- #1
In summary, The conversation is about calculating the unit normal vector for a surface, specifically for surface F Nf and surface-E Ne in a Cartesian coordinate system. The normal vector is needed to calculate the velocity component for U and can be found by finding the angle between the normal vector and U. However, more information is needed such as the coordinates or angles in order to calculate an absolute normal vector. A formula is needed for finding the normal vector with a given angle.
- #2
tiny-tim
Science Advisor
Homework Helper
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Welcome to PF!
Hello andykol! Welcome to PF!
I'm not sure what you're asking …
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.
Hello andykol! Welcome to PF!
andykol said:
I'm not sure what you're asking
…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.
- #3
slider142
- 1,016
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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.
- #4
andykol
- 9
- 0
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.
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.
- #5
tiny-tim
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andykol said:
Sorry, I still don't understand
…how is F defined?
do you have a particular example in mind?
- #6
1. What is a surface normal vector?
A surface normal vector is a mathematical concept used in 3D graphics and geometry to represent the orientation of a surface at a specific point. It is a vector that is perpendicular to the surface at that point and can be used to determine the angle of incidence and reflection of light on the surface.
2. How is the surface normal vector calculated?
The surface normal vector is calculated by taking the cross product of two non-parallel vectors on the surface. These vectors can be determined by taking the partial derivatives of the surface equation with respect to the x, y, and z coordinates.
3. Why is the surface normal vector important?
The surface normal vector is important because it provides crucial information about the orientation and curvature of a surface. It is used in many applications, such as 3D rendering, collision detection, and physics simulations.
4. How is the surface normal vector used in lighting calculations?
In lighting calculations, the surface normal vector is used to determine the angle of incidence of light on a surface, which affects the intensity and color of the light reflected or absorbed by the surface. It is also used to calculate the angle of reflection for specular lighting effects.
5. Are there any limitations to calculating surface normal vectors?
Yes, there are some limitations to calculating surface normal vectors. In some cases, the surface may be too complex or irregular to accurately calculate the normal vector at every point. Additionally, if the surface is not smooth or has discontinuities, the normal vector may not accurately represent the surface's orientation.
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