Alcuni esempi di curve di livello

 

 

Claudio Marsan

Liceo cantonale di Mendrisio

via Agostini Maspoli

CH-6850 Mendrisio

 

ultima modifica: 08.12.2006

testato con:

   MuPAD Pro 4.0.1 su Linux Ubuntu 6.10

   MuPAD Pro 4.0.1 su Windows XP Professional sp2

 

 

Esempio 1

f := (x, y) -> x^2 + y^2;

plotfunc3d(f(x,y), x=-5..5, y=-5..5)

math

MuPAD graphics

plotfunc3d(f(x,y),

           ZContours=[$ 0..5 step 1],

           XLinesVisible=FALSE, YLinesVisible=FALSE,

           CameraDirection=[0,0.01,1])

MuPAD graphics

f1 := plot::Function3d(f(x, y), x=-5..5, y=-5..5):

plot(f1, plot::modify(f1, ZContours = [Automatic, 15],

                        LineWidth = 1,

                        LineColor = RGB::Black,

                        XLinesVisible = FALSE,

                        YLinesVisible = FALSE,

                        Filled = FALSE))

MuPAD graphics

f2 := plot::Function3d(f(x, y),

                      x=-5..5, y=-5..5, Submesh=[2,2]):

plot(f2, plot::Transform3d([0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0],

             plot::modify(f2, ZContours = [Automatic, 15],

                             LineWidth = 0.5,

                             LineColor = RGB::Black,

                             XLinesVisible = FALSE,

                             YLinesVisible = FALSE,

                             Filled = FALSE)))

MuPAD graphics

 

 

Esempio 2

f := (x, y) -> x^2 - y^2;

plotfunc3d(f(x,y), x=-5..5, y=-5..5)

math

MuPAD graphics

plotfunc3d(f(x,y),

           ZContours=[$ -5..5 step 1],

           XLinesVisible=FALSE, YLinesVisible=FALSE,

           CameraDirection=[0,0.01,1])

MuPAD graphics

f1 := plot::Function3d(f(x, y), x=-5..5, y=-5..5):

plot(f1, plot::modify(f1, ZContours = [Automatic, 15],

                        LineWidth = 1,

                        LineColor = RGB::Black,

                        XLinesVisible = FALSE,

                        YLinesVisible = FALSE,

                        Filled = FALSE))

MuPAD graphics

f2 := plot::Function3d(f(x, y),

                      x=-5..5, y=-5..5, Submesh=[2,2]):

plot(f2, plot::Transform3d([0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0],

             plot::modify(f2, ZContours = [Automatic, 15],

                             LineWidth = 0.5,

                             LineColor = RGB::Black,

                             XLinesVisible = FALSE,

                             YLinesVisible = FALSE,

                             Filled = FALSE)))

MuPAD graphics

 

 

Esempio 3

f := (x, y) -> 8*sin(x-cos(y))+(x^2+x*y);

plotfunc3d(f(x,y), x = -3..3, y = -3..3)

math

MuPAD graphics

plotfunc3d(f(x,y),

           ZContours=[$ -3..3 step 1],

           XLinesVisible=FALSE, YLinesVisible=FALSE,

           CameraDirection=[0,0.01,1])

MuPAD graphics

f1 := plot::Function3d(f(x, y), x = -3..3, y = -3..3):

plot(f1, plot::modify(f1, ZContours = [Automatic, 15],

                        LineWidth = 1,

                        LineColor = RGB::Black,

                        XLinesVisible = FALSE,

                        YLinesVisible = FALSE,

                        Filled = FALSE))

MuPAD graphics

f2 := plot::Function3d(f(x,y),

                      x = -3..3, y = -3..3, Submesh=[2,2]):

plot(f2, plot::Transform3d([0, 0, 0], [1, 0, 0, 0, 1, 0, 0, 0, 0],

             plot::modify(f2, ZContours = [Automatic, 15],

                             LineWidth = 0.5,

                             LineColor = RGB::Black,

                             XLinesVisible = FALSE,

                             YLinesVisible = FALSE,

                             Filled = FALSE)))

MuPAD graphics