Complete Function Reference

Mathematical Functions

Trigonometric Functions

Function	Description	Parameters	Return Type	Vector Support
sin(x)	Sine	float|vec*	Input type	✓
cos(x)	Cosine	float|vec*	Input type	✓
tan(x)	Tangent	float|vec*	Input type	✓
asin(x)	Arcsine	float|vec*	Input type	✓
acos(x)	Arccosine	float|vec*	Input type	✓
atan(x)	Arctangent	float|vec*	Input type	✓
atan2(y, x)	Two-argument arctangent	float|vec*, float|vec*	Higher precision type	✓

// 基本的な三角関数
const angle = uniform('angle')
const wave = sin(angle.mul(PI))
const circle = vec2(cos(angle), sin(angle))

// 複数角の計算
const multiWave = sin(angle.mul(3)).add(cos(angle.mul(5)).mul(0.5))

Exponential Functions

Function	Description	Parameters	Return Type	Vector Support
pow(x, y)	Power	float|vec*, float|vec*	Higher precision type	✓
pow2(x)	Square	float|vec*	Input type	✓
pow3(x)	Cube	float|vec*	Input type	✓
pow4(x)	Fourth power	float|vec*	Input type	✓
sqrt(x)	Square root	float|vec*	Input type	✓
inverseSqrt(x)	Inverse square root	float|vec*	Input type	✓
exp(x)	Natural exponential	float|vec*	Input type	✓
exp2(x)	Base-2 exponential	float|vec*	Input type	✓
log(x)	Natural logarithm	float|vec*	Input type	✓
log2(x)	Base-2 logarithm	float|vec*	Input type	✓

// 指数・対数関数の使用例
const falloff = exp(distance.negate())
const brightness = pow(dot(normal, lightDir), shininess)
const octaves = log2(resolution)

Common Mathematical Functions

Function	Description	Parameters	Return Type	Vector Support
abs(x)	Absolute value	float|vec*	Input type	✓
sign(x)	Sign extraction	float|vec*	Input type	✓
floor(x)	Floor function	float|vec*	Input type	✓
ceil(x)	Ceiling function	float|vec*	Input type	✓
round(x)	Round to nearest	float|vec*	Input type	✓
fract(x)	Fractional part	float|vec*	Input type	✓
trunc(x)	Truncate	float|vec*	Input type	✓
mod(x, y)	Modulo	float|vec*, float|vec*	Higher precision type	✓

// 基本数学関数の組み合わせ
const pattern = fract(position.mul(10))
const stepped = floor(value.mul(8)).div(8)
const ping_pong = abs(fract(time.mul(0.5)).mul(2).sub(1))

Interpolation Functions

Function	Description	Parameters	Return Type	Vector Support
min(x, y)	Minimum	float|vec*, float|vec*	Higher precision type	✓
max(x, y)	Maximum	float|vec*, float|vec*	Higher precision type	✓
clamp(x, min, max)	Clamp to range	float|vec*, float|vec*, float|vec*	Higher precision type	✓
saturate(x)	Clamp to 0-1	float|vec*	Input type	✓
mix(x, y, a)	Linear interpolation	float|vec*, float|vec*, float|vec*	Higher precision type	✓
step(edge, x)	Step function	float|vec*, float|vec*	Higher precision type	✓
smoothstep(a, b, x)	Smooth step	float|vec*, float|vec*, float|vec*	Higher precision type	✓

// 補間関数の活用
const gradient = smoothstep(0.2, 0.8, position.y)
const masked = mix(colorA, colorB, gradient)
const threshold = step(0.5, noise)

Vector Functions

Vector Operations

Function	Description	Parameters	Return Type	Notes
length(x)	Vector length	vec*	float	Euclidean norm
distance(x, y)	Distance between points	vec*, vec*	float	Euclidean distance
dot(x, y)	Dot product	vec*, vec*	float	Scalar product
cross(x, y)	Cross product	vec3, vec3	vec3	3D only
normalize(x)	Unit vector	vec*	Input type	Length = 1
lengthSq(x)	Squared length	vec*	float	Faster than length

// ベクトル演算の実用例
const lightDir = normalize(lightPos.sub(worldPos))
const intensity = max(0, dot(normal, lightDir))
const reflection = reflect(viewDir.negate(), normal)

Vector Utilities

Function	Description	Parameters	Return Type	Notes
reflect(I, N)	Reflection vector	vec*, vec*	Input type	Mirror reflection
refract(I, N, eta)	Refraction vector	vec*, vec*, float	Input type	Snell's law
faceforward(N, I, Nref)	Orient normal	vec*, vec*, vec*	Input type	Consistent orientation

