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Signed Distance Function Evaluation

Computes distance to a shape boundary with sign indicating inside or outside.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Geometry
Difficulty: Intermediate
Family: Implicit Geometry
Tier: Extended
Status: Verified
Review: Source Checked
Sources: 2
Formulas: 1
Relationships: 2
Code example: Ready
Visualization: Ready

Overview

Signed Distance Function Evaluation returns negative, zero, or positive values depending on whether a point is inside, on, or outside a shape.

Core Concepts

implicit surfacesigned distanceinside-outside testfield composition

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(1)

Average

O(shape complexity)

Worst

O(shape complexity)

Space

O(1)

When to Use

Use when implicit shapes or distance-aware queries are easier than mesh operations.
Use when ray marching is a central requirement.

When Not to Use

Avoid when exact surface topology or mesh connectivity is required.
Avoid when floating-point precision or degenerate geometry cannot be handled robustly.

What It Does

Measures distance to a boundary
Assigns inside or outside sign
Combines primitive distances for complex shapes

Use Cases

Ray marching
Collision queries
Procedural shape modeling

Inputs

Point position
Shape parameters

Outputs

Signed distance value

Key Formulas (1)

Sphere SDF

distance = length(point − center) − radius

distance = length(point - center) - radius

Computes signed distance from a point to a sphere.

Pseudocode

1.Choose the shape's distance function
2.Evaluate distance from the query point
3.Apply sign based on inside or outside
4.Combine with other fields if needed

Canonical Example

Input: sphere center = (0,0,0), radius = 2, point = (3,0,0)
Output: distance = 1
Explanation: The point is one unit outside the sphere surface.

Implementation Notes

Keep primitive distance functions small and test them at known inside, outside, and boundary points.
Use robust predicates or tolerances when near-degenerate inputs are expected.
Keep a tiny example with expected output beside the implementation.

Common Pitfalls

Combining fields with non-distance-preserving operations can break sphere tracing assumptions.
Collinear, overlapping, and duplicate points need explicit tie-breaking rules.
Not defining boundary, empty, or degenerate inputs before implementation.

Interactive Mechanism Walkthrough

Spatial Primitive & Sweep-Line Canvas

Show contour bands around a shape where zero marks the boundary.

Step 1 of 4: Choose the shape's distance function

geometry-diagram

Notes

Exact signed distances are not always preserved after arbitrary field operations.

Sources (2)

What each reference supports for this entry.

Sphere Tracing

Paper

Reference for using signed distance functions and distance bounds in implicit surface rendering.

Open source

Physically Based Rendering

Book

Rendering reference for Signed Distance Function Evaluation's ray queries, acceleration structures, or implicit-geometry use case.