Algebraic Curves

Initialization

<< Graphics`ImplicitPlot`
<< Graphics`ContourPlot3D`
<< Graphics`Animation`

r := Random[Real, {-1, 1}]

Conics

Conics

ImplicitPlot[

(x^2)+3 x y+(y^2)+4 x-2 y+4==0

,{x, -10, 10},{y, -10, 10}]

Random Conic

ImplicitPlot[

r (x^2)+r x y+r (y^2)+r x+r y+r==0

,{x, -20, 20},{y, -20, 20}]

Morphed Conics

ShowAnimation[Table[ImplicitPlot[

(x^2)+t (y^2)+(1 - t) x==t

,{x, -2, 2},{y, -2, 2}],{t, 0, 1,  .01}]]

Intersecting Conic and Line

g1=ImplicitPlot[(x^2)-x y+2(y^2)==1,{x, -2, 2},{y, -2, 2}];
g2=ImplicitPlot[x + y == 1,{x, -2, 2},{y, -2, 2}];
Show[{g1, g2}]

Quadrics

Quadric

ContourPlot3D[

2(x^2)+(y^2)-(z^2)+x-y

,{x, -1, 1},{y, -1, 1},{z, -1, 1},PlotPoints -> {5, 5, 5}]

Random Quadric

ContourPlot3D[

r (x^2)+r (y^2)+r (z^2)+r x y+ r x z+r y z+1

,{x, -3, 3},{y, -3, 3},{z, -3, 3},PlotPoints -> {5, 5, 5}]

Morphed Quadrics

ShowAnimation[Table[ContourPlot3D[

(x^2)+(y^2)+t (z^2)-1

,{x, -2, 2},{y, -2, 2},{z, -2, 2},PlotPoints -> {5, 5, 5},Boxed -> False],{t, -1, 1,  .1}]]

Intersecting Quadric and Plane

g1=ContourPlot3D[2(x^2)-(y^2)-(z^2)+x-y-1,{x, -2, 2},{y, -2, 2},{z, -2, 2},PlotPoints -> {5, 5, 5}];
g2=ContourPlot3D[x - y + 2  z,{x, -2, 2},{y, -2, 2},{z, -2, 2}];
Show[{g1, g2}]

Angel

g1 = 
      ContourPlot3D[
        x^2 + y^2 + (z - 7)^2/2 - 1, {x, -1, 1}, {y, -1, 1}, {z, 
          5, 9}, PlotPoints -> {5, 5, 5}, Boxed -> False]; 
    g2 = ContourPlot3D[
        z - 7 + Sqrt[2] + y^2/1.3 + x^2, {x, -3, 3}, {y, -3, 3}, {z, 
          0, 6}, PlotPoints -> {5, 5, 5}, Boxed -> False]; 
    g3 = ContourPlot3D[
        3  x^2 - 2 (y -  .2)^2 - 2 (z - 5)^2 - 1, {x, -3, 3}, {y, 
          0, 2}, {z, 2, 8}, PlotPoints -> {5, 5, 5}, 
        Boxed -> False]; 
    g4 = ParametricPlot3D[{Cos[u] (1 +  .1  Cos[v]),  .5 + 
            Cos[1] Sin[u] (1 +  .1  Cos[v]) +  .1  Sin[1] Sin[v], 
          9 - Sin[1] Sin[u] (1 +  .1  Cos[v]) +  .1  Cos[1] Sin[v]}, {u, 
          0, 2  Pi}, {v, 0, 2  Pi}, Boxed -> False];  
    g5 = ParametricPlot3D[{Sinh[
              u] ( .3 +  .2  Cos[v]), - .5 + (Cosh[u] - 
                  2.5) (1 +  .2  Cos[v]), 
          6 +  .4  Sin[v] - u^2}, {u, -1.5, 1.5}, {v, 0, 
          2  Pi}]
Show[{g1, g2, g3, g4, g5}]

SpinShow[%]

Curves

Surfaces