plot::Cone(br, [bx, by, bz], tr, [tx, ty, tz]) creates a conical frustum from the base center to the top center . The base radius is br, the top radius is tr.

→ Examples

Call:

plot::Cone(br, [bx, by, bz], <tr>, [tx, ty, tz], <a = amin .. amax>, Options)

Parameters:

br:	the base radius of the cone. This must be a real numerical value or an arithmetical expression of the animation parameter a. br is equivalent to the attribute BaseRadius.
bx, by, bz:	the lower center point. The coordinates bx, by, bz must be real numerical values or arithmetical expressions of the animation parameter a. bx, by, bz are equivalent to the attributes BaseX, BaseY, BaseZ.
tr:	the top radius of the cone/conical frustum. This must be a real numerical value or an arithmetical expression of the animation parameter a. If no top radius is specified, a cone with top radius is created. tr is equivalent to the attribute TopRadius.
tx, ty, tz:	the upper center point. The coordinates tx, ty, tz must be real numerical values orarithmetical expressions of the animation parameter a. tx, ty, tz are equivalent to the attributes TopX, TopY, TopZ.

Related Functions:

plot, plot::copy

Details:

The lower center and upper center of the cone can also be passed as vectors.
The optional “top radius” tr for creating a frustum may also be specified as the attribute TopRadius = tr.
The upper and lower faces of a cone/frustum are not filled. They can be added as filled plot::Circle3ds.
Note that only circular cones can be created with plot::Cone. For elliptical bases, use a plot::Surface primitive or apply a plot::Scale3d transformation.

Example 1

We draw a cone with base radius 6:

plot(plot::Cone(6, [0, 0, 0], [0, 0, 10])):

MuPAD graphics

Example 2

We create a conical frustum by specifying a non-zero top radius. Note that no discs are attached to the base and the top. You can look through the frustum:

br := 16: base := [3, 4, 5]:
tr:= 7: top := [11, 12, 13]:
plot(plot::Cone(br, base, tr, top, FillColor = RGB::Red)):

MuPAD graphics

We add the discs at the base and the top. Their normals n are given as the vector from the base to the top:

n := zip(top, base, _subtract):
plot(plot::Circle3d(br, base, n, Filled = TRUE),
     plot::Circle3d(tr, top, n, Filled = TRUE),
     plot::Cone(br, base, tr, top),
     LinesVisible = FALSE, FillColor = RGB::Red):

MuPAD graphics

delete br, base, tr, top, n:

Example 3

A tube or cylinder (in the mathematical sense, i.e., the lateral sides of a physical cylinder) is a special case of a conical frustum with the same top and bottom radius:

plot(plot::Cone(6, [0, 0, 0], 6, [11, 12, 13],
FillColor = RGB::Yellow,
LinesVisible = TRUE)):

MuPAD graphics

Example 4

Bottom and top radii and centers can be animated:

plot(plot::Cone(sin(a)^2, [sin(2*a), cos(2*a), 0],
cos(a)^2, [cos(2*a), sin(2*a), 1],
a = 0..PI, FillColor = RGB::Green)):

MuPAD graphics

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