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plot::Pyramid – pyramids and frustums of pyramids

plot::Pyramid(br, [bx, by, bz], [tx, ty, tz]) creates a pyramid stretching from the regular base plane with a circumcircle of radius br and center [b_x, b_y, b_z] to the top [t_x, t_y, t_z].

plot::Pyramid(br, [bx, by, bz], tr, [tx, ty, tz]) creates a frustum of pyramid from the base with center [b_x, b_y, b_z] to the top with center [t_x, t_y, t_z]. The radius of the circumcircle of the regular base is br. The radius of the circumcircle of the regular top is tr.

→ Examples

Call:

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

Parameters:

br: 

the radius of the circumcircle of the regular base. 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 radius of the circumcircle of the regular top of the frustum of pyramid. This must be a real numerical value or an arithmetical expression of the animation parameter a. If no top radius is specified, a pyramid with top radius tr = 0 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 or arithmetical expressions of the animation parameter a. 
tx, ty, tz are equivalent to the attributes TopX, TopY, TopZ.

Related Domains:

plot::Cone, plot::Cylinder, plot::Prism

Related Functions:

plot, plot::copy

Details:

Example 1

We draw a pyramid with base radius 6:

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

MuPAD graphics

Example 2

We create a frustum of pyramid by specifying a non-zero top radius:

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

MuPAD graphics

delete br, base, tr, top, n:

Example 3

Bottom and top radii and centers can be animated:

plot(plot::Pyramid(sin(a)^2, [sin(2*a), cos(2*a), 0],
                cos(a)^2, [cos(2*a), sin(2*a), 1],
                a = 0..PI)):

MuPAD graphicsimage

Example 4

Additionally, the orientation of the edges of the base can be changed with the rotation angle Angle:

plot(plot::Pyramid(1/2, Angle=0),
     plot::Pyramid(1/2, Angle=PI/4, FillColor2=RGB::Yellow))

MuPAD graphics

  

 

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