// 物理的なベクトル計算
const reflected = reflect(incident, normal)
const refracted = refract(incident, normal, ior)
const oriented = faceforward(normal, viewDir, geometryNormal)

Derivative Functions

Function	Description	Parameters	Return Type	Fragment Only
dFdx(x)	X-direction derivative	float|vec*	Input type	✓
dFdy(x)	Y-direction derivative	float|vec*	Input type	✓
fwidth(x)	Derivative width	float|vec*	Input type	✓

// 偏微分を使った計算
const normalFromHeight = normalize(vec3(dFdx(heightmap).negate(), dFdy(heightmap).negate(), 1))

const antialiasing = smoothstep(0, fwidth(pattern), pattern)

Logical Functions

Boolean Vector Functions

Function	Description	Parameters	Return Type	Notes
all(x)	All components true	bvec*	bool	Logical AND
any(x)	Any component true	bvec*	bool	Logical OR
not(x)	Component-wise NOT	bvec*	Input type	Logical NOT

// 論理演算の応用
const inBounds = all(position.greaterThan(vec3(0)).and(position.lessThan(vec3(1))))
const hasColor = any(color.greaterThan(vec3(0)))

Utility Functions

Custom Utility Functions

Function	Description	Parameters	Return Type	Notes
oneMinus(x)	One minus x	float|vec*	Input type	1 - x
negate(x)	Negate value	float|vec*	Input type	-x
reciprocal(x)	Reciprocal	float|vec*	Input type	1/x
remap(x, a, b, c, d)	Remap range	float|vec*, ...	Input type	Linear remapping
remapClamp(x, a, b, c, d)	Clamped remap	float|vec*, ...	Input type	Clamped remapping

// ユーティリティ関数の活用
const inverted = oneMinus(brightness)
const normalized = remap(worldPos.y, -100, 100, 0, 1)
const safety = reciprocal(max(EPSILON, denominator))

Geometric Functions

2D Transformations

Function	Description	Parameters	Return Type	Notes
rotate(pos, angle)	2D rotation	vec2, float	vec2	Around origin
scale(pos, factor)	2D scaling	vec2, vec2|float	vec2	Non-uniform scaling

// 2D幾何変換
const rotated = rotate(uv.sub(0.5), time).add(0.5)
const scaled = scale(uv, vec2(2, 1))

Noise and Random Functions

Pseudorandom Functions

Function	Description	Parameters	Return Type	Notes
hash(seed)	Hash function	float|vec*	float	0-1 range
range(min, max)	Random range	float, float	float	Attribute-based

// ランダム関数の使用
const randomValue = hash(position.add(time))
const randomColor = vec3(hash(position), hash(position.add(1)), hash(position.add(2)))

Oscillator Functions

Wave Generation

Function	Description	Parameters	Return Type	Notes
oscSine(t)	Sine wave	float	float	-1 to 1
oscSquare(t)	Square wave	float	float	-1 to 1
oscTriangle(t)	Triangle wave	float	float	-1 to 1
oscSawtooth(t)	Sawtooth wave	float	float	-1 to 1

// オシレーター関数の組み合わせ
const wave = oscSine(time.mul(2))
        .add(oscTriangle(time.mul(4)).mul(0.5))
        .add(oscSquare(time.mul(8)).mul(0.25))

Color Space Functions

Color Utilities

Function	Description	Parameters	Return Type	Notes
directionToColor(dir)	Direction to color	vec3	vec3	Normal encoding
colorToDirection(col)	Color to direction	vec3	vec3	Normal decoding

// 色空間の変換
const encoded = directionToColor(normal)
const decoded = colorToDirection(normalTexture)

Blend Mode Functions

Color Blending

Function	Description	Parameters	Return Type	Notes
blendBurn(a, b)	Burn blend	vec3, vec3	vec3	Color burn
blendDodge(a, b)	Dodge blend	vec3, vec3	vec3	Color dodge
blendOverlay(a, b)	Overlay blend	vec3, vec3	vec3	Overlay mode
blendScreen(a, b)	Screen blend	vec3, vec3	vec3	Screen mode
blendColor(a, b)	Normal blend	vec3, vec3	vec3	Alpha blend

// ブレンドモードの適用
const result = blendOverlay(baseColor, overlayColor)
const highlight = blendScreen(color, lightColor)

GLRE の Node System は、150 以上の数学関数とユーティリティを提供し、あらゆるシェーダープログラミングのニーズに対応します。