Function Repository Resource:

SectionContourPlot

Give a contour plot of a function together with the projections onto the xy-plane of the given sections of the plot

Contributed by: Dennis M Schneider

ResourceFunction["SectionContourPlot"][f,{x,x_min,x_max},{y,y_min,y_max},opts]

plots the projections onto the xy-plane of the sections of the surface specified with the options "XSection","YSection","ZSection","VSection" and "OSection".

ResourceFunction["SectionContourPlot"][f,{x,x_min,x_max},{y,y_min,y_max},{{g_x,g_y},…},{t,t_min,t_max}]

plots the projections onto the xy-plane of the sections of the surface determined by the cylinders described parametrically by {{g_x,g_y},…},{t,t_min,t_max}, together with the projections onto the xy-plane of the other sections specified with the options "XSection","YSection","ZSection","VSection" and "OSection".

Details and Options

ResourceFunction["SectionContourPlot"] has the same relationship to the resource function SectionPlot3D that ContourPlot has to Plot3D.

ResourceFunction["SectionContourPlot"] has the same options as ContourPlot with the following additions and changes:

"DrawPoint"

{}

a list of points to be included in the plot

"DrawPointStyle"

styles to be applied to the points specified with the option "DrawPoint"

"DrawGradient"

{}

a list of points at which to draw the gradient

"GradientStyle

styles to be applied to the gradient vectors

"OSection"

{}

draws the projection onto the xy-plane of an oblique section determined by functions of the form z=f[x],z=g[y] or z=h[x,y]

"OSectionStyle"

styles to be applied to the oblique sections

"PlotPointsSection"

specifies how many initial sample points to use in plotting sections

"SectionStyle"

{Red,Thickness[.01]}

styles to be applied to sections defined parametrically by {g_x,g_y}

"VSection"

{}

draws the projection onto the xy-plane of vertical sections for a function or list of functions of the form y=f[x] or x=g[y]

"VSectionStyle"

{Red,Thickness[.01]}

styles to be applied to the vertical sections

"XSection"

{}

draws the projection onto the xy-plane of vertical sections parallel to the yz-plane determined by the value or list of values of x

"XSectionStyle"

{Red,Thickness[.01]}

styles to be applied to the x-sections

"YSection"

{}

draws the projection onto the xy-plane of vertical sections parallel to the xz-plane determined by the value or list of values of y

"YSectionStyle"

{Red,Thickness[.01]}

styles to be applied to the y-sections

"ZSection"

{}

draws the projection onto the xy-plane of horizontal sections parallel to the xy-plane determined by the value or list of values of z

"ZSectionStyle"

{Red,Thickness[.01]}

styles to be applied to the z-sections

Examples

Basic Examples (2)

A contour plot with projections of an x-section and an oblique section:

In[1]:=

Out[1]=

Display the resource function SectionPlot3D and SectionContourPlot as a row:

In[2]:=

GraphicsRow[{ResourceFunction["SectionPlot3D"][
Sin[x y], {x, -2, 2}, {y, -2, 2}, "XSection" -> 1, "OSection" -> x + y, "OSectionStyle" -> Tube[.03]], ResourceFunction["SectionContourPlot"][
Sin[x y], {x, -2, 2}, {y, -2, 2}, "XSection" -> 1, "OSection" -> x + y]}, ImageSize -> Large]

Out[2]=

A contour plot with the projection onto the xy-plane of a cylinder and a z-section:

In[3]:=

$ResourceFunction["SectionContourPlot"][ Sin[x y], {x, -3, 3}, {y, -3, 3}, {Cos[t], 2 Sin[t]}, {t, 0, 2 \[Pi]}, "ZSection" -> 1/2]$

Out[3]=

Display the resource function SectionPlot3D and SectionContourPlot as a row:

In[4]:=

$GraphicsRow[{ResourceFunction["SectionPlot3D"][ Sin[x y], {x, -3, 3}, {y, -3, 3}, {Cos[t], 2 Sin[t]}, {t, 0, 2 \[Pi]}, "ZSection" -> 1/2, "SectionStyle" -> {{Blue, Tube[.04]}}, Mesh -> None, PlotStyle -> Opacity[.6]], ResourceFunction["SectionContourPlot"][ Sin[x y], {x, -3, 3}, {y, -3, 3}, {Cos[t], 2 Sin[t]}, {t, 0, 2 \[Pi]}, "ZSection" -> 1/2, "SectionStyle" -> Blue]}, ImageSize -> Large]$

