2.    2D graphics - (the standard packages)

2.1.  ImplicitPlot
        package Graphics`ImplicitPlot`

<< Graphics`ImplicitPlot`

ImplicitPlot[x^2/4 - y^2/9 == 1, {x, -5, 5}]

ImplicitPlot[{x^2/4 - y^2/9 == 1, y == 3/2  x, 
        y == -3/2  x}, {x, -5, 5}]

hyperbola[a_, b_, p_, q_][x_, 
        y_] := 
(x - p)^2/a - (y - q)^2/b == 
        1

ImplicitPlot[
      Table[hyperbola[1, 1, 0, q][x, y], {q, -3, 3, 1}], {x, -5, 
        5}]

ImplicitPlot[y^3  x^2 - 2  y == 1, {x, -5, 5}]

ImplicitPlot[
      y^3  x^2 - 2  y == 1, {x, -5, 5}, {y, -6, 6}]

ImplicitPlot[
      y^3  x^2 - 2  y == 1, {x, -5, 5}, {y, -6, 6}, 
      AxesOrigin -> {0, 0}]

ImplicitPlot[
      y^3  x^2 - 2  y == 1, {x, -5, 5}, {y, -6, 6}, 
      AxesOrigin -> {0, 0}, PlotPoints -> 100]

cassini[a_, f_][x_, 
        y_] := (x^2 + y^2)^2 - 2  f^2 (x^2 - y^2) == 
        a^4 - f^4

ImplicitPlot[cassini[1, 1][x, y], {x, -2, 2}]

ImplicitPlot[
      Table[cassini[a, 1][x, y], {a, 0.8, 1.2, 0.1}], {x, -2, 2}, 
      Axes -> None]

\(Show[%, 
      Graphics[{Hue[1], AbsolutePointSize[4], Point[{\(-1\), 0}], 
          Point[{1, 0}]}], 
Graphics[{Text[
            FontForm[\*""\!\(F\_1\)"", {"Arial-Italic", 
                12}], {\(-1\), \(-0.1\)}], 
          Text[FontForm[\*""\!\(F\_2\)"", {"Arial-Italic", 
                12}], {1, \(-0.1\)}]}]]\)

\(ImplicitPlot[
      Table[\(cassini[a, 1]\)[x, y], {a, 0.8, 1.2, 0.1}], {x, \(-2\), 2}, 
      Axes -> 
        None, 

Epilog -> {{Hue[1], 
            AbsolutePointSize[4], Point[{\(-1\), 0}], 
            Point[{1, 0}]}, 
{Text[
              FontForm[\*""\!\(F\_1\)"", {"Arial-Italic", 
                  12}], {\(-1\), \(-0.1\)}], 
            Text[FontForm[\*""\!\(F\_2\)"", {"Arial-Italic", 
                  12}], {1, \(-0.1\)}]}}]\)

2.2. PolarPlot
       package Graphics`Graphics`

<< Graphics`Graphics`

PolarPlot[2  Cos[u], {u, 0, 2  Pi}]

PolarPlot[{2  Cos[u], 2  Sin[u]}, {u, 0, 2  Pi}]

ArhSpir[a_][u_] := a*u

PolarPlot[{ArhSpir[2][u], ArhSpir[-2][u]}, {u, 0, 
        8  Pi}, 
PlotStyle -> {Hue[1], 
          Hue[0.7]}]

logSpir[a_][u_] := a^u

PolarPlot[{logSpir[9/10][u], logSpir[10/9][u]}, {u, 0, 30}, 
      PlotStyle -> {Hue[1], Hue[0.7]}]

PasSn[a_, b_][u_] := 2  a*Cos[u] + b

PolarPlot[
      Evaluate[Table[PasSn[2, b][u], {b, 2, 6, 2}]], {u, 0, 2  Pi}, 
      PlotStyle -> {Hue[1], Hue[0.7], Hue[0.3]}]

NikCon[a_, b_][u_] := a/Sin[u] + b

PolarPlot[
      Evaluate[Table[NikCon[2, b][u], {b, 1, 3, 1}]], {u, -Pi, Pi}, 
      PlotStyle -> {Hue[1], Hue[0.7], 
          Hue[0.3]}, 
PlotRange -> {{-5, 
            5}, {-2, 5}}]

PolarPlot[
      Evaluate[Table[NikCon[2, b][u], {b, 1, 3, 1}]], {u, -Pi, 0}, 
      PlotStyle -> {Hue[1], Hue[0.7], 
          Hue[0.3]}, 
PlotRange -> {{-5, 
            5}, {-2, 5}}]

PolarPlot[
      Evaluate[Table[NikCon[2, b][u], {b, 1, 3, 1}]], {u, 0, Pi}, 
      PlotStyle -> {Hue[1], Hue[0.7], 
          Hue[0.3]}, 
PlotRange -> {{-5, 
            5}, {-2, 5}}]

Show[%, %%, Graphics[Line[{{-5, 2}, {5, 2}}]]]

2.3. FilledPlot i FilledListPlot
       package Graphics`FilledPlot`

<< Graphics`FilledPlot`

FilledPlot[Sin[x], {x, 0, 4  Pi}]

FilledPlot[{Sin[x], 2  Sin[x]}, {x, 0, 4  Pi}]

FilledPlot[{Sin[x], 2  Sin[x], 3  Sin[x], 4  Sin[x]}, {x, 0, 
        4  Pi}]

