# What is Contour plot: Definition and 15 Discussions

A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional graph of the function f(x, y) parallel to the (x, y)-plane. In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes. The contour a contour map is the difference in elevation between successive contour lines.
More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value.The gradient of the function is always perpendicular to the contour lines. When the lines are close together the magnitude of the gradient is large: the variation is steep. A level set is a generalization of a contour line for functions of any number of variables.
Contour lines are curved, straight or a mixture of both lines on a map describing the intersection of a real or hypothetical surface with one or more horizontal planes. The configuration of these contours allows map readers to infer the relative gradient of a parameter and estimate that parameter at specific places. Contour lines may be either traced on a visible three-dimensional model of the surface, as when a photogrammetrist viewing a stereo-model plots elevation contours, or interpolated from the estimated surface elevations, as when a computer program threads contours through a network of observation points of area centroids. In the latter case, the method of interpolation affects the reliability of individual isolines and their portrayal of slope, pits and peaks.

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1. ### Vector field of gradient vector and contour plot

Given the equation ##\frac{xy} 3##. It is a fact that the gradient vector function is always perpendicular to the contour graph of the origional function. However it is not so evident in the plot above. Any thought will be appreciated.
2. ### Contour plot of Earth's magnetic field in Python

The Earth's magnetic field is cylindrically symmetric and can be described using cylindrical coordinates, (ρ,z,φ). The components of the magnetic field are given by: (B_φ) = 0 (B_ρ) = −∂A/∂z, (B_z) =(1/ρ) * ∂(ρA)/∂ρ. The vector potential for a dipole field is given by (A_φ) = (B_e)(ρ) *...
3. ### MATLAB Matlab -- how to make a smooth contour plot?

I want to represent data with 2 variables in 2D format. The value is represented by color and the 2 variables as the 2 axis. I am using the contourf function to plot my data: load('data.mat') cMap=jet(256); F2=figure(1); [c,h]=contourf(xrow,ycol,BDmatrix); set(h, 'edgecolor','none'); Both xrow...
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### Mathematica Mathematica Plot Real Portion (Contour Plot)

Hi PF! In Mathematica and given the code below, I am trying to the real part of ##\sigma##, ##Re(\sigma)##, in stead of simply ##\sigma##. Any help would be awesome! Here's what I have: n = 3; ContourPlot[(\[Sigma]^2 - 2 (n - 1) (2 n + 1) \[Epsilon] \[Sigma] + (n - 1) n (n + 2)) ((...
5. ### MATLAB MATLAB: Plot Contour at 0km Depth

I'm trying to generate contours that plot with the animation using contour(X,Y) but it's not quite working. I only need it to be in the x-y plane at 0km depth (see picture for greater clarification) % A script to plot two 3D waves. clear %Define the total time for simulation T_total=10; %Set...
6. ### Help with contour plots of effective potential in R3BP.

Hello everyone! I'm currently trying to plot the effective potential for Sun-Jupiter system, to show the lagrangian points in this system. I've converted to a system of units where G=1, m_sun+m_jupiter=1 and R=1, whereby I get the following equation describing the effective potential of a third...
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### MATLAB Creating a Matlab Contour Plot with Iterative Growth - Help Request

hey pf! i am trying to plot a contour (topographic) graph the following ##f(x,y) = \frac{1}{x^2+y^2} e^{x-(x^2+y^2)^{.5}}## where ##f(x,y) = k## where ##k = .001## and doubles in size for about 8 iterations. my attempt is here: x=-3:0.25:3; y=-3:0.25:3; z=.25:.25:1; [X,Y]=meshgrid(x,y)...
8. ### What is the difference between a contour plot and a bifurcation plot?

On Wolfram Alpha it will offend give you a contour plot, and it has similarities to a bifurcation plot with respect to a variable and a parameter. What is the difference between a contour plot and a bifurcation diagram?
9. ### MATLAB Filter command for contour plot MATLAB

Hi all, I have made a BSFC plot in MATLAB with engine data tested on an eddie current dyno, The code I used for it is: >> NP=40; >> [RP TP]=meshgrid(linspace(min(RPM),max(RPM),NP),linspace(min(Torque),max(Torqu e),NP)); >> BSFC_IT=griddata(RPM,Torque,BSFC,RP,TP); >> NC=12; >>...
10. ### Mathematica Problem in reporting contour plot mathematica

Dear friends I plot a Contour plot from a function with mathematica, but I don't know how can I add a small box near my figure that explain which value refer to which color? I put my code below, please help me with adding colordata to my code for having reference for colors. t = 0.01...
11. ### How Do I Correctly Plot an Electric Field Around a Base Station Using MATLAB?

Homework Statement I need to plot an electric field in some range around base station, for example in range of 200m. EIRP=57,5dBm G=1 for the first example N=4 Homework Equations E=[2*sqrt(30*N*P*G)]/r P=10exp[(EIRP-30)/10] EIRP=57,5dBm G=1 for the first example N=4 The...
12. ### Mathematica Construct Contour Plot in Mathematica for Quasi-Linear 1-D Wave Eq

How can I construct a contour plot in Mathematica for Consider the quasi-linear 1-D wave equation $$\frac{\partial\rho}{\partial t} + 2\rho\frac{\partial\rho}{\partial x} = 0$$ with the piecewise constant initial conditions When $x_0 = \pm 1$  \rho(x,0) = \begin{cases} 4, & x < -x_0\\ 3, &...
13. ### How to Create a 2-D Contour Plot with Labels Using Gnuplot?

Hello with gnuplot I need to have 2d contour plot from a file (say ss.dat) with three column, first and secend columns are X and Y respectively and the third column is magnitude (I need to have this magnitude with labels on it in 2d plot). Thanks in advance Hamid
14. ### Plotting an intersection seam on a contour plot ?

Hi, I have two 2D functions (surfaces), s1(x,y) and s2(x,y) defined via Interpolation. They intersect forming an intersection seam (which is a line). I can plot both functions using Plot3D and I can also plot the seam on the same 3D plot by means of the MeshFunctions option. The comand I...
15. ### MATLAB Contour Plot in Matlab: DATA COLLECTED vs TIME in date and hours

Hello, All. Thank you in advance for any help, contribution and your time. I have been asked to do a contour plot with a data vs time (date and hours), I am new with Matlab and I don't really know how to make this date and hour in a time series vector to do my contour plot. I have added the data...