A closed geometry has an outer side and an inner side. The so-called outer side means that when the starting point of the normal vector is on the surface, the normal vector points to the outer side. For example, if the sphere X 2+Y 2+Z 2 = A 2, any point (X, Y, Z) has a positive and negative normal vector (X, Y, Z)/A. As for whether it is positive or negative, it is positive when the outside is taken, and it is a sign when the inside is taken. At this point it can be verified that it meets the above requirements.

The smooth surface S is divided into n blocks S 1, ..., Sn has no common interior point, and each block is still a smooth surface. Take a point p on each s, cross p as the tangent plane t of s, and project s onto t.

Extended data:

Draw several dense direct prime lines in the view reflecting the true length of the shaft, and draw several even direct prime lines in the view reflecting the true shape of the circular arc at the bottom of the cone; Draw several diagonal lines on each towel on the conical surface. Please note that the diagonal direction on the cone should point to the top of the cone.

If the limit of the sum of the areas of all these projections exists (when the diameter of all S tends to zero), it is the area of surface S. For bounded simple smooth surfaces, such a limit always exists, regardless of the choice of smooth equivalent parameter representation of the surface.

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