FilledPlot[{Sin[x], 2  Sin[x], 3  Sin[x], 4  Sin[x]}, {x, 0, 
        4  Pi}, 
Fills -> {{{1, Axis}, 
            Hue[0.1]}, {{2, 3}, Hue[1]}, {{3, 4}, Hue[0.6]}}]

FilledListPlot[{0, 3, 2, 5, 5, -1, 0}]

FilledListPlot[{{1, -2}, {5, 6}, {7, -1}}]

FilledListPlot[{0, 3, 2, 5, 5, -1, 
        0}, {{1, -2}, {5, 
          6}, {7, -1}}, 
Fills -> {CMYKColor[0, 
            0.3, 1, 0]}]

2.4. package Graphics`Arrow`

<< Graphics`Arrow`

Show[Graphics[Arrow[{0, 0}, {0, 2}]]]

Show[
      Graphics[{{Hue[1], 
            Arrow[{0, 0}, {0, 2}]}, 
{Hue[0.7], 
            AbsoluteThickness[2], Arrow[{0, 0}, {2, 2}]}}]]

Options[Arrow]

Show[
      Graphics[{{Hue[1], 
            Arrow[{0, 0}, {0, 2}, HeadScaling -> Relative]}, {Hue[0.7], 
            AbsoluteThickness[2], 
            Arrow[{0, 0}, {2, 2}, 
              HeadScaling -> Relative]}}]]

Show[
      Graphics[{{Hue[1], 
            Arrow[{0, 0}, {0, 2}, 
              HeadShape -> 
                Polygon[{{-0.05, - .05}, {0.05, - .05}, {0.05, 
                      0.05}, {-0.05, 0.05}}]]}, {Hue[0.7], 
            AbsoluteThickness[2], 
            Arrow[{0, 0}, {2, 2}, HeadScaling -> Relative]}}], 
      PlotRange -> {{-0.5, 2.5}, {-0.5, 2.5}}]

2.5. package Graphics`Spline`

<< Graphics`Spline`

pon = Table[{Cos[u], Sin[u]}, {u, 0, 2  Pi, Pi/4}]

Show[
      Graphics[Spline[pon, Cubic, 
          SplineDots -> True]], 
Graphics[{Hue[0.7], 
          Line[toc]}], 
AspectRatio -> 
        Automatic]

Show[
      Graphics[Spline[pon, Bezier, 
          SplineDots -> 
            Automatic]], 
AspectRatio -> 
        Automatic]

Show[
      Graphics[Spline[pon, CompositeBezier, 
          SplineDots -> 
            Automatic]], 
AspectRatio -> 
        Automatic]

2.6. package Graphics`Animation`

<<Graphics`Animation`

MoviePlot[i*Sin[x], {x, 0, 2  Pi}, {i, -2, 2, 0.1}, 
      PlotRange -> {{0, 2  Pi}, {-2, 2}}]

MoviePlot[Sin[x + i], {x, 0, 6  Pi}, {i, 1, 4, 0.1}]

MoviePlot[Sin[x], {x, 0, i}, {i, 0.1, 4  Pi, Pi/10}, 
      PlotRange -> {{0, 4  Pi}, {-1, 1}}]

MovieParametricPlot[{r*Cos[u], r*Sin[u]}, {u, 0, 2  Pi}, {r, 0.1, 2, 
        0.1}, AspectRatio -> Automatic, 
      PlotRange -> {{-2, 2}, {-2, 2}}]

MovieParametricPlot[{Cos[u], Sin[u]}, {u, 0, i}, {i, Pi/40, 
        2  Pi + Pi/40, Pi/20}, AspectRatio -> Automatic, 
      PlotRange -> {{-1, 1}, {-1, 1}}]

Animate[PolarPlot[PasPuz[2,b][u], {u, 0, 2 Pi}, Axes -> False], {b, 6,1,-0.25}]

Animate[PolarPlot[PasPuz[2,2.5][u], {u, 0, i},PlotRange->{{-1,8},{-5,5}}], {i, Pi/30,2Pi+Pi/30,Pi/15}]

ShowAnimation[Table[ Graphics[Line[{{0, 0}, {Cos[ t], Sin[t]}}], PlotRange -> {{-1, 1}, {-1, 1}}], {t, 0, 2Pi, Pi/8}]]

ShowAnimation[Table[ Graphics[{{Hue[0.1],Disk[{0,0},1]},{AbsoluteThickness[2],Arrow[{0, 0}, {0.8Cos[ t], 0.8Sin[t]}]}}, PlotRange -> {{-1, 1}, {-1, 1}},AspectRatio->Automatic], {t, Pi/2, -3Pi/2, -Pi/30}]]

ShowAnimation[Table[ Graphics[{{Hue[0.1],Disk[{0,0},1]},{AbsoluteThickness[3],Circle[{0,0},1]},Table[Line[{{Cos[u],Sin[u]},{0.9Cos[u],.9Sin[u]}}],{u,0,2Pi,Pi/30}],{AbsoluteThickness[2],Arrow[{0, 0}, {0.85Cos[ t], 0.85Sin[t]}]},
{Text[FontForm[(t-Pi/2)*(-30/Pi),{"Arial",16}],{1.3,-0.2}]}}, PlotRange -> {{-1, 1.5}, {-1, 1}},AspectRatio->Automatic], {t, Pi/2, -3Pi/2, -Pi/30}]]