Surface height from surface normal function

In summary, given a point (x,y) on the side of a mountain with known peak coordinates (Xp, Yp) and height (Zp), and a function G(x,y) that defines the 3D normal vector to the mountain side, you can use the surface function F(x,y,z)=0 and its gradient ∇F(x,y,z) to calculate your height. However, if the mountain is conically shaped, the normal will be independent of height.
  • #1
AndrewD
1
0
If you are standing on the side of a mountain at a point (x,y) and you know where the peak is (Xp, Yp) and how high it is (Zp) and you have a function G(x,y) that defines the 3D normal vector to the mountain side at all points on the surface, how do you calculate your height?

OK it's a simple way to put it but it expresses the problem neatly. I know that from the surface function F(x,y,z)=0, ∇F(x,y,z) will get you the surface normal at any point on the surface but I haven't found a simple way to express the reverse process. Can anyone help me?

Thanks,

Andrew
 
Physics news on Phys.org
  • #2
If the mountain is conically shaped, the normal will be independent of height.
 

1. What is a surface normal function?

A surface normal function is a mathematical representation of the direction that a surface is facing at any given point. It is used in computer graphics and other scientific fields to determine how light and other forces interact with a surface.

2. How is surface height calculated from a surface normal function?

Surface height can be calculated by integrating the surface normal function over the desired area. This essentially involves finding the average direction of the surface and using that information to determine the height of the surface at different points.

3. What is the importance of surface height from surface normal function?

Surface height from surface normal function is important in many applications, such as 3D modeling, computer graphics, and terrain mapping. It allows for the accurate representation of surfaces and their interactions with light and other forces.

4. How does surface height from surface normal function differ from surface elevation?

Surface height from surface normal function is a more precise and detailed measurement compared to surface elevation. Surface elevation is typically measured from a fixed reference point, while surface height from surface normal function takes into account the direction of the surface.

5. Can surface height from surface normal function be used for all types of surfaces?

Surface height from surface normal function can be used for a wide range of surfaces, including flat, curved, and irregular surfaces. However, it may not be suitable for certain types of surfaces, such as highly textured or translucent surfaces, where other methods may be more appropriate.

Similar threads

MHB Points of the surface with minimum distance to the point (3,0,0)
    • Topology and Analysis
Replies
4
Views
881
A A question about an 'extremal' surface
    • Differential Equations
Replies
7
Views
208
I Finding all valid surfaces that go through a vector field
    • Topology and Analysis
Replies
9
Views
2K
A Laurent series for algebraic functions
    • Topology and Analysis
Replies
9
Views
2K
Find all points where surface normal is perpendicular to plane
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Checking if a function is an equipotential surface
    • Advanced Physics Homework Help
Replies
3
Views
840
What are the forces on a cell in a tree vs on the surface of a tree
    • Introductory Physics Homework Help
Replies
4
Views
635
I Confirming my knowledge on surface integrals
    • Calculus
Replies
2
Views
1K
Evaluate the outgoing radiation from an optical fiber on a surface
    • Optics
Replies
1
Views
1K
Divergence Theorem Verification: Surface Integral
    • Calculus and Beyond Homework Help
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top