Torus Knot

Functionality

Torus Knot generator will create a torus knot based on its radii sets, curve resolution and phases.

Inputs

All inputs are vectorized and they will accept single or multiple values.

• Major Radius [1]

• Minor Radius [1]

• Exterior Radius [2]

• Interior Radius [2]

• Curve Resolution

• Revolution Phase [3]

• Spin Phase [3]

• Shift

Notes:

• [1] : Major/Minor radii are available when Major/Minor mode is elected.

• [2] : Exterior/Interior radii are available when Exterior/Interior mode is elected.

• [3] : The phase angles are in DEGREES. The Property Panel has option to set angle units as: RADIANS, DEGREES or UNITIES.

Parameters

The MODE parameter allows to switch between Major/Minor and Exterior/Interior radii values. The input socket values for the two radii are interpreted as such based on the current mode.

All parameters except mode can be given by the node or an external input.

Param	Type	Default	Description
Major Radius	Float	1.00	Major radius of the torus [1]
Minor Radius	Float	0.25	Minor radius of the torus [1]
Exterior Radius	Float	1.25	Exterior radius of the torus [2]
Interior Radius	Float	0.75	Interior radius of the torus [2]
Curve Resolution	Int	100	Number of vertices in a curve (per link)
Revolution Phase	Float	0.00	Phase revolution vertices by a radian amount [3]
Spin Phase	Float	0.00	Phase spin vertices by a radian amount [3]
Shift	Float	0.00	Shift the points along the curve (0-1) [4]

Notes:

• [1] : Major/Minor radii are available when Major/Minor mode is elected.

• [2] : Exterior/Interior radii are available when Exterior/Interior mode is elected.

• [3] : Phase angles are given by default in DEGREES. The Property Panel has option to set angle units as: RADIANS, DEGREES or UNITIES.

• [4] : shift = 0 for no shift, shift = 1 for a complete shift along the curve

Extra Parameters

A set of extra parameters are available on the property panel. These parameters do not receive external input.

Extra Param	Type	Default	Description
Angle Units	Enum RADIANS DEGREES UNITIES	DEGREES	Interprets the angle values based on the selected angle units: Radians = 0.0 - 2pi Degrees = 0.0 - 360 Unities = 0.0 - 1.0
Adaptive Resolution	Bool	False	Adjusts curve resolution dynamically
Point Density	Int	10	Number of points per unit length [1]
Multiple Links	Bool	True	Generate multiple links in a degenerate knot
Flip p	Bool	False	Flip REVOLUTION direction (P)
Flip q	Bool	False	Flip SPIN direction (Q)
P multiplier	Int	1	Multiplies the p count [2]
Q multiplier	Int	1	Multiplies the q count [2]
Height	Float	1.00	Scales the vertices along Z by this amount
Scale	Float	1.00	Scales both radii by this amount
Normalize Tangents	Bool	True	Normalize the TANGENT vectors [3]
Normalize Normals	Bool	True	Normalize the NORMAL vectors [3]

Notes:

• [1] : Used only when the Adaptive Resolution is on

• [2] : Used without adaptive resolution these allow to create aliased torus knots resulting in all sorts of interesting shaped knots. See: https://github.com/nortikin/sverchok/issues/4746#issuecomment-1304820037

• [3] : Turn off normalization to save computation whenever the output vectors do not need to be normalized.

Outputs

Vertices, Edges, Tangents and Normals All outputs will be generated when connected.

Example of usage