Sysquake Pro – Table of Contents

Sysquake for LaTeX – Table of Contents

# Library -
`solids`

Library `solids` implements functions which create solid shapes
in 3D. Solids are generated with parametric equations and displayed with
`surf`.
When called without output argument, with an optional trailing
string argument for the edge style, the solid is displayed with the current scaling and
color map. With output arguments, arrays `X`, `Y`, `Z`
expected by
`surf` or
`mesh` are produced. They can
be modified to move, scale or stretch the solids.

The following statement makes available functions defined in `solids`:

use solids

## Functions

### cone

Cone.

#### Syntax

use solids cone cone(cap) cone(cap, n) cone(cap, n, style) (X, Y, Z) = cone (X, Y, Z) = cone(n)

#### Description

Without output argument, `cone` draws a cone approximated
by a polyhedron. The optional first input argument, a logical value which is true
by default, specifies if the cap is included. The optional second input argument,
an integer, specifies the number of discrete values for the parameter which describes
its surface.

By default, edges are not drawn. An optional third input argument, a string,
specifies the edge style; it corresponds to the style argument of `surf`.

With three output arguments, `cone` produces the `X`,
`Y`, and `Z` arrays expected by
`surf` or `mesh`, and it does not display anything.

#### See also

### crosscap

Cross-cap.

#### Syntax

use solids crosscap crosscap(n) crosscap(n, style) (X, Y, Z) = crosscap (X, Y, Z) = crosscap(n)

#### Description

Without output argument, `crosscap` draws a cross-cap (a self-intersecting surface)
approximated by a polyhedron. With an input argument, `crosscap(n)` draws a cross-cap
where the two parameters which describe its surface are sampled with `n`
discrete values.

By default, edges are not drawn. An optional second input argument, a string,
specifies the edge style; it corresponds to the style argument of `surf`.

With three output arguments, `crosscap` produces the `X`,
`Y`, and `Z` arrays expected by
`surf` or `mesh`, and it does not display anything.

#### See also

`klein`,
`klein8`,
`sphere`,
`sphericon`,
`surf`

### cylinder

Cylinder.

#### Syntax

use solids cylinder cylinder(cap) cylinder(cap, n) cylinder(cap, n, style) (X, Y, Z) = cylinder (X, Y, Z) = cylinder(n)

#### Description

Without output argument, `cylinder` draws a cylinder approximated
by a polyhedron. The optional first input argument, a logical value which is true
by default, specifies if caps are included. The optional second input argument,
an integer, specifies the number of discrete values for the parameter which describes
its surface.

By default, edges are not drawn. An optional third input argument, a string,
specifies the edge style; it corresponds to the style argument of `surf`.

With three output arguments, `cylinder` produces the `X`,
`Y`, and `Z` arrays expected by
`surf` or `mesh`, and it does not display anything.

#### See also

`cone`,
`sphere`,
`torus`,
`cube`,
`surf`

### klein

Klein bottle.

#### Syntax

use solids klein klein(p) klein(p, n) klein(p, n, style) (X, Y, Z) = ...

#### Description

Without output argument, `klein` draws a Klein bottle approximated
by a polyhedron. With an input
argument, `klein(p)` uses parameters stored in structure `p`.
The following fields are used:

Field | Description | Default value |
---|---|---|

r0 | average tube radius | 0.7 |

d | tube variation | 0.5 |

h | half height | 3 |

With two input arguments, `klein(p,n)` draws a Klein bottle
where the two parameters which describe its surface are sampled with `n`
discrete values.

By default, edges are not drawn. An optional third input argument, a string,
specifies the edge style; it corresponds to the style argument of `surf`.

With three output arguments, `klein` produces the `X`,
`Y`, and `Z` arrays expected by
`surf` or `mesh`, and it does not display anything.

#### See also

### klein8

Figure 8 Klein bottle immersion.

#### Syntax

use solids klein8 klein8(r) klein8(r, n) klein8(r, n, style) (X, Y, Z) = ...

#### Description

Without output argument, `klein8` draws a figure 8 Klein bottle immersion
(a closed, self-intersecting surface with one face) approximated by a polyhedron. With an input
argument, `klein8(r)` draws the surface with a main radius of `r`
(the default value is 1).

With two input arguments, `klein8(r,n)` samples the two parameters which describe
its surface with `n` discrete values.

`surf`.

With three output arguments, `klein8` produces the `X`,
`Y`, and `Z` arrays expected by
`surf` or `mesh`, and it does not display anything.

#### See also

### sphere

Sphere.

#### Syntax

use solids sphere sphere(n) sphere(n, style) (X, Y, Z) = sphere (X, Y, Z) = sphere(n)

#### Description

Without output argument, `sphere` draws a sphere approximated
by a polyhedron. With an input argument, `sphere(n)` draws a sphere
where the two parameters which describe its surface are sampled with `n`
discrete values.

By default, edges are not drawn. An optional second input argument, a string,
specifies the edge style; it corresponds to the style argument of `surf`.

With three output arguments, `sphere` produces the `X`,
`Y`, and `Z` arrays expected by
`surf` or `mesh`, and it does not display anything.

#### See also

`cylinder`,
`cone`,
`torus`,
`cube`,
`surf`

### sphericon

Sphericon.

#### Syntax

use solids sphericon sphericon(n) sphericon(n, style) (X, Y, Z) = sphericon (X, Y, Z) = sphericon(n)

#### Description

Without output argument, `sphericon` draws a sphericon (a 3D shape made
from a bicone with a 90-degree apex, cut by a plane containing both apices, where
one half is rotated by 90 degrees) approximated
by a polyhedron. With an input argument, `sphericon(n)` draws a sphericon
where the two parameters which describe its surface are sampled with `n`
discrete values.

By default, edges are not drawn. An optional second input argument, a string,
specifies the edge style; it corresponds to the style argument of `surf`.

With three output arguments, `sphericon` produces the `X`,
`Y`, and `Z` arrays expected by
`surf` or `mesh`, and it does not display anything.

#### See also

### torus

Torus.

#### Syntax

use solids torus torus(r) torus(r, n) torus(r, n, style) (X, Y, Z) = ...

#### Description

Without output argument, `torus` draws a torus approximated
by a polyhedron with a main radius of 1 and a tube radius of 0.5. With an input
argument, `torus(r)` draws a torus with tube radius `r`.
With two input arguments, `torus(r,n)` draws a torus
where the two parameters which describe its surface are sampled with `n`
discrete values.

`surf`.

With three output arguments, `torus` produces the `X`,
`Y`, and `Z` arrays expected by
`surf` or `mesh`, and it does not display anything.