Calculating surface normal vector

AI Thread Summary
To calculate the normal vector for surface F, the discussion emphasizes the importance of understanding the angle θ between the normal vector Nf and the velocity component U. It is noted that the normal component of U can be derived using the formula Ucosθ, eliminating the need for the absolute normal vector in certain cases. The conversation highlights that in a two-dimensional context, the normal vector can be determined by the negative reciprocal slope of the vector it is normal to, but specific coordinates or angles are required for precise calculations. The user seeks a formula for calculating the unit normal vector for surface F at a given angle, particularly in a Cartesian coordinate system. Clarification on the definition of surface F and specific examples is requested to provide a more accurate response.
andykol
Messages
9
Reaction score
0
Hello,
I am trying to calculate normal vector for surface F Nf (see attached picture) to calculate velocity component for U. I tried to get more info but got confused.
Please tell me how I can calculate Nf.
Thanks in advance.
 

Attachments

  • Vector.JPG
    Vector.JPG
    3.1 KB · Views: 646
Mathematics news on Phys.org
Welcome to PF!

Hello andykol! Welcome to PF! :smile:
andykol said:
I am trying to calculate normal vector for surface F Nf (see attached picture) to calculate velocity component for U. I tried to get more info but got confused.

I'm not sure what you're asking :confused: …

you don't need the normal vector …

to calculate the normal component for U, all you need is the angle, θ, between Nf and U …

the normal component of U is simply Ucosθ. :wink:
 
More information is necessary. In any coordinate system, a vector normal to another vector has a dot product of 0 with that vector. In 2 dimensions, this simplifies to the normal vector having the negative reciprocal slope of the vector it is normal to. you haven't given two-dimensional coordinates to the points, nor angles, so there is no way to calculate an absolute normal vector, but if the problem does not relate to any particular coordinate system (ie., there is no potential field; gravity, electromagnetism) then choose a convenient set of coordinates; ie., let that rectangle be horizontal with vertical sides; then the normal vector points along the positive x-axis. You still need the angle between F and N.
 
Thank you for reply.

But I need to calculate unit normal vector for surface F. I am looking for formula that calculates normal vector of surface with any given angle.
 
andykol said:
But I need to calculate unit normal vector for surface F. I am looking for formula that calculates normal vector of surface with any given angle.

Sorry, I still don't understand :confused: …

how is F defined?

do you have a particular example in mind?
 
Hello tiny-tim,

I have attached detailed picture. I have to calculate unit vector for surface-E Ne. For given Cartesian coordinates, how I can calculate surface normal?
E.g. 2D Cartesian mesh- I got surface-E at an angle θ.
 

Attachments

  • Vector.JPG
    Vector.JPG
    5.1 KB · Views: 679
Last edited:

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Thread 'Six Pencil Puzzle'

Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.
View full post »

Similar threads

I Area of an inclined surface with respect to the original surface
Replies
5
Views
5K
A A question about an 'extremal' surface
Replies
7
Views
2K
I Excellent 3D Graphics thing at math3d.org
Replies
7
Views
2K
I Solving simultaneous vector equations
Replies
11
Views
3K
Normal vector of an embedding surface
Replies
1
Views
1K
B Calculating the perfect tennis shot using vectors
Replies
2
Views
2K
Calculating Normal Vectors for 2D Surfaces: A Scientific Approach
Replies
6
Views
3K
Knowing when to decompose weight vector vs. normal vector
Replies
6
Views
2K
I Finance: does the volatility of a stock follow a certain distribution?
Replies
24
Views
4K
I Equation for circle points in 3D
Replies
3
Views
3K

Hot Threads

Recent Insights

Back
Top