Math Distance*

Introduction
Key Features
Deep Dive: Metric Geometry
Parameters
Quick Recipes

Performance Cost 🟢 Low

Signal Type Vector → Float

Implementation Native Compiled C++

Devices (Cycles) CPU / GPU (1:1)

Math Distance calculates the spatial separation or relationship between two vectors. While the standard "Distance" node only offers Euclidean length, this utility provides a comprehensive set of 5 distinct metrics: Euclidean, Manhattan, Chebyshev, Minkowski, and Cosine. These different modes allow you to shape distance fields into spheres, diamonds, cubes, or angular gradients, making it a fundamental building block for procedural shaping, proximity effects, and pattern generation.

Usage & Behavior

Vector Logic: Practical Applications

The power of this node comes from what vectors you compare. Here are three standard workflows:

1. The Snow Mask (Direction)

                            Mode: COSINE

                            Input 1: Surface Normal (N)

                            Input 2: Vector (0, 0, 1) [Up]

By calculating the Cosine Distance between the surface Normal and the "Up" vector, you isolate surfaces facing the sky. Use this to mask snow, dust, or rain wetness on top of objects.

2. The Proximity Field (Position)

                            Mode: EUCLIDEAN

                            Input 1: Shading Point (P)

                            Input 2: Object Location

Calculates the physical distance from the shading point to a specific object (like an Empty). Use the result to drive a glow that gets brighter as an object gets closer, or to create a spherical mask in 3D space.

3. The Shape Generator (UV)

                            Mode: CHEBYSHEV / MANHATTAN

                            Input 1: UV Coordinate

                            Input 2: Center (0.5, 0.5, 0)

By measuring the distance from the center of a UV tile, you create geometric gradients. Chebyshev creates a square box gradient (perfect for paneling), while Manhattan creates a diamond gradient (sci-fi shields).

Euclidean

Manhattan

Chebyshev

Cosine (Normal and Up Vector)

The visual output of this node changes drastically depending on the Mode. If you calculate the distance from the center (0,0,0) to the current shading point (P), Euclidean creates a smooth radial gradient (like a ball), while Manhattan creates a pyramid/diamond shape, and Chebyshev creates a box. Cosine is unique—it doesn't measure length, but direction.

Best Used For: Custom falloff shapes (Box/Diamond/Sphere), Voronoi-style cell generation, comparing similarity between colors, and checking if two objects are facing the same direction.

Key Features

5 Geometric Norms: Covers L1, L2, L-Infinity, and Angular metrics.
Optimized Math: Calculates complex relationships in a single atomic operation.
Shape Control: Turns simple distance gradients into geometric primitives.

Deep Dive: Metric Geometry

How you measure "distance" defines the shape of the world.

Euclidean ($L^2$)

The ruler distance. "As the crow flies."
Shape: Sphere / Circle.

Manhattan ($L^1$)

Taxicab geometry. $|x| + |y| + |z|$.
Shape: Diamond / Octahedron.

Chebyshev ($L^\infty$)

Chessboard distance. $max(|x|, |y|, |z|)$.
Shape: Cube / Square.

Cosine Similarity

Angular difference. Ignored length.
Shape: Conical Gradient.

Parameters

Mode Enum

Selects the distance metric to use:

EUCLIDEAN: Standard physical distance. $ \sqrt{x^2 + y^2 + z^2} $.
MANHATTAN: Sum of absolute differences. Useful for "tech" patterns or circuit logic.
CHEBYSHEV: Maximum axis difference. Creates square/box falloffs.
MINKOWSKI: Generalized $L^p$ distance.
COSINE: Returns the cosine of the angle between the two vectors (1.0 = Same direction, 0.0 = 90 deg, -1.0 = Opposite).

Input 1 Vector

The starting point/vector.

Input 2 Vector

The target point/vector.

Quick Recipes

Practical uses for different metrics.

Box Mask

Mode CHEBYSHEV
Input 1 Object Coords
Input 2 (0,0,0)

Creates a square/cube gradient radiating from the center. Useful for masking boxy objects.

Facing Ratio

Mode COSINE
Input 1 Normal (N)
Input 2 (0,0,1) [Up]

Checks how much the surface is facing "Up". Returns 1.0 for flat tops, 0.0 for vertical walls.

Tech Forcefield

Mode MANHATTAN
Input 1 Object Coords
Math Fraction

Applying a modulo/fraction to Manhattan distance creates repeating diamond-shaped pulses.

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