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Ray Marching

Renders by stepping along rays until they hit or pass through scene features.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Rendering
Difficulty: Advanced
Family: Ray-Based Rendering
Tier: Extended
Status: Verified
Review: Source Checked
Sources: 1
Formulas: 1
Relationships: 4
Code example: Not ready
Visualization: Ready

Overview

Ray Marching samples points along a ray, often using distance estimates or volume density to decide how far to step.

Core Concepts

rendered imageray stepgeometric calculationray-based renderingscene representationvisibility testpixel output

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(p)

Average

O(p s)

Worst

O(p s)

Space

O(1)

When to Use

Use Ray Marching when you need to advance along camera rays in steps.
Use it for volumetric rendering with inputs like ray origin and direction.
Use it when the scene representation and quality target match the rendering tradeoff.
Use it when the Ray-Based Rendering tradeoff is acceptable for the problem size.

When Not to Use

Avoid it when the cost per pixel or sample is too high for the desired frame rate.
Avoid it when the required output is not pixel color or hit result.

What It Does

Advances along camera rays in steps
Detects surfaces or accumulates volume contributions

Use Cases

Volumetric rendering
Signed distance fields
Procedural scenes

Inputs

Ray origin and direction
Distance or density function

Outputs

Pixel color or hit result

Key Formulas (1)

March step

point_next = point + step_size · ray_direction

point_next = point + step_size * ray_direction

Samples a ray at regular or adaptive intervals.

Pseudocode

1.Create a camera ray
2.Sample or estimate the scene at the current point
3.Advance the ray by a chosen step
4.Stop on hit, opacity, or max distance
5.Shade the result

Canonical Example

Input: scene = one triangle, one camera, one light
Output: image pixels showing the visible triangle
Explanation: Ray Marching: The algorithm converts scene data into visible pixel results.

Implementation Notes

Keep the input contract explicit: Ray origin and direction; Distance or density function.
Use this step as the implementation spine: Create a camera ray.
Then preserve the next state change: Sample or estimate the scene at the current point.
Build tiny scenes with known geometry before testing complex materials or lighting.

Common Pitfalls

Step strategy controls both image quality and performance.
Ignoring coordinate spaces, depth precision, or sampling noise while debugging image artifacts.
Returning pixel color or hit result without handling empty, invalid, or boundary inputs.

Interactive Mechanism Walkthrough

Spatial Primitive & Sweep-Line Canvas

Show rays advancing through space in repeated steps.

Step 1 of 5: Create a camera ray

ray-steps

Notes

Ray Marching operates in O(p s) time and O(1) space within the Ray-Based Rendering family. Key governing relation: point_next = point + step_size * ray_direction. Often compared with Sphere Tracing and Marching Cubes.