The plane represented by the equation ax+by+cz=d, and the vector (A, B, C) is its normal.
If s is a surface represented by curve coordinates x(s, t), where s and t are real variables, then the normal represented by the cross product of partial derivatives is:
If the surface S is represented by an implicit function and the point set (x, y, z) satisfies F(x, y, z)=0, the surface normal at the point (x, y, z) is represented by a gradient:
If a surface has no tangent plane at a certain point, then there is no normal at that point. For example, the vertex and bottom edge of a cone have no normals, but the normals of the cone exist almost everywhere. Usually, a surface that satisfies Lipschitz continuity can be considered that normals exist almost everywhere.
Extended data:
The normal is a theoretical straight line perpendicular to the polygon surface, and there are infinite normal vectors on the plane. In the field of computer graphics, the normal determines the brightness of the surface and light source. For each point light source position, its brightness depends on the normal direction of the surface.
If the non-zero vector n is perpendicular to the plane A, the vector n is called the normal vector of the plane A. The vector represented by the straight line perpendicular to the plane is the normal vector of the plane. Every plane has countless normal vectors.
A vector can be represented by a directed line segment. The length of the directed line segment indicates the size of the vector, the size of the vector, that is, the length of the vector. A vector with a length of 0 is called a zero vector and recorded as a vector with a length equal to 1 unit. The direction indicated by the arrow indicates the direction of the vector.
Baidu Encyclopedia-Normal Vector