Home > Commands -> Vector Functions of Curves

See also: Parametric Plot Command

See also YouTubes: What's a Curve, What's a Parameter?, What do we need to parameterize?, Parameterize in 2D, Parameterize unit circle, Parameterize any circle, Parameterize any ellipse, Parameterize a piece of ellipse, Parameterize Curve in 3D 1, Parameterize Curve in 3D 2

Define and plot a vector function of a curve

Step 1: Declare the variable Step 2: Define the function. Use DOUBLE parentheses! Step 3: Use parametric_plot.

Example 1 - vector function with 2 components and 2D plot

var ('t') r=vector((t,t^2)) parametric_plot(r,(t,-2,2))

Example 2 - vector function with 3 components and 3D plot

var ('t') r=vector((sin(t),cos(t),t)) parametric_plot(r,(t,-2*pi,2*pi),color='purple',thickness=3, aspect_ratio=(3,3,1))

Extract component functions of vector function of a curve

Example 3 - Projecting a 3d parametric curve onto the x0y plane and

var ('t') r=vector((sin(t),cos(t),t)) r2=vector((r[0],r[1]))

p2=parametric_plot(r2,(t,-2*pi,2*pi),rgbcolor=(1,0,0),thickness=2, aspect_ratio=1) show(p2, figsize=3)

Example 4 - Plot 2d curve in 3d -it appears that adding a plot of a 3d vector function will force a 3d plot!

Notice that you CAN plot a 2d vector function in 3d. (It will plot at z=0.)

p3=parametric_plot(r,(t,-2*pi,2*pi),color='purple',thickness=3, aspect_ratio=(3,3,1)) p2in3=parametric_plot(r2,(t,-2*pi,2*pi),color='red',thickness=5, aspect_ratio=(3,3,1)) show(p3+p2in3)

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Vector Functions of Curves## EXAMPLES ON MY SAGE PAGE: Vector Functions of Curves in Sage

curve have 1 parameter, i.e. 1 variable (regardless of the number of components).DOUBLEparentheses to define a vector function!definingandplottingvector (parametric) functions of curves.evaluating r[t=3], extracting components r[0], magnitude abs(r), norm(r), derivatives diff(r)

See also: Parametric Plot Command

See also

YouTubes: What's a Curve, What's a Parameter?, What do we need to parameterize?, Parameterize in 2D,Parameterize unit circle, Parameterize any circle, Parameterize any ellipse, Parameterize a piece of ellipse, Parameterize Curve in 3D 1, Parameterize Curve in 3D 2

Define and plot a vector function of a curveStep 1: Declare the variable

Step 2: Define the function. Use

DOUBLEparentheses!Step 3: Use parametric_plot.

Example 1 - vector function with 2 componentsand 2D plotvar ('t')

r=vector((t,t^2))

parametric_plot(r,(t,-2,2))

Example 2 - vector function with 3 componentsand 3D plotvar ('t')

r=vector((sin(t),cos(t),t))

parametric_plot(r,(t,-2*pi,2*pi),color='purple',thickness=3, aspect_ratio=(3,3,1))

Extract component functions of vector function of a curveExample 3 - Projecting a 3d parametric curve onto the x0y plane andvar ('t')

r=vector((sin(t),cos(t),t))

r2=vector((r[0],r[1]))

p2=parametric_plot(r2,(t,-2*pi,2*pi),rgbcolor=(1,0,0),thickness=2, aspect_ratio=1)

show(p2, figsize=3)

Example 4 - Plot 2d curve in 3d -it appears thatadding a plot of a 3d vector function will force a 3d plot!Notice that you CAN plot a 2d vector function in 3d. (It will plot at z=0.)

var ('t')

r=vector((sin(t),cos(t),t))

r2=vector((r[0],r[1]))

p3=parametric_plot(r,(t,-2*pi,2*pi),color='purple',thickness=3, aspect_ratio=(3,3,1))

p2in3=parametric_plot(r2,(t,-2*pi,2*pi),color='red',thickness=5, aspect_ratio=(3,3,1))

show(p3+p2in3)

Keywords: sage, vector, curve, function, parameter, parametric_plot