In Mathematical, Geometry and in particular in differential Geometry, the apparent contour of a Surface or a parameterized Nappe is the whole of the regular not S such as their tangent plan is parallel to a direction.

In particular, the Silhouette of such a figure such as it intuitively is conceived is included in apparent contour.

Definition

Formally, one defines a vector U which will be the direction of sight, and surfaces it by a Cartesian equation:

$\backslash \; Phi\; \backslash \; left\; (X,\; there,\; Z\; \backslash \; right)\; =\; 0$,

then the tangent plan in this point has as a normal the vector N such as

$n\; =\; \backslash \; mathrm\; \{grad\}\; \backslash ,\; \backslash \; Phi$.

So that the plan is parallel to U , it is necessary and it is enough that:

$n.u\; =\; 0$.

In conclusion, a point M of space is on the apparent contour of a surface S defined by Φ if and only if the two following conditions are vérifées:

$\backslash \; Phi\; \backslash \; left\; (M\; \backslash \; right)\; =\; 0$, so that it belongs to S ;

$\backslash \; left\; (\backslash \; mathrm\; \{grad\}\; \backslash ,\; \backslash \; Phi\; \backslash \; left\; (M\; \backslash \; right)\; |\; U\; \backslash \; right)$, so that the tangent plan is parallel to U .

Particular cases

• For a Sphere, whatever the vector U , apparent contour is a Cercle of ray equal to that of the sphere;
• For a Quadric , apparent contour is always a Conique.

See too

Related articles

• apparent Diameter, a dependant but distinct concept.

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