Math Module | BWSL Docs

Constants, safe math helpers, remapping, easing, waves, and scalar/vector utility functions.

Import

bwsl

import Math

This module has no module imports.

Usage Examples

Stabilize Lighting and Direction Math

Use Math when a value can become degenerate at runtime: zero-length normals, tiny denominators, or dot products that need a clean lighting range.

bwsl

import Math

float3 normal = Math::safe_normalize(input.normal);
float3 lightDir = Math::safe_normalize(resources.lightPosition - input.worldPos);
float ndotl = Math::saturate_dot(normal, lightDir);

float distanceToLight = length(resources.lightPosition - input.worldPos);
float attenuation = Math::safe_rcp(distanceToLight * distanceToLight);

output.color = float4(resources.lightColor * ndotl * attenuation, 1.0);

Remap Gameplay or Material Values

Use the remap helpers when host values arrive in engine units but the shader wants normalized ranges, artist-facing ramps, or clamped fade factors.

bwsl

import Math

float height01 = Math::inverse_lerp_clamped(resources.waterLevel, resources.snowLine, input.worldPos.y);
float foam = Math::remap_clamped(resources.waveEnergy, 0.2, 0.8, 0.0, 1.0);
float windPhase = Math::triangle_wave(resources.time * resources.windSpeed);

float3 low = float3(0.05, 0.18, 0.1);
float3 high = float3(0.8, 0.85, 0.9);
float3 terrainColor = lerp(low, high, height01) + foam * float3(0.12);

output.color = float4(terrainColor * (0.85 + windPhase * 0.15), 1.0);

Constants

const float PI = 3.14159265358979323846const float TAU = 6.28318530717958647692const float E = 2.71828182845904523536const float PHI = 1.61803398874989484820const float INV_PI = 0.31830988618379067154const float INV_TAU = 0.15915494309189533577const float EPSILON = 1e-6const float SQRT_2 = 1.41421356237309504880const float INV_SQRT_2 = 0.70710678118654752440

Structs

No structs found.

Enums

No enums found.

Functions

inverse_lerp

Returns the interpolation factor for value in the range [a, b].

bwsl

inverse_lerp :: (float a, float b, float value) -> float

inverse_lerp

Returns the component-wise interpolation factor for value in [a, b].

bwsl

inverse_lerp :: (float2 a, float2 b, float2 value) -> float2

inverse_lerp

Returns the component-wise interpolation factor for value in [a, b].

bwsl

inverse_lerp :: (float3 a, float3 b, float3 value) -> float3

inverse_lerp

Returns the component-wise interpolation factor for value in [a, b].

bwsl

inverse_lerp :: (float4 a, float4 b, float4 value) -> float4

inverse_lerp_clamped

Returns saturate(inverse_lerp(a, b, value)).

bwsl

inverse_lerp_clamped :: (float a, float b, float value) -> float

remap

Remaps a scalar from one range to another.

bwsl

remap :: (float value, float in_min, float in_max, float out_min, float out_max) -> float

remap

Remaps a vector from one range to another component-wise.

bwsl

remap :: (float2 value, float2 in_min, float2 in_max, float2 out_min, float2 out_max) -> float2

remap

Remaps a vector from one range to another component-wise.

bwsl

remap :: (float3 value, float3 in_min, float3 in_max, float3 out_min, float3 out_max) -> float3

remap

Remaps a vector from one range to another component-wise.

bwsl

remap :: (float4 value, float4 in_min, float4 in_max, float4 out_min, float4 out_max) -> float4

remap_clamped

Remaps a scalar from one range to another, clamping the input range factor to [0, 1].

bwsl

remap_clamped :: (float value, float in_min, float in_max, float out_min, float out_max) -> float

safe_rcp

Returns 1 / x, or 0 when x is too close to zero.

bwsl

safe_rcp :: (float x) -> float

safe_divide

Returns a / b, or 0 when b is too close to zero.

bwsl

safe_divide :: (float a, float b) -> float

safe_divide

Returns a / b, or fallback when b is too close to zero.

