cone - Maple Help

plottools

 cone
 generate 3-D plot object for a cone

 Calling Sequence cone(c, r, h, capopt, npopt, options)

Parameters

 c - vertex of the cone r - (optional) radius of base circle of the cone; default is 1 h - (optional) height of the cone; default is 1 capopt - (optional) the keyword capped npopt - (optional) an equation of the form numpoints=posint options - (optional) equations of the form option=value. For a complete list, see plot3d/option.

Description

 • The cone command creates a three-dimensional plot data object, which when displayed is a cone of height h.  The vertex of the cone is located at c.  The base circle of the cone is centered at c + [0,0,h] and of radius r.
 • The plot data object produced by the cone command can be used in a PLOT3D data structure, or displayed using the plots:-display command.
 • By default, the cone does not have a disc covering the base. If you include the capped keyword, such a disc is added.
 • The cone returned is approximated by a number of polygons. In particular, the base circle is approximated by a regular polygon; the edges of this polygon are then connected to the vertex. The more edges, the better it approximates a circular cone; the fewer edges, the more efficiently Maple can manipulate the 3-D objects involved. The number of edges is determined as follows:
 – If the numpoints = n option is given, then the base is an n-gon.
 – Otherwise, if the grid = [n+1, m] is given, it is ignored, except that the base is taken to be an n-gon. This is because the plot structure used to be generated with plot3d, placing the n+1 points determined by the grid around the full base circle, leading to n segments in between.
 – If neither option is given, the base is a 100-gon.
 • Remaining arguments are interpreted as options, which are specified as equations of the form option = value. For more information, see plottools and plot3d/option.

Examples

 > $\mathrm{with}\left(\mathrm{plottools}\right):$
 > $\mathrm{with}\left(\mathrm{plots}\right):$

An artificial ice-cream cone.

 > $\mathrm{icecream}≔\mathrm{cone}\left(\left[0,0,-2\right],0.7,2,\mathrm{color}="Tan"\right),\mathrm{sphere}\left(\left[0,0,0.2\right],0.75,\mathrm{color}="Pink",\mathrm{style}=\mathrm{patchnogrid}\right):$
 > $\mathrm{display}\left(\mathrm{icecream},\mathrm{scaling}=\mathrm{constrained},\mathrm{orientation}=\left[45,70\right]\right)$

This shows approximations to cones with a decreasing degree of faithfulness.

 > $\mathrm{cones}≔\mathrm{Array}\left(\left[\mathrm{seq}\left(\mathrm{cone}\left(\left[0,0,0\right],\mathrm{numpoints}=n\right),n=\left[100,20,12,8,5\right]\right)\right]\right):$
 > $\mathrm{display}\left(\mathrm{cones},\mathrm{orientation}=\left[50,35,5\right]\right)$

A cone with a triangle as the base, including a cap; that is, a tetrahedron.

 > $\mathrm{tetra}≔\mathrm{cone}\left(\left[0,0,0\right],1,\mathrm{sqrt}\left(2\right),'\mathrm{capped}','\mathrm{numpoints}'=3\right):$
 > $\mathrm{display}\left(\mathrm{tetra},'\mathrm{scaling}'='\mathrm{constrained}'\right)$

Compatibility

 • The plottools:-cone command was updated in Maple 2024.
 • The capped and numpoints options were introduced in Maple 2024.