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physiker99
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How do I find "surface normal direction" for a plane on a point with coordinates specified?
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physiker99 said:i need to find normal directions for r^2=9 and x+y+z^2=1 at the point (2,-2,1)
[PLAIN]http://en.wikipedia.org/wiki/Surface_normal said:If[/PLAIN] a surface S is given implicitly as the set of points [itex](x,y,z)[/itex] satisfying [itex]F(x,y,z)=0[/itex], then, a normal at a point [itex](x,y,z)[/itex] on the surface is given by the gradient:
[tex]\mathbf{N}=\mathbf{\nabla}F [/tex]
since the gradient at any point is perpendicular to the level set, and [itex]F(x,y,z) = 0[/itex] (the surface) is a level set of [itex]F[/itex].
A surface normal direction refers to the direction that a surface is facing or oriented towards. It is a vector that is perpendicular to the surface at a specific point.
The surface normal direction is calculated by finding the cross product of two 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.
The surface normal direction is important in graphics and computer vision because it helps determine the orientation and shading of an object, which can make it appear more realistic and three-dimensional. It also helps with tasks such as object recognition and shape analysis.
Yes, the surface normal direction can change at different points on a surface. This is because the surface may be curved or have varying slopes, resulting in different perpendicular vectors at different points.
The surface normal direction is used in lighting calculations to determine how light will reflect off the surface. By knowing the direction of the surface normal, the angle of incidence can be calculated, and the appropriate amount of light can be reflected or absorbed, resulting in realistic lighting effects in graphics and computer vision applications.