bwsl

safe_divide :: (float a, float b, float fallback) -> float

safe_divide

Returns component-wise a / b, using zero for near-zero denominators.

bwsl

safe_divide :: (float2 a, float2 b) -> float2

safe_divide

Returns component-wise a / b, using zero for near-zero denominators.

bwsl

safe_divide :: (float3 a, float3 b) -> float3

safe_divide

Returns component-wise a / b, using zero for near-zero denominators.

bwsl

safe_divide :: (float4 a, float4 b) -> float4

safe_normalize

Normalizes a float2, returning +X when length is too small.

bwsl

safe_normalize :: (float2 v) -> float2

safe_normalize_with_fallback

Normalizes a float2, returning fallback when length is too small.

bwsl

safe_normalize_with_fallback :: (float2 v, float2 fallback) -> float2

safe_normalize

Normalizes a float3, returning +Y when length is too small.

bwsl

safe_normalize :: (float3 v) -> float3

safe_normalize_with_fallback

Normalizes a float3, returning fallback when length is too small.

bwsl

safe_normalize_with_fallback :: (float3 v, float3 fallback) -> float3

safe_normalize

Normalizes a float4, returning +W when length is too small.

bwsl

safe_normalize :: (float4 v) -> float4

safe_normalize_with_fallback

Normalizes a float4, returning fallback when length is too small.

bwsl

safe_normalize_with_fallback :: (float4 v, float4 fallback) -> float4

length_squared

Returns dot(v, v) without taking a square root.

bwsl

length_squared :: (float2 v) -> float

length_squared

Returns dot(v, v) without taking a square root.

bwsl

length_squared :: (float3 v) -> float

length_squared

Returns dot(v, v) without taking a square root.

bwsl

length_squared :: (float4 v) -> float

distance_squared

Returns squared distance between two points without taking a square root.

bwsl

distance_squared :: (float2 a, float2 b) -> float

distance_squared

Returns squared distance between two points without taking a square root.

bwsl

distance_squared :: (float3 a, float3 b) -> float

distance_squared

Returns squared distance between two points without taking a square root.

bwsl

distance_squared :: (float4 a, float4 b) -> float

saturate_dot

Returns max(dot(a, b), 0), common in lighting equations.

bwsl

saturate_dot :: (float3 a, float3 b) -> float

clamped_dot

Returns clamp(dot(a, b), -1, 1), useful before acos.

bwsl

clamped_dot :: (float3 a, float3 b) -> float

angle_between

Reference: https://en.wikipedia.org/wiki/Dot_product

bwsl

angle_between :: (float3 a, float3 b) -> float

project_onto

Reference: https://en.wikipedia.org/wiki/Vector_projection

bwsl

project_onto :: (float3 v, float3 onto) -> float3

reject_from

Reference: https://en.wikipedia.org/wiki/Vector_projection

bwsl

reject_from :: (float3 v, float3 onto) -> float3

orthonormal_tangent

Reference: https://en.wikipedia.org/wiki/Orthonormal_basis

bwsl

orthonormal_tangent :: (float3 normal) -> float3

face_same_hemisphere

Returns a unit vector facing the same hemisphere as reference.

bwsl

face_same_hemisphere :: (float3 v, float3 reference) -> float3

square

Returns x squared.

bwsl

square :: (float x) -> float

square

Returns x squared component-wise.

bwsl

square :: (float2 x) -> float2

square

Returns x squared component-wise.

bwsl

square :: (float3 x) -> float3

square

Returns x squared component-wise.

bwsl

square :: (float4 x) -> float4

cube

Returns x cubed.

bwsl

cube :: (float x) -> float

cube

Returns x cubed component-wise.

bwsl

cube :: (float2 x) -> float2

cube

Returns x cubed component-wise.

bwsl

cube :: (float3 x) -> float3

cube

Returns x cubed component-wise.

bwsl

cube :: (float4 x) -> float4

pow4

Returns x^4.