Out[4]=

View the resource function SectionPlot3D directly from above to illustrate the projection of the sections onto the xy-plane:

In[5]:=

$GraphicsRow[{ResourceFunction["SectionPlot3D"][ Sin[x y], {x, -3, 3}, {y, -3, 3}, {Cos[t], 2 Sin[t]}, {t, 0, 2 \[Pi]}, "ZSection" -> 1/2, "ZSectionStyle" -> Tube[.05], "SectionStyle" -> {{Blue, Tube[.05]}}, Mesh -> None, PlotStyle -> Opacity[.6], ViewPoint -> {0, 0, 5}], ResourceFunction["SectionContourPlot"][ Sin[x y], {x, -3, 3}, {y, -3, 3}, {Cos[t], 2 Sin[t]}, {t, 0, 2 \[Pi]}, "ZSection" -> 1/2, "ZSectionStyle" -> AbsoluteThickness[2.5], "SectionStyle" -> {{AbsoluteThickness[2.5], Blue}}]}, ImageSize -> Large]$

Out[5]=

Options (9)

DrawPoint and DrawPointStyle (1)

Add points to the contour plot and add styles to the points:

In[6]:=

$GraphicsRow[{ResourceFunction["SectionContourPlot"][ Sin[x y], {x, -\[Pi], \[Pi]}, {y, -\[Pi], \[Pi]}, "DrawPoint" -> {{1, 0}, {-1, 0}, {-2, \[Pi]/2}, {2, -\[Pi]/2}}], ResourceFunction["SectionContourPlot"][ Sin[x y], {x, -\[Pi], \[Pi]}, {y, -\[Pi], \[Pi]}, "DrawPoint" -> {{1, 0}, {-1, 0}, {-2, \[Pi]/2}, {2, -\[Pi]/2}}, "DrawPointStyle" -> {Black, Green, Blue, {PointSize[.08], Yellow}}]}]$

Out[6]=

DrawGradient and GradientStyle (1)

Plot the gradient of the function at several points and apply styles to the gradients:

In[7]:=

GraphicsRow[{ResourceFunction["SectionContourPlot"][
Sin[x y], {x, -2, 2}, {y, -2, 2}, "DrawGradient" -> {{1.5, 0}, {-1, 1}, {1, -1}, {-1, 0}}] , ResourceFunction["SectionContourPlot"][
Sin[x y], {x, -2, 2}, {y, -2, 2}, "DrawGradient" -> {{1.5, 0}, {-1, 1}, {1, -1}, {-1, 0}}, "GradientStyle" -> {{Blue, PointSize[.05]}, {Red, Dashed, PointSize[Large]}, {Green, Dashed, PointSize[Large]}, {Purple, Dashed, PointSize[Large]}}]}]

Out[7]=

OSection and OSectionStyle (1)

Oblique sections with a style set for each:

In[8]:=

Out[8]=

PlotPointsSection (1)

Setting the number of points used to plot the sections:

In[9]:=

$GraphicsGrid[{{ResourceFunction["SectionContourPlot"][ Sin[x^2 y], {x, -2, 2}, {y, -2, 2}, "OSection" -> x^2 + y, "PlotPointsSection" -> 7, MaxRecursion -> 0], ResourceFunction["SectionContourPlot"][ Sin[x^2 y], {x, -2, 2}, {y, -2, 2}, "OSection" -> x^2 + y, "PlotPointsSection" -> Automatic]}}, ImageSize -> Medium]$

Out[9]=

SectionStyle (1)

Parametrically defined sections with a style set for each:

In[10]:=

$ResourceFunction["SectionContourPlot"][ Sin[x y], {x, -3, 3}, {y, -3, 3}, {{2 Cos[t], Sin[t]}, {Cos[t], 2 Sin[t]}}, {t, 0, 2 \[Pi]}, "SectionStyle" -> {Magenta, {Thickness[.025], Orange}}]$

Out[10]=

VSection and VSectionStyle (1)

Vertical sections with a style set for each:

In[11]:=

$ResourceFunction["SectionContourPlot"][ Sin[x y], {x, -3, 3}, {y, -3, 3}, "VSection" -> {2 x^2 - 2, -x^2}, "VSectionStyle" -> {Green, {Pink, Dashed, Thickness[.015]}}]$