tangent plane

This time one takes planes parallel to the tangent plane.

Such a surface is also the envelope of the tangent planes to the curve.

Two different hyperbola will be formed on either side of the tangent plane.

S then obtains Ss former position as a tangent plane.

At such points the surface will be dome like, locally lying on one side of its tangent plane.

The geocentric latitude is not the appropriate up direction for the local tangent plane.

For example the tangent planes to a surface along a curve in the surface form such a family.

For these points there exist no tangent planes.

The curve is similar to the intersection of the surface with a parallel to the tangent plane and indefinitely near it.

Draw a plane parallel to the tangent plane and a small distance away from it.

That is to say, the starting point goes to the tangent plane from through the inverse of the exponential map.

This identification of the tangent planes along the curve corresponds to parallel transport.

The tangent plane is the best linear approximation, or linearization, of a surface at a point.

These identifications are always given by affine transformations from one tangent plane to another.

Since is convex, is always above the tangent plane of at any point :

In such a hexlet there is only one tangent plane to the hexlet.

The width of a surface is the distance between pairs of parallel tangent planes.

Thus tangent planes along a curve can be identified using the intrinsic geometry, even when the surface itself is not parallelizable.

This identification allows parallel transport to be defined, because in the Euclidean plane all tangent planes are identified with the space itself.

Also, horizontal planes can intersect when they are tangent planes to separated points on the surface of the earth.

If C is even larger than that, a hyperbolic hexlet is formed, and now there are no tangent planes at all.

The Dupin indicatrix is the result of the limiting process as the plane approaches the tangent plane.

The equations for the orthographic projection onto the (x, y) tangent plane reduce to the following:

The Jacobian of a function describes the orientation of a tangent plane to the function at a given point.

Tangent plane and normal.