asymptote line Figure 2.1:(a) Descartes;(b)Hyperbola Axis dependent. ( Difficult to transform to another coordinate system) Example: If the circle is represented by an explicit equation, it must be divided into two segments, with y=+Vr2-x2 for the upper half and y=-Vr2-a2 for the low half, see Figure 2.2. This kind of segmentation creates cases which are inconvenient in computer programming and graphics Figure 2.2: Description of a circle with an explicit equation Note: The derivative of y=va at the origin a =0 is infinite, see Figure 2.3 · Parametric curves x=x(t),y=y(t),t1≤t≤t 2D coordinates (, y) can be expressed as functions of a parameter t Example: a= a cos(t) sin(t),0≤t<2r-3 -2 -1 0 1 2 -3 -2 -1 0 1 2 X Y asymptote line x+y+1=0 multi-valued -3 -2 -1 0 1 2 3 -2 -1 0 1 2 3 4 X Y Figure 2.1: (a) Descartes; (b) Hyperbola. – Axis dependent. (Difficult to transform to another coordinate system). Example: If the circle is represented by an explicit equation, it must be divided into two segments, with y = + √ r 2 − x 2 for the upper half and y = − √ r 2 − x 2 for the lower half, see Figure 2.2. This kind of segmentation creates cases which are inconvenient in computer programming and graphics. y = + r − x 2 2 y = − r − x 2 2 x y o Figure 2.2: Description of a circle with an explicit equation. Note: The derivative of y = √ x at the origin x = 0 is infinite, see Figure 2.3. • Parametric curves x = x(t), y = y(t), t1 ≤ t ≤ t2 2D coordinates (x, y) can be expressed as functions of a parameter t. Example: x = a cos(t), y = a sin(t), 0 ≤ t < 2π 3