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Ray marching is a method of iteratively stepping through a scene until a collision is detected, often for the purpose of 3D rendering which this article focuses on. Ray marching is not to be confused with the similarly-named ray casting or ray tracing.
The basic ray marching algorithm using SDFs works by estimating the closest distance, moving the ray that distance, and repeating the process over and over until the ray intersects with the object. Ray marching is useful in situations where estimating a distance to the scene's shapes are efficient, such as in fractals. Elsewhere, ray marching is slower than ray tracing due to the need for many steps.
Tutorial
An SDF based ray marcher uses SDFs, which stands for Signed Distance Functions. These are calculations and instructions used to see if the ray has touched an object. Another thing that makes this special is that it draws individual pixels instead of columns, and can easily draw objects at different heights.
Variables needed
(Ray X) (Ray Y) (Ray Z) (Length) (Origin X) (Origin Y) (Origin Z) (Camera X) (Camera Y) (Camera Z) (Collided?) (Distance :: variables) (Render Distance) (Pen Size) (Nearest Distance) (Color)
Main Loop
This starts all the other scripts.
when gf clicked erase all set [Render Distance v] to (5000) set [Pen Size v] to (15) //Can be any size greater than 0 but this is better for speed set [Camera X v] to (0) set [Camera Y v] to (0) set [Camera Z v] to (-100) go to x: (-240) y: (-180) forever go to x: (-240) y: (-180) repeat (((360)/(Pen Size))+(1)) set x to (-240) repeat (((480)/(Pen Size))+(1)) read keys :: custom //We will cover this later raycast pixel :: custom //Next script in the tutorial change x by (Pen Size) end change y by (Pen Size) end erase all end
Ray Marching Script
This script is what casts the ray.
define raycast pixel set [Nearest Distance v] to (Render Distance) set [Collision? v] to (0) set [Ray X v] to (Center X) set [Ray Y v] to (Center Y) set [Ray Z v] to (Center Z) set [Distance v] to (0) set pen color to (#000000) repeat until <<(Collision?) = (1)> or <(Dist) > (Render Distance)>> check distances :: custom //Will be covered later move (5) steps in direction (y position) (x position) :: custom // Next in tutorial end if <(Collision?) = (1)> then set pen color to (#FF0000) set pen (color v) to (Color) end pen down pen up
Moving the Ray
define move (n) steps in direction (rotation x) (rotation y) change [Ray X v] by ([sin v] of (rotation y)) change [Ray Y v] by ([cos v] of (rotation y)) change [Ray Z v] by ([sin v] of (rotation x))
Checking If the Ray Has Collided
This is the distance function that will be used to get the distance from any point to the ray position.
define length (a) (b) (c) set [Length v] to ([sqrt v] of ((((a) - (Ray X)) * ((a) - (Ray X))) + ((((b) - (Ray Y)) * ((b) - (Ray Y))) + (((c) - (Ray Z)) * ((c) - (Ray Z)))))
This checks collision with a sphere.
define sphere (x) (y) (z) (radius) (color) length (x) (y) (z) :: custom //Distance from center of sphere to ray set [Distance v] to ((Length) - (Radius)) collision (color) define collision (color) if <not<(Distance :: variables) > (0)>> then if <(Distance :: variables) < (Nearest Distance)> then set [Nearest Distance v] to (Distance :: variables) set [color v] to (color) end set [collision v] to (1)
This block contains all the SDFs and will check collisions with all objects.
define check distances sphere (0) (0) (0) (50) (50) :: custom //Add as much as you want
Moving the Camera
define read keys change [Camera X v] by (<key (d v) pressed?> - <key (a v) pressed?>) change [Camera Y v] by (<key (q v) pressed?> - <key (z v) pressed?>) change [Camera Z v] by (<key (w v) pressed?> - <key (s v) pressed?>)
Your SDF-based ray marcher is now ready!
Examples
- (100% pen) 3D Raymarcher by Howtomakeausername
- Menger Sponge Raymarcher! by piano_miles
- Realistic raymarcher by BasisEssence779
- Raymarching Tutorial — Part I: Objects by Raihan142857
- 3D fractal raymarcher & point cloud renderer by PeaBrainProgram
- Minecraft Scene Raymarcher by MyRaycasterArchives
- Ray Marching 3D SDFs by sureornot
