# Math

LunchBox’s Math components enable users to create mathematically defined shapes.

#### Component Descriptions

Below, each component is described and visual examples are given. We’ve also included special Notes and Tips that can help users with less familiar situations.

#### 3D Supershapes

Creates a mathematical supershape at the origin of the Rhino document.

Input:

• A U Value. Tip: use an even number to close the shape
• A V Value
• An integer for the m parameter, which determines the frequency of the deformations.
• A b parameter
• An n1 parameter
• An n2 parameter
• An n3 parameter
• An S parameter, to set the scale of the object
• A domain for D1, which sets the number number of intervals in the horizontal direction. Tip: Set from -Pi to Pi to enclose the shape.
• A domain for D2, which sets the number of intervals in the vertical direction. Tip: Set from -Pi/2 to Pi/2 to enclose the shape.

Results:

• A supershape

#### Conoid Surface

Creates a mathematical conoid surface.

Input:

• A U Value
• A V Value
• an R parameter, which affects the height of the shape
• A T parameter, which affects the number of revolutions of the shape.
• An S value, which scales the shape
• A domain for D1
• A domain for D2

Results:

• A conoid surface

#### Enneper Surface

Creates a mathematical Enneper Surface, a self-intersecting minimal surface, at the origin of the Rhino document.

Input:

• A U Value
• A V Value
• an R parameter. This affects the frequency of the variations around the edges of the shape.
• A domain for D1, which affects the overall width of the shape.
• A domain for D2, which affects the radial area of the shape.

Results:

• An Enneper surface

#### Helicoid Surface

Creates a Helicoid surface around the Rhino document’s origin point

Input:

• A U value
• A V value
• An integer for the R parameter, which affects the frequency width of the spiral in the V direction
• An integer for the T parameter, which subdivides the frequency width set by R
• An integer for S, which sets the scale of the object
• A domain for D1, which affects the outer radius of the object
• A domain for D2, which affects the height of the object (the number of periods)

Results:

• A helicoid surface

#### Hyperbolic Paraboloid

Creates a Hyperbolic Paraboloid

Input:

• A U value
• A V value
• A parameter for a, which sets the parabola width for the paraboloid in one direction
• A parameter for b, which sets the parabola width for the paraboloid in one direction
• An integer to set S, which affects the scale of the object
• A domain for D1, which affects the length of the Paraboloid
• A domain for D2, which affects the depth of the paraboloid

Results:

• A hyperbolic paraboloid shape

#### Klein Surface

Creates a mathematical Klein surface about the origin of the document.

Input:

• A U value
• A V value
• An integer for the R parameter, which affects width (radius) of the object
• An integer for the T parameter, which affects the incremental rotation of the cross sectional geometry of the object.
• An integer to set S, which affects the scale of the object
• A domain for D1, which affects length of the object. Note: 0 to 4Pi is 2 complete rotations.
• A domain for D2, which affects completion of the cross sectional geometry of the object. Note: 0 to Pi completes the rotation.

Results:

• A Klein surface

#### Mobius Surface

Creates a mathematical Mobius surface about the origin point of the document.

Input:

• A U value
• A V value
• An integer for the R parameter, which affects width (radius) of the object
• An integer for the T parameter, which affects the incremental rotation of the cross sectional geometry of the object.
• An integer to set S, which affects the scale of the object
• A domain for D1, which affects length of the object. Note: -Pi to Pi is 1 complete rotation.
• A domain for D2, which affects the width of the cross sectional geometry of the object, about the midpoint of the cross-section.

Results:

• A mobius surface

#### Torus Surface

Creates a mathematical torus (the most delicious of the mathematical surface shapes) about the origin point of the document.

Input:

• A U value
• A V value
• An integer for the C parameter, which affects width (radius) of the object
• An integer for the R parameter, which affects width (radius) of the cross-sectional geometry of the object
• An integer for the T parameter, which affects the length of the cross-sectional geometry of the object.
• An integer to set S, which affects the scale of the object
• A domain for D1, which affects the length of the object along its horizontal plane.
• A domain for D2, which affects the length of the object along its cross-sectional plane.

Results:

• A torus.

#### Platonic Cube

Creates a mathematical Platonic Cube about a specified plane.

Input:

• A list of planes, which will determine the location(s) of the results.
• An integer for the radius of a sphere. The resulting platonic form will fit inside the sphere.
• An integer between 0 and 1 to determine the amount of truncation at the corners of the cube. This adjusts also the object’s size to fit inside the radius of the theoretical sphere.

Results:

• A list of platonic cubes.

#### Platonic Dodecahedron

Creates a Platonic Dodecahedron about the given plane.

Input:

• A list of planes, which will determine the location(s) of the results.
• A integer to set the Radius of the object

Results:

• A platonic dodecahedron shape

#### Platonic Icosahedron

Creates a Platonic Icosahedron about the given plane.

Input:

• A list of planes, which will determine the location(s) of the results.
• An integer for the Radius of the shape.
• An integer between 0 and 1 to determine the amount of truncation at the corners of the shape.

Results:

• A Platonic Icosahedron

#### Platonic Octahedron

Creates a Platonic Octahedron about the given plane.

Input:

• A list of planes, which will determine the location(s) of the results.
• An integer for the Radius of the shape.
• An integer between 0 and 1 to determine the amount of truncation at the corners of the shape.

Results:

• A platonic octahedron

#### Platonic Tetrahedron

Creates a Platonic Tetrahedron about the given plane.

Input:

• A list of planes, which will determine the location(s) of the results.
• An integer for the Radius of the shape.
• An integer between 0 and 1 to determine the amount of truncation at the corners of the shape.

Results:

• A platonic tetrahedron