Homology Homology
The term, from the greek homoios ("similar, equal") and logos ("speech"), means "the same logic , the same speech. " Homology is the logical match between two things, so what happens in a case also in the other because of the same logic. Counterpart is therefore synonymous with similar, though not only mean a similarity but an identity.In descriptive geometry 's homology is the product of two perspectivist space.
In other words, is the relationship of correspondence between points of two generic shapes Δ1 and Δ2, in the state in which such figures were obtained as projections on the same floor and two separate centers, the same figure Δ.
has collaborated in the drafting of this lesson the arch. A. Paolillo
perspectivist
Two plane figures are said to correspond when they are derived from each other by a projection operation.two floors are given π and π 'is not parallel to each other and a center C projection out of them. At each step of the plan π C is projected from the center plane π 'one and only one point. A lag between the two plans-one correspondence without exception: in fact, staring at point A on the plane π, is obtained as its projection on the plane π 'Point A' and vice versa. Points A and A 'are related by a center perspectivist C. If you move point A along the line r, its corresponding A 'describes the plane π' the line r ', the two lines have a common intersection point between the two planes (D = D' point unit). All points on the line of intersection between the planes π and π 'have the same properties: this line is called straight points together or axis of perspectivist ; also the point at infinity ∞ P r of the line has finished as the corresponding point P 'on the line r'.
- couples of corresponding points (A and A ') are aligned with the center C of perspectivist;
- pairs of lines corresponding to (re r') meet on the axis of perspectivist (u straight, instead of united points and intersection plans π and π ').
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