Putting 3D in Perspective Question 1: What Points Should Be Clipped?

In this video I go over Question 1 of the Laboratory Project: Putting 3D in Perspective and this time determine the points at which a 3D line needs to be clipped before it is projected onto a 2D screen. To do this, I first obtain the equations of the 4 clipping planes which project from the point of view of the camera or eyes and unto the vertices of the projected screen. Then we can plug in the equation of the 3D line into each linear equation of the planes and obtain points at which the line and planes intersect. Graphing this out in the amazing GeoGebra 3D graphing calculator, it becomes clear that the line only needs to be clipped at the left and top clipping planes. This is an important exercise in the mathematics of projecting 3D images onto 2D screens, which are used throughout computer graphics programming.

Here is a link to GeoGebra if you want to play around with the projection: https://www.geogebra.org/calculator/twezjbu5

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

• Laboratory Project: Putting 3D in Perspective: 0:00
• Question 1: Clipping a 3D Line: 2:08
• Solution: Graphing out the question in GeoGebra: 2:38
• We need 4 clipping planes: 4:35
• Recap on the equations of lines and planes: 6:58
• Vector and Parametric Equations of the 3D line: 8:17
• Equation of the right clipping plane: 12:21
  • Note on simplified vectors: 21:49
  • Linear equation of the right clipping plane: 22:49
  • Plugging in equation of a line into the equation of a plane: 24:30
  • Plotting our right clipping plane in GeoGebra: 30:49
• Equation of the top clipping plane: 32:47
  • Plugging in equation of a line into the equation of a plane: 40:46
• Equation of the left clipping plane: 47:13
  • Plugging in L into the plane equation: 50:42
• Equation of the bottom clipping plane: 58:52
  • Plugging in L into the plane equation: 1:01:04
• Summary: Line is clipped at left and top clipping planes: 1:03:08

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

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Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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