Name: Putting 3D in Perspective: Projecting a 3D Rectangle to 2D
Uploaded: 2023-10-31T05:01:46+00:00
Duration: 53 min 51 s
Description: 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 rect

2 years ago

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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