Yan - Bin Jia Oct 17 , 2017
نویسنده
چکیده
in x and y. The degree of the curve is the degree of the polynomial f(x, y). A parametric curve α(t) = (p(t), q(t)), where p(t) and q(t) are polynomials in t, is an algebraic curve. This is because we can eliminate t from the two polynomial equations x = p(t) and y = q(t) using the resultant technique, and obtain a polynomial equation, called their resultant, in x and y. The resultant has a degree no more than max(deg(p),deg(q)). Given a curve f(x, y) = 0, we can often derive a simplified equation via rotation and translation. The geometry of the curve will not be affected though. Suppose the curve undergoes a rotation of θ about the origin, followed by a translation (x0, y0). Every point (x, y) on the curve moves to the point (u, v) = (x cos θ − y sin θ + x0, x sin θ + y cos θ + y0). Conversely, we express (x, y) in terms of (u, v):
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