Vol.2, No 1, 1999 pp. 7-13
UDC 514.752.2(045)

---

CRITERIA FOR CONSTRUCTIVE DERIVATION OF THE REAL DOUBLE POINTS OF THE BICIRCULAR 4TH DEGREE CURVES
Biserka Marković, Sonja Krasić
Faculty of Civil Engineering and Architecture, Beogradska 14, 18000 Niš, YU
E-mail: bisam@mail.gaf.ni.ac.yu, sonjak@ mail.gaf.ni.ac.yu

---

Abstract. It is a known fact that the 2nd degree surfaces, regardless of their reality, induce the identical involutory series in the generatrices of a 3rd degree rectilinear surface whose 4th degree piercing curve of a 1st kind of the given surfaces are its double points. It is also known that two 2nd degree surfaces, regardless of their reality, determine a tuft of 2nd degree surface. The paper researches the 3rd degree rectilinear surfaces in the tufts of the quadrics, having in mind all the kinds of tufts, as well as the possibility of constructive determination of the generatrices of those surfaces. It is demonstrated that the number of those surfaces depends on the type of the tufts of the quadric as well as of the reality of the apexes and the faces of the common autopolar tetrahedron.
Key words: bicircular curves, double points, polarity, pencil of circumferences, involuntary series

---

KRITERIJUMI ZA KONSTRUKTIVNO ODREDJIVANJE REALNIH DVOSTRUKIH TAČAKA
BICIRKULARNIH KRIVIH 4. REDA U ovom radu analizirani su kriterijumi pod kojima se mogu odrediti bicirkularne krive 4. reda. Konstruktivno izvodjenje izabranih krivih ostvareno je kvadratnom transformacijom u odgovarajućem modelu  transformacije. Podešavanjem performansi modela postignuto je da prikazane bicirkularne krive nemaju realne beskonačno daleke tačke. Analizirani su uslovi pod kojima se, daljom spejalizacijom usvojenog modela transformacije, konstruktivno nalaze realne dvostruke tačke ovih krivih, odredjuje njihov broj i karakteristike: oblik petlje ili oblik šiljka.