contour

(noun)

a line on a map or chart delineating those points which have the same altitude or other plotted quantity: a contour line or isopleth

Related Terms

  • gradient

Examples of contour in the following topics:

  • Contour Line

    • The contour line is the simplest of the varieties of line.
    • Contour means 'outline', and presents exterior edges of objects.
    • While contour lines create a path around the edge of a shape, cross contour lines follow paths across a shape to delineate differences in surface features.
    • Contour drawing is an artistic technique in which the artist sketches the contour of a subject by drawing lines that result in a completed drawing that is essentially an outline .
    • An example of a contour drawing by the artist Egon Schiele.
  • Contour Plots

    • Contour plots portray data for three variables in two dimensions.
    • The plot contains a number of contour lines.
    • Each contour line is shown in an X-Y plot and has a constant value on a third variable.
    • A contour plot showing calories as a function of fat and carbohydrates
    • A contour plot showing calories as a function of fat and carbohydrates with areas shaded.
  • Lagrange Multiplers

    • We can visualize contours of $f$ given by $f(x, y)=d$ for various values of $d$, and the contour of $g$ given by $g (x, y) = c$.
    • Suppose we walk along the contour line with $g = c$.
    • In general, the contour lines of $f$ and $g$ may be distinct, so following the contour line for $g = c$, one could intersect with or cross the contour lines of $f$.
    • When the contour line for $g = c$ meets contour lines of $f$ tangentially we neither increase nor decrease the value of $f$—that is, when the contour lines touch but do not cross.
    • The contour lines of $f$ and $g$ touch when the tangent vectors of the contour lines are parallel.
  • The Shape or Contour of a Melody

    • Such a line gives the contour or shape of the melodic line.
    • Please see The Shape of a Melody for children's activities covering melodic contour.
  • The Drawing Process

    • Contour drawing is an artistic technique used in the field of art in which the artist sketches the contour of a subject by drawing lines that result in a drawing that is essentially an outline (the French word contour, indeed, means "outline").
    • The purpose of contour drawing is to emphasize the mass, volume, and outlined shape of the subject rather than the details .
    • However, because contour can convey a three-dimensional perspective, length and width as well as thickness and depth are important; not all contours exist along the outlines of a subject.
    • Blind contour drawing is a method of drawing where an artist draws the contour of a subject without looking at the paper.
    • The purpose of contour drawing is to emphasize the mass, volume, and outlined shape of the subject rather than the details.
  • Qualities of Line

    • Contour lines define the outer edges of an object.
    • Contoured hatching refers to hatching using curved lines in order to describe light and form of contours.
  • Exercises

    • For the "SAT and College GPA" case study data, create a contour plot looking at College GPA as a function of Math SAT and High School GPA.
  • An Example

    • Lx = 1.5; Ly = 1; c = 1; d[x_,y_,m_,n_]= Sin[m Pi x/Lx]Sin[n Pi y/Ly]; w[n_,m_] = c Sqrt[(m Pi /Lx)^2 + (n Pi/Ly)^2]; Do[Do[ContourPlot[d[x,y,m,n],{x,0,Lx},{y,0,Ly},AspectRatio->Ly/Lx];,{m,2}];,{n,2}];
  • Varieties of Line

    • There are six important varieties of line: actual, implied, straight, expressive, contour, and hatch lines.
    • The 'outline' or 'contour line' creates a border or path around the edge of a shape, thereby outlining and defining it.
    • 'Cross contour lines' delineate differences in the features of a surface.
  • Isentropic flows

    • taken along some closed contour that moves with the fluid.
    • if $\displaystyle {\bf F}/m = -\nabla \phi$, so the circulation around a contour moving with the fluid is constant if the flow is isentropic.
    • The circulation around a close contour (bold lines) that travels with the fluid along the streamlines (light lines) is conserved if the fluid is isentropic.
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