bwsl

pow4 :: (float x) -> float

pow5

Reference: https://en.wikipedia.org/wiki/Schlick%27s_approximation

bwsl

pow5 :: (float x) -> float

pow5

Returns x^5 component-wise.

bwsl

pow5 :: (float3 x) -> float3

rotate_2d

Reference: https://en.wikipedia.org/wiki/Rotation_matrix

bwsl

rotate_2d :: (float2 p, float angle) -> float2

rotate_axis_angle

Reference: https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula

bwsl

rotate_axis_angle :: (float3 v, float3 axis, float angle) -> float3

linear_step

Returns a clamped linear step from edge0 to edge1.

bwsl

linear_step :: (float edge0, float edge1, float x) -> float

linear_step

Returns a clamped linear step from edge0 to edge1 component-wise.

bwsl

linear_step :: (float2 edge0, float2 edge1, float2 x) -> float2

linear_step

Returns a clamped linear step from edge0 to edge1 component-wise.

bwsl

linear_step :: (float3 edge0, float3 edge1, float3 x) -> float3

smootherstep

Reference: https://en.wikipedia.org/wiki/Smoothstep

bwsl

smootherstep :: (float edge0, float edge1, float x) -> float

smootherstep

Reference: https://en.wikipedia.org/wiki/Smoothstep

bwsl

smootherstep :: (float2 edge0, float2 edge1, float2 x) -> float2

smootherstep

Reference: https://en.wikipedia.org/wiki/Smoothstep

bwsl

smootherstep :: (float3 edge0, float3 edge1, float3 x) -> float3

ease_in_quad

Reference: https://easings.net/#easeInQuad

bwsl

ease_in_quad :: (float t) -> float

ease_out_quad

Reference: https://easings.net/#easeOutQuad

bwsl

ease_out_quad :: (float t) -> float

ease_in_out_quad

Reference: https://easings.net/#easeInOutQuad

bwsl

ease_in_out_quad :: (float t) -> float

ease_in_cubic

Reference: https://easings.net/#easeInCubic

bwsl

ease_in_cubic :: (float t) -> float

ease_out_cubic

Reference: https://easings.net/#easeOutCubic

bwsl

ease_out_cubic :: (float t) -> float

ease_in_out_cubic

Reference: https://easings.net/#easeInOutCubic

bwsl

ease_in_out_cubic :: (float t) -> float

ease_in_quart

Reference: https://easings.net/#easeInQuart

bwsl

ease_in_quart :: (float t) -> float

ease_out_quart

Reference: https://easings.net/#easeOutQuart

bwsl

ease_out_quart :: (float t) -> float

ease_in_out_quart

Reference: https://easings.net/#easeInOutQuart

bwsl

ease_in_out_quart :: (float t) -> float

ease_in_expo

Reference: https://easings.net/#easeInExpo

bwsl

ease_in_expo :: (float t) -> float

ease_out_expo

Reference: https://easings.net/#easeOutExpo

bwsl

ease_out_expo :: (float t) -> float

ease_out_elastic

Reference: https://easings.net/#easeOutElastic

bwsl

ease_out_elastic :: (float t) -> float

ease_out_bounce

Reference: https://easings.net/#easeOutBounce

bwsl

ease_out_bounce :: (float t) -> float

triangle_wave

Reference: https://en.wikipedia.org/wiki/Triangle_wave

bwsl

triangle_wave :: (float x) -> float

sawtooth_wave

Reference: https://en.wikipedia.org/wiki/Sawtooth_wave

bwsl

sawtooth_wave :: (float x) -> float

sin01

Sine wave remapped to [0, 1].

bwsl

sin01 :: (float x) -> float

cos01

Cosine wave remapped to [0, 1].

bwsl

cos01 :: (float x) -> float

fast_sin

Cheap sine approximation for visual effects. Best for inputs in radians.

bwsl

fast_sin :: (float x) -> float

Source

Generated from compiler-reference/modules/math.bwsl.