Math

TD COMPs / TOPs / 2023 – Present

This category of components extends upon TouchDesigner’s built‐in mathematical operations, introducing components that apply explicit numerical logic to image‐based data. These operators translate familiar mathematical concepts into a visual, procedural context, allowing for direct manipulation of images as numerical fields.

To maintain clarity and scalability, this collection is divided into subcategories:

1. Arithmetic:

   Extends TouchDesigner’s scalar operations with explicit mathematical definitions. These components perform per‐pixel computations such as averaging and other basic arithmetic functions — forming the foundation for quantitative image manipulation and compositing workflows.




2. Calculus:

   Implements integral‐based operators that accumulate or measure variation across an image. While derivative‐based operators like Sobel or Laplacian belong to the Edge Detectors category, these Calculus components focus on the complementary process of integration — aggregating values spatially to reveal cumulative intensity, energy, or density across an image.




3. Vector:

   Provides tools for directional computation and multi‐component manipulation. These components handle operations such as dot and cross products, projection, normalization, and magnitude — essential for UV manipulation, directional filtering, and procedural spatial logic.




4. Matrix:

   Performs per‐pixel matrix operations across multiple image inputs. Instead of treating matrices as abstract numerical arrays, these components interpret each image as an individual matrix element — allowing determinant, trace, or eigenvalue computations to be performed spatially.

Together, these subcategories form a mathematical toolkit that bridges TouchDesigner’s visual workflow with formal computation. Whether used for analysis, compositing, or generative design, the Math components provide a foundation for translating mathematical theory into creative image processing practice.