What is the angle between a disc and a vertical surface?

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SUMMARY

The discussion focuses on calculating the angle between a disc and a vertical surface, specifically when the disc is oriented at 45 degrees horizontally and 45 degrees vertically. The user successfully computes the dihedral angles between the disc and other planes, such as the road and building, but seeks to determine the angle 'a' that the disc makes with the vertical surface. The approximate angle is identified as 35 degrees, indicating a need for clarity in visualizing and calculating angles in three-dimensional space.

PREREQUISITES
  • Understanding of surface normals in 3D geometry
  • Knowledge of dihedral angles and their calculations
  • Familiarity with basic trigonometry
  • Ability to visualize 3D geometric relationships
NEXT STEPS
  • Research methods for calculating angles between planes in 3D space
  • Explore the use of vector mathematics for angle determination
  • Learn about graphical representations of 3D objects and their orientations
  • Investigate software tools for 3D modeling and angle calculations, such as AutoCAD or Blender
USEFUL FOR

This discussion is beneficial for mathematicians, engineers, architects, and anyone involved in 3D modeling or geometric analysis who needs to understand the relationships between different planes and angles in three-dimensional space.

con20or
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Hello all, i wonder if you can help me with a problem I am having.

I have a disc and three planes (representing a road, building and roof). For this problem, the disc can be considered a plane.

http://i3.photobucket.com/albums/y60/con20or/Fig1.png

I know the orientation of each of the planes. The disc is orientated 45horizontal x 45vertical. I can caluate surface normals for each element. With these I can calculate the dihedral angle between the disc and the road, and also the disc and the building, but what I am really looking to find is when looking directly at a vertical surface (middle image) what angle does the plane make on the vertical surface? Its approx 35^ in this case.

This is really bugging me, I'm sure there's an easy way of doing this.

Thanks in advance.
 
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