Function Repository Resource:

ManipulateParametricPlot3D

Create a dynamic interface for a three-dimensional curve being traced out by the tip of the vector

Contributed by: Dennis M Schneider

ResourceFunction["ManipulateParametricPlot3D"][{f_x(t),f_y(t),f_z(t)},{t,tmin,tmax}]

produces a Manipulate of the curve (f_x(t),f_y(t),f_z(t)) being traced out when t runs from tmin to tmax.

Details and Options

In addition to the options of ParametricPlot3D and the resource function PlotVector3D, the following options are supported:

"DrawVector"

False

show the path followed by a particle as it moves along the curve

"PointStyle"

specifies a style for the point

VectorStyle

Red

specifies a style for the vector

Examples

Basic Examples

Make a Manipulate for a curve:

In[1]:=

$ResourceFunction[ "ManipulateParametricPlot3D"][{t Cos[2 \[Pi] t], t Sin[2 \[Pi] t], t}, {t, 0, 2}, VectorStyle -> Red]$

Out[1]=

A particle moving along a helix collides with a particle moving around a circle when t=1:

In[2]:=

$ResourceFunction[ "ManipulateParametricPlot3D"][{{Cos[2 \[Pi] t], Sin[2 \[Pi] t], 1}, {t Cos[2 \[Pi] t], t Sin[2 \[Pi] t], t}}, {t, 0, 2}, "DrawVector" -> False, "PointStyle" -> {{PointSize[.025], Blue}, {PointSize[.025], Red}}, ImageSize -> Medium]$