Scalar Field Formula¶

https://github.com/nortikin/sverchok/assets/14288520/fa9a8540-ba21-47e8-bf16-c70a1492d824

Functionality¶

This node generates a Scalar Field, defined by some user-provided formula.

The formula should map the coordinates of the point in 3D space (in one of supported coordinate systems) into some number.

It is possible to use additional parameters in the formula, they will become inputs of the node.

It is also possible to use the value of some other Scalar Field in the same point in the formula.

https://github.com/nortikin/sverchok/assets/14288520/47b24ebf-8ac2-4c71-abc6-f15bc0eca0ce

Expression syntax¶

Syntax being used for formulas is standard Python’s syntax for expressions. For exact syntax definition, please refer to https://docs.python.org/3/reference/expressions.html.

In short, you can use usual mathematical operations (+, -, *, /, ** for power), numbers, variables, parenthesis, and function call, such as sin(x).

One difference with Python’s syntax is that you can call only restricted number of Python’s functions. Allowed are:

Functions from math module:
- acos, acosh, asin, asinh, atan, atan2, atanh, ceil, copysign, cos, cosh, degrees, erf, erfc, exp, expm1, fabs, factorial, floor, fmod, frexp, fsum, gamma, hypot, isfinite, isinf, isnan, ldexp, lgamma, log, log10, log1p, log2, modf, pow, radians, sin, sinh, sqrt, tan, tanh, trunc;
Constants from math module: pi, e;
Additional functions: abs, sign;
From mathutlis module: Vector, Matrix;
Python type conversions: tuple, list, dict.

This restriction is for security reasons. However, Python’s ecosystem does not guarantee that no one can call some unsafe operations by using some sort of language-level hacks. So, please be warned that usage of this node with JSON definition obtained from unknown or untrusted source can potentially harm your system or data.

Examples of valid expressions are:

1.0
x
x+1
0.75*X + 0.25*Y
R * sin(phi)

Inputs¶

This node has the following input:

Field. A scalar field, whose values can be used in the formula. This input is required only if the formula involves the V variable. (see example below)

Each variable used in the formula, except for V and the coordinate variables, also becomes additional input.

The following variables are considered to be point coordinates:

For Cartesian mode: x, y and z;
For Cylindrical mode: rho, phi and z;
For Spherical mode: rho, phi and theta.

Parameters¶

This node has the following parameters:

Input. This defines the coordinate system being used. The available values are Carhtesian, Cylindrical and Spherical. The default value is Cartesian.
Formula. The formula which defines the scalar field. The default formula is x*x + y*y + z*z.
Vectorize. This parameter is available in the N panel only. If enabled, then to evaluate formulas for a series of input values, the node will use NumPy functions to perform several computations at a time; otherwise, the formulas will be evaluated separately for each input value. The use of vectorization usually makes computations a lot faster (2x to 100x). The parameter is enabled by default. If you experience some kind of troubles with calculating some of functions (errors or not good enough precision), you can disable this parameter.