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Math

Forge supports a small but growing set of scalar, vector, and noise helpers.

Scalar and Vector Basics​

  • vec3(x) / vec3(x, y, z): Builds a vec3; the one-argument form broadcasts the same value to all components.
  • dot(a, b): Dot product between two vectors.
  • length(v): Vector length.
  • normalize(v): Returns a unit-length version of the vector.
  • abs(x): Absolute value for scalars, or per-component absolute value for vec3.
  • min(a, b), max(a, b): Scalar or per-component minimum/maximum.
  • clamp(x, a, b): Restricts a value or vector to a range.
  • mix(a, b, t): Blends between a and b; 0 gives a, 1 gives b.
  • step(edge, x): Returns 0 below the edge and 1 at or above it.
  • smoothstep(a, b, x): Smoothly blends from 0 at a to 1 at b.
let n = normalize(vec3(1.0, 2.0, 3.0));
let lit = max(dot(n, vec3(0.0, 1.0, 0.0)), 0.0);
let tint = mix(#44515f, #d3d9de, 0.35);

Arithmetic and Trig​

  • sin(x), cos(x): Standard trigonometric functions.
  • sqrt(x): Square root.
  • floor(x), ceil(x): Round down or up.
  • fract(x): Fractional part of a value.

These work well for masks, waves, and procedural breakup:

let bands = sin(p.y * 24.0);
let mask = smoothstep(0.2, 0.8, fract(p.x * 3.0));

3D Noise​

  • value_noise_3d(p[, scale]): Smooth scalar value noise in 3D; larger scale makes the noise field denser.
  • fbm_3d(p, octaves[, scale[, lacunarity]]): Fractal 3D noise built from repeated value-noise octaves; more octaves add detail, scale sets the base frequency, and lacunarity controls how quickly frequency increases.

These are most useful in:

  • material masks
  • breakup and wear
  • procedural dirt or moss coverage
  • custom SDF logic
let broad = fbm_3d(ctx.local_position, 5.0, 1.2, 2.0);
let detail = value_noise_3d(ctx.local_position, 3.0);
let moss = smoothstep(0.35, 0.62, broad + detail * 0.15);

Primitive Distance Calls​

Forge also exposes native primitive SDF intrinsics with an object-oriented surface:

  • Box.distance(p, half_size): Signed distance to a box defined by half extents.
  • Sphere.distance(p, radius): Signed distance to a sphere.
  • Cylinder.distance(p, radius, half_height): Signed distance to a cylinder aligned to the canonical local bind axis.
  • Torus.distance(p, major_radius, minor_radius): Signed distance to a torus.
  • box_shell_sdf(p, half, wall, round): Hollow rounded box shell with preserved outer dimensions.
  • cylinder_x_sdf(p, radius, half_len), cylinder_y_sdf(...), cylinder_z_sdf(...): Axis-aligned cylinder SDF helpers.
  • hole_line_x_sdf(p, radius, half_len, spacing, count), hole_line_y_sdf(...), hole_line_z_sdf(...): Repeated axis-aligned cylindrical holes spaced along local Z.

These are especially useful inside custom Forge assets because they avoid repeating low-level shape code while staying on the native/JIT path.

let shell = Box.distance(p, vec3(0.4, 0.2, 0.8));
let cap = Sphere.distance(p - vec3(0.0, 0.0, 0.8), 0.18);