Derivative And Integral

by Crys in Modifier Setups


Introduction

A series of nodes that allow to calculate the derivative and the integral of a function. This last approach is used to propose two new functions: the gamma and beta functions


Features and description of the parameters


there are 7 different geometry nodes ; to use them, just drag and drop into the “geometry node” window




abscissa_gen to generate a «abscissa » field


Input

• abscissa start : begining of the field

• abscissa end : end of the field

• subdivision : number of points

Output

• abscissa gen : begining of the field

• abscissa geometry : a mesh composed of the previous field

• subdivision : number of points

p { line-height: 115%; margin-bottom: 0.25cm; background: transparent }


Derivative : to compute the derivative of a function


Input

• abscissa field : has to be linked with abcissa_gen

• ordinate field : has to be linked with the generated function

• abscissa mesh : has to be linked with abcissa_geometry

Output

• derivate field : values of the derivative (field)

• Starting function : mesh of the function

• derivate mesh : mesh of the derivate

p { line-height: 115%; margin-bottom: 0.25cm; background: transparent }


gen_function : to plot a function


Input

• abscissa field: has to be linked to abcissa_gen

• ordinate field : has to be linked with the generated function

• abscissa mesh : has to be linked with abcissa_geometry

• material : material of the resulting mesh

• Start plot : the point at which the plot begins

• End plot : the point at which the plot ends

• Radius : radius of the curve


Output

• mesh geometry : mesh of the derivative

• curve geometry : here is the curve

p { line-height: 115%; margin-bottom: 0.25cm; background: transparent }


Integrate : to compute the integral of a function


Input

• abscissa field: has to be linked to abcissa_gen

• ordinate field : has to be linked with the generated function

• abscissa mesh : has to be linked with abcissa_geometry

• subdivision : has to be linked to abcissa_gen

Output

• String result : result of the integral « in a text form »

• Mesh area : show the area between the function and the abcissa axis

• Starting function : mesh of the function

• Integration result : (float) result of the computation

p { line-height: 115%; margin-bottom: 0.25cm; background: transparent }


representation grid : to show the cartesian frame


Input

• y range : y-size of the frame

• x range : x-size of the frame

• hide basis : show/hide the basis of the frame

Output

• Geometry : mesh of the frame

p { line-height: 115%; margin-bottom: 0.25cm; background: transparent }


The possibility of calculating integrals allows to create new functions


- gamma function : node which calculate the gamma function which allow to compute the factorial owing to the relationship :


- beta function : node which calculate the beta function




Published about 1 month ago
Blender Version 3.2, 3.3
License Royalty Free
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