut down - 391
442K2.41K -
2:06:37
Steven Crowder
2 days agoREBUTTAL: Jon Stewart is WRONG about Gun Violence
526K914 -
LIVE
Right Side Broadcasting Network
7 days agoLIVE: President Trump Holds a MAGA Rally in Philadelphia - 6/22/24
4,064 watching -
21:49
Stephen Gardner
12 hours ago🔴BREAKING: GAME OVER! Congress EXPOSED for abusing security clearance to ENRICH THEMSELVES!!
90.7K156 -
1:47:21
Candace Owens
1 day agoThe Great Debate: Israel v Palestine | Candace Ep 10
59.4K257 -
2:49:14
Jewels Jones Live ®
1 day agoBIDEN'S DECLINE | A Political Rendezvous - Ep. 81
94.2K36 -
23:11
Chicks in the Office
17 hours agoFinish This Quote From Miss Congeniality - Pop Culture Trivia: Beat Ria & Fran Game 129
83.8K4